diff --git "a/mindgames.jsonl" "b/mindgames.jsonl"
--- "a/mindgames.jsonl"
+++ "b/mindgames.jsonl"
@@ -1,3672 +1,3 @@
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances knows whether Hannah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Kevin can now know that Frances can know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frances","Kevin","Hannah","Trent"],"index":4908,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858406782,"difficulty":0.0141593218}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mary can now know whether Ruth can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shane","Mary","Ruth"],"index":7339,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8593667746,"difficulty":0.1406332254}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Debra can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Debra","Lisa","Joseph"],"index":9365,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9803562164,"difficulty":0.0196437836}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia knows whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ronald can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Todd","Marty","Ronald"],"index":2259,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9627821445,"difficulty":0.0372178555}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is muddy. It is publicly announced that Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Joseph can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Gloria","Nancy"],"index":6698,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857797623,"difficulty":0.0142202377}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vernice's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Vernice can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Carl","Vernice"],"index":3496,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.976842761,"difficulty":0.023157239}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Jesse. Jesse's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Raymond knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Raymond knows whether someone picked a red card. It is publicly announced that Raymond knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jesse can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jesse","Raymond"],"index":1604,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9761373401,"difficulty":0.0238626599}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Dawn is not thirsty. It is publicly announced that Beth does not know whether Walter is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Dawn can now know whether Beth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dawn","Walter","Jeannie","Beth"],"index":4758,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6776565909,"difficulty":1.6776565909}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Milton does not know whether Alvin is thirsty. It is publicly announced that Alvin is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Denise does not know whether Milton is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Denise can now know whether Denise is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alvin","Rose","Denise","Milton"],"index":6049,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6512076259,"difficulty":0.3487923741}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tami's card is shown to Kenneth. Erin's card is shown to Jose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know that Tami picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Tami","Erin","Jose"],"index":6530,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9793511629,"difficulty":0.0206488371}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ramona's card is shown to Micheal. Kandi's card is shown to Ramona. Ramona's card is shown to Lakisha. Kandi's card is shown to Lakisha. Ramona's card is shown to Kandi. Lakisha's card is shown to Kandi. It is publicly announced that someone picked a red card. It is publicly announced that Ramona does not know whether Lakisha picked a red card. It is publicly announced that Lakisha does not know whether or not everyone picked a red card. It is publicly announced that Micheal does not know whether Micheal picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Ramona can now know that Micheal can know whether Lakisha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Micheal","Ramona","Lakisha","Kandi"],"index":7596,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6398462057,"difficulty":1.6398462057}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marina can now know that Annice can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marina","Danielle","Annice","Tony"],"index":6034,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9801110625,"difficulty":0.0198889375}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herbert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Herbert can now know that Herbert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Herbert","Devin","Kenneth"],"index":8172,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9765897393,"difficulty":0.0234102607}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elliott's card is shown to Lynne. Norman's card is shown to Lynne. Elliott's card is shown to Norman. Norman's card is shown to Erin. It is publicly announced that someone picked a red card. It is publicly announced that Elliott does not know whether Erin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Lynne can now know whether Elliott can know that Elliott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lynne","Elliott","Norman","Erin"],"index":9096,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7091322541,"difficulty":0.2908677459}
-{"premise":"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 or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Laura can now know whether Ronni can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Elena","Laura","Ronni"],"index":965,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9538528919,"difficulty":0.0461471081}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marvin does not know whether Donald is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Richard can now know whether Marvin can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marvin","Donald","Richard"],"index":5926,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9751200676,"difficulty":0.0248799324}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Clara can now know that Linda can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Linda","Clara"],"index":6384,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9819384813,"difficulty":0.0180615187}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Theodore's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brett can now know whether Dorothy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Theodore","Linda","Brett","Dorothy"],"index":4263,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9727502465,"difficulty":0.0272497535}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sophia's card is shown to Benjamin. Kimberly's card is shown to Sophia. It is publicly announced that someone picked a red card. It is publicly announced that Benjamin does not know whether or not everyone picked a red card. It is publicly announced that Benjamin knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Benjamin can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Benjamin","Kimberly","Sophia"],"index":4423,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9772450328,"difficulty":0.0227549672}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Chad can now know whether Marjorie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Chad","Marjorie"],"index":9211,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9706783295,"difficulty":0.0293216705}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Kayleigh can now know that Scott can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Kayleigh","Jocelyn","Joe"],"index":4101,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.973995924,"difficulty":0.026004076}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ebony does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ebony","Margaret"],"index":3133,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.970349431,"difficulty":0.029650569}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel knows whether someone is thirsty. It is publicly announced that Samuel knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kathleen can now know that Daniel can know that Kathleen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Kathleen","Samuel"],"index":2646,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.962849319,"difficulty":0.037150681}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ana's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 (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":"Willie can now know that Emily can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ana","Emily","Mary","Willie"],"index":4773,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823302031,"difficulty":0.0176697969}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Jaime can now know that Bridget can know whether Jaime's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jaime","Bridget"],"index":8099,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9603676796,"difficulty":0.0396323204}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debbie knows whether someone's forehead is muddy. It is publicly announced that Olen knows whether Debbie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Olen can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debbie","Olen","Richard"],"index":968,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.972312212,"difficulty":0.027687788}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Perry can now know that Cindy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Perry","David","Charles","Cindy"],"index":8846,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9600375295,"difficulty":0.0399624705}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Francine can now know that Christopher can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Francine","Christopher","Ron"],"index":7311,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9701814651,"difficulty":0.0298185349}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Bruce can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gale","Wanda","Charles","Bruce"],"index":1350,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.6381438971,"difficulty":0.3618561029}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Doreen can now know whether Gina can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gina","Herbert","Doreen","Jennifer"],"index":7080,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9731916189,"difficulty":0.0268083811}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Maria. Maria's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Maria picked a black card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(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) ] [ ! (~(1&2)) ] 0","hypothesis":"Maria can now know that David can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maria","David"],"index":8444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9710575938,"difficulty":0.0289424062}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steve's card is shown to Cathy. Steve's card is shown to Anthony. Cathy's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Steve does not know whether Anthony picked a red card. It is publicly announced that Cathy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Anthony can now know that Cathy can know whether Cathy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cathy","Anthony","Steve"],"index":7286,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6604016423,"difficulty":1.6604016423}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 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":"Maren can now know whether Joseph can know whether Benjamin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stanley","Joseph","Benjamin","Maren"],"index":1790,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9451358318,"difficulty":0.0548641682}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Catherine can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Catherine","Rosemary","Lois"],"index":1952,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859681129,"difficulty":0.0140318871}
-{"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 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":"Timothy can now know whether Erin can know whether Erin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Lester","Timothy","Erin"],"index":8097,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9409341812,"difficulty":1.9409341812}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Leonard","Robert"],"index":3957,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9582383037,"difficulty":0.0417616963}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Annie. Annie's card is shown to Edward. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Annie can now know that Edward can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Annie","Edward"],"index":3148,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9780814052,"difficulty":0.0219185948}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michel does not know whether Michel's forehead is muddy. It is publicly announced that Frances knows whether Loretta's forehead is muddy. It is publicly announced that Andrew's forehead is not 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) ] [ ! (Agentb knows whether 4) ] [ ! ~(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) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Michel can now know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michel","Frances","Andrew","Loretta"],"index":1253,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9766921997,"difficulty":0.0233078003}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monique's card is shown to Robert. Charlene's card is shown to Robert. Charlene's card is shown to Monique. Monique's card is shown to Charlene. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Charlene can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Monique","Charlene"],"index":709,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9776071906,"difficulty":0.0223928094}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorraine does not know whether Lorraine's forehead is muddy. It is publicly announced that Lorraine knows whether or not nobody's forehead is muddy. It is publicly announced that Lorraine 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) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lorraine","Michael","Roger"],"index":5716,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.942850709,"difficulty":1.942850709}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Gino can now know whether Jean can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jean","Richard","Gino","Maria"],"index":592,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.979221642,"difficulty":0.020778358}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sean's forehead is muddy. It is publicly announced that Sean's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Janice can now know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janice","Linda","Sean"],"index":4570,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.961671412,"difficulty":0.038328588}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Maria. Maria's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","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":"Joseph can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Maria","Joseph"],"index":1088,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.977083981,"difficulty":0.022916019}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Robert can now know that Eugene can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Eugene","Robert"],"index":3685,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9800941348,"difficulty":0.0199058652}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony does not know whether Anthony's forehead is muddy. It is publicly announced that Toni does not know whether Toni's forehead is muddy. It is publicly announced that Anthony'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 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Anthony can now know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Toni","Anthony","Kimberly"],"index":5542,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8909220099,"difficulty":0.1090779901}
-{"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 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":"Patricia can now know that William can know that Rowena's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","William","Patricia","Rowena"],"index":254,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9824153781,"difficulty":0.0175846219}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roman's card is shown to Elaine. Elaine's card is shown to Roman. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Elaine can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Elaine","Roman"],"index":6224,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9797564149,"difficulty":0.0202435851}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luis's card is shown to Emma. Emma's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Emma picked a black card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(1&2)) ] 0","hypothesis":"Luis can now know that Emma can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Emma","Luis"],"index":4277,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9714359641,"difficulty":0.0285640359}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lester knows whether Lester is thirsty. It is publicly announced that Linda does not know whether Joanna is thirsty. It is publicly announced that Lester is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Elmer can now know that Elmer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elmer","Lester","Linda","Joanna"],"index":6577,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9729353786,"difficulty":0.0270646214}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Kirk's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Susan can now know that Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kirk","Susan"],"index":5306,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9537742734,"difficulty":0.0462257266}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jack can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roy","Stephen","Jack"],"index":940,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9755751491,"difficulty":0.0244248509}
-{"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 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":"Nikole can now know whether Tony can know that Nikole's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Jared","Nikole","Tony"],"index":6057,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7123769522,"difficulty":1.7123769522}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eddie's card is shown to Katie. Wilma's card is shown to Eddie. Katie's card is shown to Wilma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Wilma can now know that Katie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katie","Eddie","Wilma"],"index":599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9789084196,"difficulty":0.0210915804}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Cathy. Cathy's card is shown to Karla. John's card is shown to Karla. Cathy's card is shown to John. Karla's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Cathy can now know whether Karla can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cathy","Karla","John"],"index":5061,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8980579972,"difficulty":0.1019420028}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shelly can now know that Alexander can know whether Shelly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shelly","Joe","Alexander"],"index":281,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9577280879,"difficulty":0.0422719121}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jan can now know whether William can know whether Pierre is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Jan","William","Pierre"],"index":2931,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8131087422,"difficulty":0.1868912578}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know that Rodney can know that Anna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rodney","Harold","Anna","Viola"],"index":3476,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864923358,"difficulty":0.0135076642}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Noella can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Noella","Jean","Lorrie","Michael"],"index":5611,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9790380001,"difficulty":0.0209619999}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hester knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Hester can now know whether Jessica can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hester","Jessica"],"index":8303,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.978993535,"difficulty":0.021006465}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cedric does not know whether Lynn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jeffrey can now know whether Cedric can know that Lynn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Cedric","Robert","Lynn"],"index":6413,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.60706985,"difficulty":0.39293015}
-{"premise":"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 Benjamin's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Benjamin can now know that Carol can know that Benjamin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Benjamin","Carol"],"index":9493,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9806650877,"difficulty":0.0193349123}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jill is not thirsty. It is publicly announced that Kristy is not thirsty. It is publicly announced that Jill does not know whether Fred is thirsty. It is publicly announced that Fred knows whether Fred is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Kristy can now know whether Rebecca can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Jill","Kristy","Fred"],"index":5889,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9238176346,"difficulty":0.0761823654}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mara knows whether Horace's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Horace can now know whether Horace's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mara","Frederick","Janeth","Horace"],"index":5783,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9108092785,"difficulty":1.9108092785}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Caron can now know that Tim can know that Lola's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bruce","Lola","Caron","Tim"],"index":4403,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864596128,"difficulty":0.0135403872}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is thirsty. It is publicly announced that Michelle knows whether someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Marcus does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Michelle can now know whether Marcus can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Marcus","John"],"index":3045,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9712647796,"difficulty":0.0287352204}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilyn does not know whether Marilyn's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilyn does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Robin can now know whether Marilyn can know that Robin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robin","Marilyn"],"index":3978,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7989092469,"difficulty":0.2010907531}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Renay's card is shown to David. David's card is shown to Renay. Renay's card is shown to Evita. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Renay can now know that Evita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Renay","Evita"],"index":3529,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9777678847,"difficulty":0.0222321153}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Mary can now know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Barbara","Maureen","Patricia"],"index":4398,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9589295983,"difficulty":0.0410704017}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tracey does not know whether Kurt is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mildred can now know whether Tracey can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracey","Mildred","Kurt"],"index":4727,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.975233078,"difficulty":0.024766922}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know that Albert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Albert","Brian","Jessica"],"index":9215,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9828836322,"difficulty":0.0171163678}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrea is thirsty. It is publicly announced that Santo knows whether Andrea is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Laura can now know that Santo is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrea","Santo","Laura"],"index":4704,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9777578712,"difficulty":0.0222421288}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Marci knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kenneth can now know whether Jerry can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debbie","Marci","Kenneth","Jerry"],"index":7064,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9793669581,"difficulty":0.0206330419}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know that Tim can know whether Gonzalo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Justin","Tim","Michelle","Gonzalo"],"index":6906,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6199867725,"difficulty":0.3800132275}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marco knows whether someone is thirsty. It is publicly announced that Marco does not know whether Mandy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mandy can now know that Marco can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marco","Mandy"],"index":5857,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9144825935,"difficulty":0.0855174065}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodney knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Rodney can now know that Andrea can know that Andrea's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rodney","Andrea"],"index":7531,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9759284854,"difficulty":0.0240715146}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ezekiel's card is shown to Jon. Jon's card is shown to Ezekiel. It is publicly announced that someone picked a red card. It is publicly announced that Ezekiel knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (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":"Jon can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jon","Ezekiel"],"index":5814,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9719611406,"difficulty":0.0280388594}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether Valencia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Valencia can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Curtis","Doris","Valencia"],"index":9586,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853690267,"difficulty":0.0146309733}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"James can now know that Joshua can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Joshua","James","Keith"],"index":8572,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.985594511,"difficulty":0.014405489}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stacey can now know whether Alexis can know that Alexis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alexis","Tammy","Pasquale","Stacey"],"index":8064,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5115240216,"difficulty":0.4884759784}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Margaret can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Oscar","Peggy","Margaret"],"index":4890,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7965508699,"difficulty":0.2034491301}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"William can now know that Bruce can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bruce","William"],"index":3306,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9763932228,"difficulty":0.0236067772}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether Shirley's forehead is muddy. It is publicly announced that Shirley knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Shirley can now know whether Shirley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Shirley","Maria"],"index":6396,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9639590979,"difficulty":0.0360409021}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Mary. Mary's card is shown to Judy. Mitch's card is shown to Judy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Mitch can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Mitch","Judy"],"index":9580,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9697880149,"difficulty":0.0302119851}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyler's card is shown to Marina. Brian's card is shown to Nancy. Tyler's card is shown to Nancy. Marina's card is shown to Brian. Nancy's card is shown to Brian. Marina's card is shown to Tyler. Brian's card is shown to Tyler. It is publicly announced that someone picked a red card. It is publicly announced that Marina picked a red card. It is publicly announced that Tyler does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Marina can now know whether Nancy can know that Tyler picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marina","Nancy","Brian","Tyler"],"index":8919,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6132851243,"difficulty":0.3867148757}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicky knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Nicky can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Philip","William","Nicky","Michelle"],"index":5223,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9768759608,"difficulty":0.0231240392}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Paul can now know that Ramon can know that Ramon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ramon","Grace","Phyllis","Paul"],"index":798,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9816768169,"difficulty":0.0183231831}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Miguel can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anna","Miguel"],"index":2982,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9782779217,"difficulty":0.0217220783}
-{"premise":"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 Maude knows whether Andrew's forehead is muddy. It is publicly announced that Maude knows whether Philip's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Andrew can now know whether Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Philip","Maude","Andrew"],"index":5360,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8911995888,"difficulty":0.1088004112}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Calvin can now know that Donald can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Olivia","Deborah","Donald","Calvin"],"index":5242,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856125116,"difficulty":0.0143874884}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether Rose's forehead is muddy. It is publicly announced that Dorothy knows whether or not nobody's forehead is muddy. It is publicly announced that Rose knows whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dorothy can now know whether Rose can know whether Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rose","Dorothy"],"index":4507,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.969195962,"difficulty":0.030804038}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ryan does not know whether Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jennifer can now know that Evelyn can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ryan","Jennifer","Evelyn"],"index":1459,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.977034688,"difficulty":0.022965312}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy knows whether someone's forehead is muddy. It is publicly announced that Virginia knows whether Jimmy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Alice can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jimmy","Virginia","Alice"],"index":3334,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9683103561,"difficulty":0.0316896439}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wendy knows whether someone is thirsty. It is publicly announced that Jacquelyn knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Melanie can now know that Wendy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wendy","Melanie","Jacquelyn"],"index":979,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.966793716,"difficulty":0.033206284}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that Terry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Angelique","Terry"],"index":364,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9828960299,"difficulty":0.0171039701}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rosemary can now know that Tyler can know that Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rosemary","Ruth","Cayla","Tyler"],"index":7112,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864796996,"difficulty":0.0135203004}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Helen. Murray's card is shown to Helen. Helen's card is shown to Joyce. It is publicly announced that someone picked a red card. It is publicly announced that Joyce does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 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 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Joyce can now know that Helen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Helen","Joyce","Murray"],"index":8419,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9656297565,"difficulty":1.9656297565}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Roger","Jeremy","Dalton"],"index":9495,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8271725774,"difficulty":1.8271725774}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Frederick can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Robert","Frederick"],"index":8409,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5783037543,"difficulty":0.4216962457}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Dorothy can now know that Jose can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","William","Jose"],"index":5231,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9779755473,"difficulty":0.0220244527}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Elsie. Jean's card is shown to Elsie. Elsie's card is shown to George. Elsie's card is shown to Jean. George's card is shown to Jean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"George can now know whether Jean can know whether George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elsie","George","Jean"],"index":2240,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.896739006,"difficulty":0.103260994}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Vera's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Marie can now know whether Vera can know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Lavenia","Vera","Marie"],"index":9126,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9540078044,"difficulty":0.0459921956}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether or not everyone's forehead is muddy. It is publicly announced that Tory knows whether someone's forehead is muddy. It is publicly announced that Melissa does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Tory can now know whether Melissa can know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melissa","Tory"],"index":262,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9398726821,"difficulty":0.0601273179}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy's forehead is muddy. It is publicly announced that Faye does not know whether Faye's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows 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":"Amy can now know that Faye can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Faye","Amy"],"index":2148,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9787654281,"difficulty":0.0212345719}
-{"premise":"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 James'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) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Barry"],"index":473,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9574146867,"difficulty":0.0425853133}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pam knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows that (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":"Karen can now know whether Pam can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pam","Karen"],"index":22,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9474204183,"difficulty":0.0525795817}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barry does not know whether Carl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Barry can now know whether Michael can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barry","Michelle","Michael","Carl"],"index":8219,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9556255341,"difficulty":0.0443744659}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doris is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Kim can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andre","Kim","Doris","Corinne"],"index":1044,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9703862667,"difficulty":0.0296137333}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Marilyn can now know whether Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sarah","Walter","Marilyn"],"index":3537,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.960712254,"difficulty":0.039287746}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Danielle can now know whether Frederick can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frederick","Andrew","Danielle"],"index":2220,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8152253032,"difficulty":0.1847746968}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to Edward. Edward's card is shown to Janice. James's card is shown to Janice. Janice's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edward","Janice","James"],"index":6390,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9785895944,"difficulty":0.0214104056}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chan's card is shown to Edward. Edward's card is shown to Jean. Edward's card is shown to Chan. It is publicly announced that someone picked a red card. It is publicly announced that Chan does not know whether Chan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Edward can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edward","Jean","Chan"],"index":4141,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.975456953,"difficulty":0.024543047}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kandace can now know that Michael can know that Kandace's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Michael","Charlotte","Kandace"],"index":2224,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864624143,"difficulty":0.0135375857}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Hector can now know that Philip can know that Hector's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Philip","Hector","Dianne"],"index":1002,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865043163,"difficulty":0.0134956837}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 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":"Leann can now know that George can know whether Leann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Lawrence","Richard","Leann"],"index":1713,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8365950584,"difficulty":0.1634049416}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yasmin knows whether or not nobody's forehead is muddy. It is publicly announced that Guy does not know whether Guy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Yasmin can now know whether Betty can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Guy","Frances","Yasmin"],"index":3880,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8939042687,"difficulty":1.8939042687}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jasper can now know whether Maryann is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Claire","Jasper","Maryann"],"index":9403,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6245492101,"difficulty":0.3754507899}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to Jeffrey. Roland's card is shown to Jeffrey. Jeffery's card is shown to Erin. Jeffrey's card is shown to Roland. Jeffrey's card is shown to Jeffery. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether or not everyone picked a red card. It is publicly announced that Jeffery knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Roland can now know whether Erin can know that Jeffery picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Erin","Roland","Jeffery"],"index":1875,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6534914374,"difficulty":1.6534914374}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Micki. Micki's card is shown to Jason. Tara's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Micki can now know whether Micki picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Micki","Jason","Christopher","Tara"],"index":3867,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.681597352,"difficulty":1.681597352}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether Frederick is thirsty. It is publicly announced that Paul knows whether Paul is thirsty. It is publicly announced that Jessie does not know whether Frederick is thirsty. It is publicly announced that Jessie knows whether Jessie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Paul can now know whether Jessie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessie","Paul","Frederick"],"index":1236,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9372031093,"difficulty":0.0627968907}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn knows whether Shawn's forehead is muddy. It is publicly announced that Shawn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Elton can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elton","Jeremy","Shawn"],"index":5468,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853947163,"difficulty":0.0146052837}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Jessica. Dara's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dara can now know that Jessica can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dara","Jessica","Thomas"],"index":3711,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9741200805,"difficulty":0.0258799195}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Emily. Emily's card is shown to Jesse. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Jesse can now know whether Emily can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Emily","Jesse"],"index":7953,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9346544743,"difficulty":0.0653455257}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol'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":"Carol can now know that Brenda can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brenda","Carol"],"index":6269,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7069255114,"difficulty":1.7069255114}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan does not know whether Alan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Alan can now know that Meaghan can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alan","Meaghan","Marcia","Sarah"],"index":3656,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9732120633,"difficulty":0.0267879367}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know that Yetta can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Yetta","Kenneth"],"index":7570,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9753335714,"difficulty":0.0246664286}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Elizabeth can now know whether Bobby can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bobby","Elizabeth"],"index":6928,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9751116037,"difficulty":0.0248883963}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Christina can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Christina","Wayne"],"index":1925,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.979862988,"difficulty":0.020137012}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patsy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"James can now know whether Patsy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patsy","James"],"index":28,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9756656289,"difficulty":0.0243343711}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rudolph knows whether Rudolph's forehead is muddy. It is publicly announced that Rudolph's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Tonya can now know that Darrell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Darrell","Tonya","Rudolph"],"index":8382,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853443503,"difficulty":0.0146556497}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katelyn's card is shown to Douglas. Walter's card is shown to Douglas. Katelyn's card is shown to William. William's card is shown to Katelyn. Katelyn's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card. It is publicly announced that Douglas does not know whether William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Walter can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Douglas","William","Katelyn","Walter"],"index":675,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9680492878,"difficulty":0.0319507122}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelley knows whether or not everyone's forehead is muddy. It is publicly announced that Anna knows whether Anna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Anna can now know that Kelley can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kelley","Anna"],"index":1785,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9777429104,"difficulty":0.0222570896}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Clyde can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joshua","Clyde","Michelle"],"index":6532,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859470129,"difficulty":0.0140529871}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donna can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edwin","William","Donna","Thomas"],"index":6061,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9863772392,"difficulty":0.0136227608}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bob's card is shown to Judith. Judith's card is shown to Bob. It is publicly announced that someone picked a red card. It is publicly announced that Judith picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Judith can now know whether Bob can know whether Bob picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Judith","Bob"],"index":40,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9056110382,"difficulty":0.0943889618}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Karlyn is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know whether Charlotte can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Charlotte","Michael","Karlyn"],"index":6170,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9747741222,"difficulty":0.0252258778}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marc knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Marc can now know that Aaron can know whether Aaron is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Aaron","Christopher","Marc"],"index":8230,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5701069832,"difficulty":0.4298930168}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Misty. Misty's card is shown to Julie. Robert's card is shown to Julie. Misty's card is shown to Robert. Julie's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Robert does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Julie can now know whether Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Misty","Julie","Robert"],"index":7676,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9630973935,"difficulty":0.0369026065}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacklyn does not know whether Jacklyn's forehead is muddy. It is publicly announced that Jarrod does not know whether Jarrod's forehead is muddy. It is publicly announced that Jarrod 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Jarrod's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jarrod","Mary","Jacklyn"],"index":1535,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.956677556,"difficulty":0.043322444}
-{"premise":"There are three 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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Ruth can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patty","Ruth","James"],"index":6227,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9560915828,"difficulty":0.0439084172}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doris does not know whether Sarah is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Doris can now know that Mildred can know that Sarah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","Doris","Mildred","Michael"],"index":1723,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9764261842,"difficulty":0.0235738158}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Doug. Willie's card is shown to Anthony. Anthony's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Doug picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Willie can now know whether Doug can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doug","Anthony","Willie"],"index":8501,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9735914469,"difficulty":0.0264085531}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christina's card is shown to Eula. James's card is shown to Eula. Arthur's card is shown to Eula. James's card is shown to Christina. Arthur's card is shown to Christina. Eula's card is shown to James. Christina's card is shown to Arthur. James's card is shown to Arthur. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Arthur picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eula","Christina","James","Arthur"],"index":3342,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.977109015,"difficulty":0.022890985}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Breanne. Breanne's card is shown to John. Sung's card is shown to John. Breanne's card is shown to Sung. It is publicly announced that someone picked a red card. It is publicly announced that John picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Sung can now know that Breanne can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Breanne","John","Sung"],"index":7232,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7183862925,"difficulty":0.2816137075}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Mary can now know that James can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Mary"],"index":4481,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9763205647,"difficulty":0.0236794353}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Paula can now know that Martha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Martha","Paula"],"index":9512,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9854296446,"difficulty":0.0145703554}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lena can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Debra","Michael","David","Lena"],"index":3831,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9809019566,"difficulty":0.0190980434}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Alberto. Christopher's card is shown to Alberto. Christopher's card is shown to Grace. Grace's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Grace picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Christopher can now know that Grace can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alberto","Grace","Christopher"],"index":8210,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9707373977,"difficulty":0.0292626023}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Ophelia can now know whether Rosemary can know whether Rosemary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ophelia","Rosemary"],"index":4852,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9701185226,"difficulty":0.0298814774}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty is thirsty. It is publicly announced that Betty does not know whether Annette is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Annette can now know that Betty can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christian","Annette","Betty","Kenneth"],"index":6668,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9767255187,"difficulty":0.0232744813}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gordon does not know whether Kimberly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ollie can now know whether Kimberly can know whether Ollie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gordon","Jaime","Kimberly","Ollie"],"index":868,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8596866131,"difficulty":0.1403133869}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy does not know whether Todd is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Amy can now know that Troy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Todd","Troy","Amy"],"index":268,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9295408726,"difficulty":0.0704591274}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Lillian. Lillian's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Mary knows whether Lillian picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] (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) ] 0","hypothesis":"Mary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lillian","Mary"],"index":881,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9778223634,"difficulty":0.0221776366}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Curtis does not know whether Meg is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Mercedes can now know whether Curtis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mercedes","Curtis","Johnnie","Meg"],"index":7986,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.571797967,"difficulty":1.571797967}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Anna can now know whether Matthew can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Connie","Ray","Anna","Matthew"],"index":577,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9566913247,"difficulty":0.0433086753}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Scott can now know that Keith can know that Keith is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Henry","Jason","Keith"],"index":5665,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9800778627,"difficulty":0.0199221373}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know whether Nicholas can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Betty","Nicholas","Michelle"],"index":2438,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9426817298,"difficulty":0.0573182702}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laurel","Linda","Mary","Robert"],"index":396,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6896681786,"difficulty":1.6896681786}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether 2)","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 that Earl can know whether Earl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Earl"],"index":5984,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8919069767,"difficulty":1.8919069767}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Beverly does not know whether Tracy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Beverly can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Sarah","Tracy","Beverly"],"index":8201,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9756150246,"difficulty":0.0243849754}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Barbara. Barbara's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Anthony can now know whether Barbara can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barbara","Anthony"],"index":1397,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6087645292,"difficulty":0.3912354708}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Loretta can now know that Jimmy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jimmy","Loretta","Todd","Margaret"],"index":7041,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8299366832,"difficulty":0.1700633168}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Maria can now know whether Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ellen","Maria","Latisha"],"index":1626,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8169247508,"difficulty":1.8169247508}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristina's card is shown to Judy. Roberta's card is shown to Cristina. Cristina's card is shown to Robert. Roberta's card is shown to Robert. Cristina's card is shown to Roberta. Robert's card is shown to Roberta. It is publicly announced that someone picked a red card. It is publicly announced that Cristina does not know whether Robert picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Judy does not know whether Judy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Cristina can now know whether Roberta can know that Cristina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judy","Cristina","Robert","Roberta"],"index":4717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5490278006,"difficulty":0.4509721994}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janice can now know that Kathy can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marc","Margaret","Kathy","Janice"],"index":3185,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865273833,"difficulty":0.0134726167}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tammy's card is shown to Donald. Lois's card is shown to Donald. Donald's card is shown to Jack. Lois's card is shown to Jack. Donald's card is shown to Tammy. Donald's card is shown to Lois. Tammy's card is shown to Lois. It is publicly announced that someone picked a red card. It is publicly announced that Lois does not know whether Lois picked a red card. It is publicly announced that Donald does not know whether Jack picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lois can now know that Lois picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Jack","Tammy","Lois"],"index":2253,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9741952419,"difficulty":0.0258047581}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Sean can now know that Beverly can know that Sean is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Beverly","Sean"],"index":6674,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9795023799,"difficulty":1.9795023799}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander 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)","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":"Alexander can now know whether Alexander's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alexander","Allen"],"index":7201,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.882111609,"difficulty":1.882111609}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathy can now know whether Matthew can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Daniel","Kathy"],"index":2928,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9466738105,"difficulty":0.0533261895}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Margaret can now know whether Janice can know whether Janice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Margaret","Janice"],"index":9441,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.970000267,"difficulty":0.029999733}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 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":"George can now know that Dorothy can know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Robert","Dorothy","George"],"index":5991,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9822334647,"difficulty":0.0177665353}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sadie knows whether Cheryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"William can now know whether Brett can know whether Cheryl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Sadie","William","Brett"],"index":1403,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9712151885,"difficulty":0.0287848115}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce does not know whether Bruce's forehead is muddy. It is publicly announced that Christine's forehead is not muddy. It is publicly announced that Bruce's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] [ ! ~(2) ] 0","hypothesis":"Bruce can now know that Sandra can know whether Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Bruce","Johnny","Christine"],"index":6056,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9067304134,"difficulty":1.9067304134}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Harry can now know that Larry can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Harry","Larry"],"index":7672,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.985701561,"difficulty":0.014298439}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Thomas. Trudy's card is shown to Thomas. Thomas's card is shown to Trudy. Teresa's card is shown to Trudy. It is publicly announced that someone picked a red card. It is publicly announced that Thomas picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Thomas can now know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Teresa","Trudy"],"index":899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6954780817,"difficulty":0.3045219183}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know whether Robert can know whether Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","David","Robert","Kevin"],"index":8140,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9711368084,"difficulty":0.0288631916}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Verna does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Verna can now know whether Paula can know that Verna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Verna","Paula"],"index":3888,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.606487453,"difficulty":1.606487453}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Colby's card is shown to Gary. Gary's card is shown to Colby. It is publicly announced that someone picked a red card. It is publicly announced that Colby does not know whether Colby picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows 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":"Colby can now know whether Gary can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gary","Colby"],"index":748,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9759913087,"difficulty":0.0240086913}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Eric. Eric's card is shown to Hugh. Thomas's card is shown to Hugh. Hugh's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Hugh can know whether Hugh picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eric","Hugh","Thomas"],"index":2234,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6878273487,"difficulty":1.6878273487}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Brianna can now know that Brianna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brianna","Larry","Ashley","Thomas"],"index":3968,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9799235463,"difficulty":0.0200764537}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Darlene can now know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eric","Darlene","John"],"index":1062,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9632397294,"difficulty":0.0367602706}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcella's card is shown to Gerald. Gerald's card is shown to Marcella. It is publicly announced that someone picked a red card. It is publicly announced that Marcella does not know whether Marcella picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Marcella can now know whether Gerald can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gerald","Marcella"],"index":9062,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9737502337,"difficulty":0.0262497663}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Melvin. Jason's card is shown to Lucille. Lucille's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jason can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melvin","Lucille","Jason","William"],"index":8850,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9792451859,"difficulty":0.0207548141}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tennie's card is shown to Harold. Harold's card is shown to Tennie. Tennie's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Earl does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Harold can now know that Tennie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harold","Tennie","Earl"],"index":8715,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9650107622,"difficulty":0.0349892378}
-{"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":"Herman can now know whether Andrea can know that Andrea's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Sonja","Herman","Andrea"],"index":8168,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.730697155,"difficulty":1.730697155}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Missy. Sean's card is shown to Missy. Sean's card is shown to Ralph. William's card is shown to Sean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Ralph can know whether Ralph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Missy","William","Ralph","Sean"],"index":181,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6686526537,"difficulty":1.6686526537}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether Robert's forehead is muddy. It is publicly announced that Robert knows whether Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Maria can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jane","Robert","Maria"],"index":3926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9844682813,"difficulty":0.0155317187}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bridget's card is shown to Carol. Carol's card is shown to Bridget. It is publicly announced that someone picked a red card. It is publicly announced that Carol does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows 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":"Bridget can now know that Carol can know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carol","Bridget"],"index":3161,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6002597213,"difficulty":1.6002597213}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danny's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"John can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffrey","Danny","John"],"index":9412,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9771552086,"difficulty":0.0228447914}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Irene can now know whether Frank can know whether Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Gregory","Irene","Carol"],"index":3196,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9717409015,"difficulty":0.0282590985}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Justin can now know whether Ida can know whether Justin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ida","Justin"],"index":2631,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8428229094,"difficulty":1.8428229094}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Brad can now know that Helen can know that Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brad","Helen","Ronald"],"index":1963,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9852869511,"difficulty":0.0147130489}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dion's card is shown to Ethel. Jennifer's card is shown to Ethel. Jennifer's card is shown to Dion. Ethel's card is shown to Jennifer. Dion's card is shown to Jennifer. Ethel's card is shown to Maynard. It is publicly announced that someone picked a red card. It is publicly announced that Maynard knows whether someone picked a red card. It is publicly announced that Jennifer does not know whether Jennifer picked a red card. It is publicly announced that Jennifer knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Jennifer can now know that Dion can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ethel","Dion","Jennifer","Maynard"],"index":6593,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6973186731,"difficulty":1.6973186731}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is not muddy. It is publicly announced that Della knows whether Della's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Chelsea can now know that Della can know whether Chelsea's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chelsea","Della","John"],"index":720,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9116542935,"difficulty":0.0883457065}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Frank can now know that Frank's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Frank","Donald"],"index":7474,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864608049,"difficulty":0.0135391951}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Audrey. Susan's card is shown to Dorothy. Audrey's card is shown to Dorothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Audrey can now know whether Susan can know whether Audrey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Audrey","Dorothy"],"index":7981,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9003534913,"difficulty":0.0996465087}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emilie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dorothy can now know whether Lyman can know that Dorothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emilie","Lyman","Dorothy"],"index":4730,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5928689241,"difficulty":1.5928689241}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lois does not know whether Sherry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Sherry can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lois","Shelley","Sherry","Charles"],"index":7668,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9630785584,"difficulty":0.0369214416}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Darlene. Darlene's card is shown to Jennifer. Clorinda's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Darlene","Jennifer","Clorinda"],"index":406,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9197395444,"difficulty":0.0802604556}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Robert knows whether Angel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Angel can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Charles","Angel"],"index":5581,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9706231952,"difficulty":0.0293768048}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leopoldo does not know whether or not everyone's forehead is muddy. It is publicly announced that Linda knows whether someone's forehead is muddy. It is publicly announced that Leopoldo does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Linda can now know that Leopoldo can know whether Leopoldo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leopoldo","Linda"],"index":6901,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8978649974,"difficulty":0.1021350026}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Victoria knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Victoria can now know whether Truman can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Victoria","Truman","Mabel"],"index":8188,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9720544219,"difficulty":0.0279455781}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maryjane's card is shown to Charles. Charles's card is shown to Maryjane. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether someone picked a red card. It is publicly announced that Charles picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Maryjane can now know that Maryjane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Maryjane"],"index":6694,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9717668295,"difficulty":1.9717668295}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catherine is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Roger can now know whether Catherine can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roger","Stephanie","Catherine"],"index":9544,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9530724287,"difficulty":0.0469275713}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Shalonda knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Katina can now know whether Werner is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shalonda","Katina","Werner"],"index":4736,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6226662397,"difficulty":1.6226662397}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Karen. Karen's card is shown to Peter. Peter's card is shown to Maryann. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Maryann can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Peter","Maryann"],"index":9248,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9777491689,"difficulty":0.0222508311}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie's forehead is muddy. It is publicly announced that Holly does not know whether Holly's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (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":"Marjorie can now know that Holly can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Holly","Marjorie"],"index":4131,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6378233433,"difficulty":0.3621766567}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Lilly. Sarah's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Lilly does not know whether Lilly picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lilly can now know that Sarah can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lilly","Sarah","Donna"],"index":5687,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9764047861,"difficulty":0.0235952139}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michelle can now know whether Manuel can know that Manuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Francis","Manuel"],"index":9497,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9415069818,"difficulty":0.0584930182}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roseanne's card is shown to Wm. Wm's card is shown to Bradley. Wm's card is shown to Roseanne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Wm can now know that Wm picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wm","Bradley","Roseanne"],"index":2911,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9782689214,"difficulty":0.0217310786}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Chelsea can now know that Darlene can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlene","Linda","Chelsea","Clarence"],"index":8754,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9786105156,"difficulty":0.0213894844}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sonya does not know whether or not everyone is thirsty. It is publicly announced that Erica does not know whether Terri is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Sonya can now know whether Sonya is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Terri","Sonya","Erica"],"index":3236,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5035692453,"difficulty":0.4964307547}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessica can now know that Joshua can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Joyce","Joshua","Willis"],"index":19,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.6426727176,"difficulty":0.3573272824}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Darryl can now know whether Darryl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eva","Leslie","Darryl"],"index":5715,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9571649432,"difficulty":0.0428350568}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chrystal knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jerome can now know that Mary can know that Jerome's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Chrystal","Jerome","Albert"],"index":1382,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9812961221,"difficulty":0.0187038779}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether someone's forehead is muddy.","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":"Dennis can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dorothy","Dennis"],"index":4336,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9681922197,"difficulty":0.0318077803}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dawn does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Alan can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dawn","Alan"],"index":9185,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9682322145,"difficulty":0.0317677855}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Candace. Candace's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Candace picked a black card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(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) ] [ ! ~(1) ] [ ! (~(1&2)) ] 0","hypothesis":"Susan can now know whether Candace can know whether Candace picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Candace","Susan"],"index":7127,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8982005119,"difficulty":0.1017994881}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dewey's card is shown to Luz. Gwendolyn's card is shown to Luz. Luz's card is shown to Gwendolyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Luz can now know whether Dewey can know whether Calvin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Luz","Dewey","Calvin","Gwendolyn"],"index":7894,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8989744782,"difficulty":0.1010255218}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Natalia 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 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":"Donnie can now know that Natalia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Natalia","Donnie"],"index":303,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9605631828,"difficulty":0.0394368172}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Kellie. Danny's card is shown to Phillip. Kellie's card is shown to Phillip. It is publicly announced that someone picked a red card. It is publicly announced that Kellie does not know whether Phillip picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Danny can now know whether Phillip picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Danny","Kellie","Phillip"],"index":2961,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7629503608,"difficulty":0.2370496392}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Thomas's forehead is muddy. It is publicly announced that Dennis knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Thomas can now know that Dennis can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dennis","Thomas"],"index":4949,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9713096619,"difficulty":0.0286903381}
-{"premise":"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. It is publicly announced that William's forehead is not muddy. It is publicly announced that Steve's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] [ ! ~(2) ] Agentc knows whether (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] [ ! ~(2) ] 0","hypothesis":"Sharell can now know whether William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","Steve","Sharell","William"],"index":2761,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.854252696,"difficulty":0.145747304}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carla's card is shown to Josefina. Carla's card is shown to Debbie. Josefina's card is shown to Carla. Josefina's card is shown to Douglass. Debbie's card is shown to Douglass. It is publicly announced that someone picked a red card. It is publicly announced that Douglass does not know whether Carla picked a red card. It is publicly announced that Carla does not know whether Carla picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(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:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Carla can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Josefina","Debbie","Carla","Douglass"],"index":9056,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9731729627,"difficulty":0.0268270373}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Humberto does not know whether Elisabeth is thirsty. It is publicly announced that Robert does not know whether Elisabeth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Elisabeth can now know whether Robert can know whether Emmanuel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Elisabeth","Emmanuel","Humberto"],"index":9506,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8659126759,"difficulty":0.1340873241}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Robert. Maria's card is shown to Robert. Robert's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Donald can now know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Donald","Maria"],"index":2139,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6180618405,"difficulty":1.6180618405}
-{"premise":"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 James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Paul can now know that James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Paul"],"index":1359,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.977935195,"difficulty":0.022064805}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Briana. Briana's card is shown to Samuel. Briana's card is shown to Jared. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Samuel can now know whether Samuel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Briana","Samuel","Jared"],"index":1924,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6428966522,"difficulty":1.6428966522}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa does not know whether Andrew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Candice can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Teresa","Candice","Andrew"],"index":8696,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9751983285,"difficulty":0.0248016715}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Gerald. Vicki's card is shown to Gerald. Gerald's card is shown to Roger. Michael's card is shown to Roger. Gerald's card is shown to Vicki. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know that Vicki picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gerald","Michael","Roger","Vicki"],"index":7161,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9778253436,"difficulty":0.0221746564}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that Julian can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Larry","Robert","Julian"],"index":5610,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9359634519,"difficulty":0.0640365481}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marshall knows whether Duane's forehead is muddy. It is publicly announced that Duane does not know whether or not everyone's forehead is muddy. It is publicly announced that Duane does not know whether Duane's forehead 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 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Marshall can now know whether Joseph can know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Freda","Duane","Marshall"],"index":4547,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8570711613,"difficulty":0.1429288387}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clara knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Erich can now know whether Clara can know that Delbert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Erich","Delbert","Andrew","Clara"],"index":6139,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.950922668,"difficulty":0.049077332}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rudolph can now know that Brian can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rudolph","Monika","Joyce","Brian"],"index":8929,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859338403,"difficulty":0.0140661597}
-{"premise":"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 Nichole's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentd knows that (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) ] 0","hypothesis":"Melissa can now know that Kim can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nichole","Mark","Kim","Melissa"],"index":4630,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9780899286,"difficulty":0.0219100714}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bertha does not know whether Bertha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Bertha can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bertha","Joseph","Laura","Scott"],"index":4652,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9788244963,"difficulty":0.0211755037}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clayton's card is shown to Earnestine. Nathan's card is shown to Earnestine. Earnestine's card is shown to Clayton. Nathan's card is shown to Lorenza. Earnestine's card is shown to Nathan. Lorenza's card is shown to Nathan. It is publicly announced that someone picked a red card. It is publicly announced that Earnestine knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Clayton can now know whether Lorenza can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earnestine","Clayton","Lorenza","Nathan"],"index":4724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9723395705,"difficulty":0.0276604295}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Maxine can now know whether Rita can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Rita","David","Maxine"],"index":4953,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9751224518,"difficulty":0.0248775482}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terry can now know that James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eleanor","James","Frank","Terry"],"index":2504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9824758768,"difficulty":0.0175241232}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Michelle. Jose's card is shown to Karen. Jane's card is shown to Karen. Jane's card is shown to Jose. Michelle's card is shown to Jane. Jose's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Jane does not know whether Karen picked a red card. It is publicly announced that Michelle does not know whether Karen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Michelle can now know that Karen can know that Jose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Karen","Jose","Jane"],"index":1146,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9730978012,"difficulty":0.0269021988}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roger knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Ronald can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Roger","Ronald"],"index":2181,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9753687382,"difficulty":0.0246312618}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"David can now know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Estela","Scott","David"],"index":155,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9750452638,"difficulty":0.0249547362}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Carrie knows whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"James can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carrie","Steven","James","Robyn"],"index":2805,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9768258333,"difficulty":0.0231741667}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonna's card is shown to Ana. Jonna's card is shown to Misty. Ana's card is shown to Jonna. Misty's card is shown to Jonna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ana can now know whether Ana picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ana","Misty","Jonna"],"index":1115,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6622844338,"difficulty":1.6622844338}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Eva can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Eva","Michael"],"index":9174,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9804682732,"difficulty":0.0195317268}
-{"premise":"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 Steven's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(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 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Nancy can now know that Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Steven","Nancy"],"index":2563,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9753720164,"difficulty":0.0246279836}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gretchen's card is shown to Jill. Gretchen's card is shown to Dinah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jill can now know whether Dinah can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jill","Dinah","Gretchen"],"index":2169,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9762622714,"difficulty":0.0237377286}
-{"premise":"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 knows whether Dwayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mary can now know that Dwayne can know whether Joshua's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dwayne","Richard","Mary","Joshua"],"index":2217,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9139035344,"difficulty":0.0860964656}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shirley can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Tyrone","Shirley"],"index":6949,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857923388,"difficulty":0.0142076612}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether Natalie is thirsty. It is publicly announced that George knows whether someone is thirsty. It is publicly announced that Milton does not know whether or not everyone is thirsty. It is publicly announced that Milton does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Eric can now know that Milton can know whether Eric is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Milton","Natalie","Eric","George"],"index":2813,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6379321218,"difficulty":1.6379321218}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanne knows whether Jeanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Jeanne can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dallas","Andrea","Milton","Jeanne"],"index":4858,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9769095778,"difficulty":0.0230904222}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_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":"Lloyd can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonathan","Lloyd","Luz"],"index":2355,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8095784783,"difficulty":0.1904215217}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vincent's card is shown to Cheryl. Cheryl's card is shown to Vincent. Cheryl's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether someone picked a red card. It is publicly announced that Vincent picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that Vincent picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cheryl","Vincent","Mary"],"index":6972,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9704948664,"difficulty":0.0295051336}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether Ronald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Jessica can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Ronald","Jessica","Brenda"],"index":8127,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.975276649,"difficulty":0.024723351}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Helen can now know that John can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amanda","John","Helen"],"index":6616,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9254603982,"difficulty":0.0745396018}
-{"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 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":"Paul can now know whether Bernadette can know that Emma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Emma","Bernadette"],"index":8608,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7569391131,"difficulty":0.2430608869}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Mary can now know whether Lajuana can know that Lajuana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Lajuana","Martha","Andrew"],"index":7926,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9507780075,"difficulty":0.0492219925}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Ashley can now know that Lawrence can know that Lawrence is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lawrence","Daniel","Jose","Ashley"],"index":9485,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9790598154,"difficulty":0.0209401846}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Derek. Derek's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Derek picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"John can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Derek","John"],"index":1900,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9662905335,"difficulty":0.0337094665}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Anna can now know that Teresa can know that Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anna","Teresa"],"index":6437,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9768480062,"difficulty":0.0231519938}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lloyd can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steve","Scott","Lloyd"],"index":6759,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9804978371,"difficulty":0.0195021629}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chris does not know whether Jo is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Jo can now know that Paula is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jo","Chris","Paula"],"index":1441,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.976385951,"difficulty":1.976385951}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mae can now know whether Maria can know whether Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christina","Mae","Maria"],"index":3163,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9438145757,"difficulty":1.9438145757}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernesto's card is shown to Kate. Carrie's card is shown to Jamel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kate can now know whether Jamel can know that Ernesto picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kate","Jamel","Carrie","Ernesto"],"index":6441,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6466058493,"difficulty":0.3533941507}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nicole can now know whether Antione can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Isaiah","Nicole","Antione"],"index":2837,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9749526978,"difficulty":0.0250473022}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori does not know whether Lori's forehead is muddy. It is publicly announced that Nicole knows whether someone'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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nicole can now know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lori","Carrie","Nicole","Thomas"],"index":8650,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9343146086,"difficulty":0.0656853914}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Katherine can now know whether Jennifer can know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katherine","Miguel","Jennifer","Thomasina"],"index":7651,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8177309036,"difficulty":0.1822690964}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillian knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lillian can now know whether Ruby can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stan","Ruby","Ben","Lillian"],"index":7621,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.963660717,"difficulty":0.036339283}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Lisa. Brian's card is shown to Lisa. Helen's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Helen can now know that Helen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Lisa","Brian"],"index":5791,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9790509939,"difficulty":0.0209490061}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Racheal's card is shown to Vera. Vera's card is shown to Racheal. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Vera can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vera","Racheal"],"index":2735,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9767383337,"difficulty":0.0232616663}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Faye can now know whether Harold's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Faye","Jerome","Nathaniel","Harold"],"index":7537,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9619825482,"difficulty":0.0380174518}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Glen can now know that Marie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marisa","Sandra","Glen","Marie"],"index":2267,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9789546132,"difficulty":0.0210453868}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Cleo is thirsty. It is publicly announced that Betty does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Angela can now know whether Richard can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Angela","Betty","Cleo"],"index":8398,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9716750979,"difficulty":0.0283249021}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Julia. Carman's card is shown to Julia. Elizabeth's card is shown to Julia. Carman's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Julia can now know whether Maria can know that Julia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julia","Maria","Carman","Elizabeth"],"index":3806,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6477727294,"difficulty":0.3522272706}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tara knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Tara can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maurine","Tara","Cynthia"],"index":8629,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9781628251,"difficulty":0.0218371749}
-{"premise":"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 Lisa knows whether or not everyone'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 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Helen can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sharon","Lisa","Helen"],"index":8047,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9769743085,"difficulty":0.0230256915}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Spencer knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Spencer can now know whether Charles can know that Spencer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Spencer","Charles"],"index":1911,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.946338892,"difficulty":0.053661108}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Rachel. Rachel's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Rachel can now know whether George can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rachel","George"],"index":6703,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9738276601,"difficulty":0.0261723399}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joshua can now know that Frank can know that Pamela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frank","Joshua","Pamela"],"index":3027,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864554405,"difficulty":0.0135445595}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Greta does not know whether or not everyone's forehead is muddy. It is publicly announced that Greta does not know whether or not everyone's forehead is muddy. It is publicly announced that Robin 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 whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Greta can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robin","Greta"],"index":7657,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9683588743,"difficulty":0.0316411257}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kurtis does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Billy can now know whether Felipe can know whether Billy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kurtis","Felipe","Billy"],"index":2336,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9359853864,"difficulty":0.0640146136}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alvin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Alvin can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alvin","Tosha","Hai"],"index":3177,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9764547944,"difficulty":0.0235452056}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robbie can now know whether Eddy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robbie","Lindsey","Eddy"],"index":4310,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5954102874,"difficulty":0.4045897126}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Donald can now know whether Paul can know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Paul","Brian","Donald"],"index":5069,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7279260159,"difficulty":0.2720739841}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy.","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 (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Ella can now know whether Charles can know that Ella's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Ella","Shantell"],"index":4022,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8121370077,"difficulty":1.8121370077}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carla can now know that William can know whether Carla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carla","William","Dale"],"index":8724,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9576314092,"difficulty":0.0423685908}
-{"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 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 Wesley can know that Wesley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Priscilla","Wesley","Ronald","John"],"index":9145,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9825099707,"difficulty":0.0174900293}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joyce does not know whether Annette is thirsty. It is publicly announced that Lisa does not know whether Jeffrey is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Joyce can now know that Annette can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Joyce","Annette","Jeffrey"],"index":5898,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9748924375,"difficulty":0.0251075625}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darlene does not know whether Kelly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Terry can now know whether Darlene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Darlene","Terry","Kelly"],"index":4219,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5932818055,"difficulty":1.5932818055}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Elizabeth is thirsty. It is publicly announced that Brian is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Raymond can now know that Raymond is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Elizabeth","Brian"],"index":8183,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9755920768,"difficulty":0.0244079232}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jana's card is shown to Ronnie. Edgar's card is shown to Jana. Jana's card is shown to Edgar. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edgar can now know whether Jana picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronnie","Jana","Edgar","Anne"],"index":8757,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6574204564,"difficulty":0.3425795436}
-{"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 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":"Maria can now know that James can know that Dean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Maria","Dean","Leonard"],"index":4176,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823932648,"difficulty":0.0176067352}
-{"premise":"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)","n_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":"Matthew can now know that Melody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melody","Matthew","Deborah"],"index":8104,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9812520742,"difficulty":0.0187479258}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyler's card is shown to Cecil. Flo's card is shown to Cecil. Flo's card is shown to Tyler. Cecil's card is shown to Flo. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Flo can now know that Cecil picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cecil","Tyler","Flo"],"index":4737,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9766671658,"difficulty":0.0233328342}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronnie's card is shown to Carmen. Carolyn's card is shown to Brandon. Ronnie's card is shown to Brandon. Brandon's card is shown to Carolyn. Ronnie's card is shown to Carolyn. Carmen's card is shown to Ronnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandon can now know that Brandon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carmen","Brandon","Carolyn","Ronnie"],"index":7763,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9778462052,"difficulty":0.0221537948}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty does not know whether Erin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Betty can now know that Philip is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Philip","Erin","Betty"],"index":5266,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9763966203,"difficulty":0.0236033797}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah does not know whether Rickey is thirsty. It is publicly announced that Sarah knows whether or not everyone is thirsty. It is publicly announced that Jill knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Sarah can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rickey","Jill","Sarah"],"index":1407,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9494412541,"difficulty":0.0505587459}
-{"premise":"There are three 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 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Lena can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carla","Cindy","Lena"],"index":992,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9824051261,"difficulty":0.0175948739}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Devon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"David can now know whether Michael can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Heather","Devon","Michael"],"index":1439,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9751403928,"difficulty":0.0248596072}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Cathy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentd knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"William can now know that Crystal can know whether Crystal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Cathy","Crystal","William"],"index":6198,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5091529489,"difficulty":1.5091529489}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danny's card is shown to Julia. Jonathon's card is shown to Julia. Jonathon's card is shown to Danny. Danny's card is shown to Jonathon. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc: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:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Danny can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julia","Danny","Jonathon"],"index":3083,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9772990346,"difficulty":0.0227009654}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether Elaine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Freda can now know whether Sam can know whether Freda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elaine","Andrew","Sam","Freda"],"index":9447,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9707933664,"difficulty":0.0292066336}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Ingrid. Rebecca's card is shown to Jerry. Ingrid's card is shown to Jerry. It is publicly announced that someone picked a red card. It is publicly announced that Ingrid does not know whether Jerry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rebecca can now know whether Ingrid can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rebecca","Ingrid","Jerry"],"index":1823,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9660691023,"difficulty":0.0339308977}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kim knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Sarah can now know whether Kim's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Kim","Charles","Sarah"],"index":7215,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9030132294,"difficulty":0.0969867706}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheryl does not know whether or not everyone's forehead is muddy. It is publicly announced that Carol knows whether Carol'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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Sheryl can now know that Floyd's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Floyd","Sheryl"],"index":6958,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9539616108,"difficulty":1.9539616108}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwayne's card is shown to Richard. Richard's card is shown to Dwayne. It is publicly announced that someone picked a red card. It is publicly announced that Dwayne knows whether Dwayne picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dwayne can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Richard","Dwayne"],"index":7149,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9731715322,"difficulty":0.0268284678}
-{"premise":"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 America knows whether or not everyone's forehead is muddy. It is publicly announced that America does not know whether America's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (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) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Karen can now know that Cindy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cindy","America","Karen"],"index":2826,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9643816352,"difficulty":0.0356183648}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Cynthia. Vivian's card is shown to Jeffrey. Cynthia's card is shown to Vivian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vivian can now know that Jeffrey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cynthia","Jeffrey","Vivian"],"index":1663,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9172314405,"difficulty":0.0827685595}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clifton's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Rudolph can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clifton","Eugene","Paul","Rudolph"],"index":4474,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9788113236,"difficulty":0.0211886764}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kareem can now know that Barbara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Andres","Kareem"],"index":7766,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.980520308,"difficulty":0.019479692}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henry's card is shown to Maria. Michael's card is shown to Henry. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Maria can now know whether Michael can know that Henry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Michael","Henry"],"index":524,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5891287923,"difficulty":0.4108712077}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know that Lisa can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlotte","Kevin","Gloria","Lisa"],"index":9299,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9828369617,"difficulty":0.0171630383}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Waneta knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Carla can now know that Christopher can know that Terry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Terry","Christopher","Carla","Waneta"],"index":6768,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9701007605,"difficulty":0.0298992395}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarissa's card is shown to Francis. Francis's card is shown to Felix. Francis's card is shown to Jarred. Francis's card is shown to Clarissa. Felix's card is shown to Clarissa. It is publicly announced that someone picked a red card. It is publicly announced that Jarred does not know whether Jarred picked a red card. It is publicly announced that Felix knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Francis can now know that Felix picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francis","Felix","Jarred","Clarissa"],"index":927,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.965652287,"difficulty":0.034347713}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Henrietta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Ramona can now know whether Ramona's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ramona","Mary","Henrietta"],"index":1579,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9632818699,"difficulty":0.0367181301}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether Anna is thirsty. It is publicly announced that Robert does not know whether Jesus is thirsty. It is publicly announced that Jesus knows whether Jesus is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentd knows whether 4) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Anna can now know whether Anna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Stephen","Anna","Jesus"],"index":516,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7694939971,"difficulty":0.2305060029}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glen's card is shown to Harvey. Harvey's card is shown to Joseph. Glen's card is shown to Joseph. Harvey's card is shown to Glen. Joseph's card is shown to Glen. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Glen does not know whether Glen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Joseph can now know that Harvey can know that Harvey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harvey","Joseph","Glen"],"index":8554,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9745500088,"difficulty":0.0254499912}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jonas does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jonas can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonas","Lisa","Alfredo"],"index":8155,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9762979746,"difficulty":0.0237020254}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Kate is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Mary can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Kevin","Joel","Kate"],"index":5177,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.975662291,"difficulty":0.024337709}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether 3)","n_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":"Sue can now know that Mark can know whether Christina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sue","Mark","Christina"],"index":6520,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9289107919,"difficulty":0.0710892081}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Rita can now know that Elizabeth can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","James","Rita","Joe"],"index":9431,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.974108696,"difficulty":0.025891304}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Margaret. Margaret's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Patricia can now know that Margaret can know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Margaret","Patricia"],"index":7937,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9789084196,"difficulty":1.9789084196}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Danny can now know whether Herman can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herman","Ronald","Danny"],"index":4523,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9617117047,"difficulty":0.0382882953}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michelle does not know whether Annabelle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Monique can now know that Effie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annabelle","Michelle","Monique","Effie"],"index":1081,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9710509181,"difficulty":0.0289490819}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Debra can now know that Brittany can know whether Peter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alyssa","Peter","Brittany","Debra"],"index":9417,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.874602735,"difficulty":0.125397265}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyler's card is shown to Pedro. Melissa's card is shown to Pedro. Melissa's card is shown to Tyler. Joyce's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tyler can now know that Pedro can know that Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pedro","Joyce","Tyler","Melissa"],"index":475,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9783053994,"difficulty":0.0216946006}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henrietta knows whether Eric's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Eric can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Henrietta","Eric","Kent"],"index":1097,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9818233252,"difficulty":0.0181766748}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mary can now know whether Melissa can know that Melissa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Melissa","Paul"],"index":4820,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5677660704,"difficulty":1.5677660704}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Catherine. Irene's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Catherine can now know whether Catherine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Catherine","Jesse","Irene","William"],"index":3112,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6559135914,"difficulty":1.6559135914}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Edwin. Jo's card is shown to Edwin. Edwin's card is shown to Mary. Angela's card is shown to Mary. Edwin's card is shown to Jo. Mary's card is shown to Jo. Edwin's card is shown to Angela. Mary's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Angela picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jo can now know that Mary can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edwin","Mary","Jo","Angela"],"index":8835,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9244811535,"difficulty":1.9244811535}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cesar knows whether Cesar's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Carl can now know that Eleanor can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carl","Eleanor","Cesar","Everett"],"index":5860,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.985699594,"difficulty":0.014300406}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Raymond. Raymond's card is shown to Rafael. Raymond's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rafael can now know that Joseph can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raymond","Rafael","Joseph"],"index":7072,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9788777232,"difficulty":0.0211222768}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether Ronald's forehead is muddy. It is publicly announced that Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Lorrie can now know whether Shirley can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lorrie","Shirley","Ronald"],"index":131,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9533869624,"difficulty":1.9533869624}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Graciela knows whether Jessica's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Graciela can now know whether Graciela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Graciela","Jessica"],"index":5685,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9637140036,"difficulty":0.0362859964}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dena knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alan can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alan","Dena","Dennis","Johnnie"],"index":6074,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.970666647,"difficulty":0.029333353}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maryann's card is shown to Frank. Alexander's card is shown to Frank. Myra's card is shown to Frank. Alexander's card is shown to Maryann. Myra's card is shown to Maryann. Frank's card is shown to Alexander. Myra's card is shown to Alexander. Maryann's card is shown to Myra. It is publicly announced that someone picked a red card. It is publicly announced that Alexander does not know whether Maryann picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Maryann can now know whether Myra can know that Frank picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Maryann","Alexander","Myra"],"index":684,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6858198047,"difficulty":0.3141801953}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether someone's forehead is muddy. It is publicly announced that Rebecca knows whether Georgia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Angela can now know whether Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rebecca","Georgia","Angela","Steven"],"index":4628,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9633274078,"difficulty":0.0366725922}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 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":"Kathryn can now know whether Christian can know whether Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Thomas","Kimberly","Christian"],"index":885,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9469923377,"difficulty":0.0530076623}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to James. Gwyn's card is shown to Linda. Linda's card is shown to Gwyn. Linda's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Andrew picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Linda can now know that Andrew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Linda","Gwyn","Andrew"],"index":9193,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9754264355,"difficulty":0.0245735645}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Emma can now know whether Maria can know that Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Maria","Emma"],"index":5254,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5632586479,"difficulty":1.5632586479}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carole 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 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":"Carole can now know that Carole's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Patricia","Carole"],"index":7774,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9610068798,"difficulty":0.0389931202}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anisa does not know whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jessica can now know that Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Anisa","Thomas","Jerry"],"index":2023,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.975581646,"difficulty":0.024418354}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eileen does not know whether Allison is thirsty. It is publicly announced that Heather is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] 0","hypothesis":"Heather can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Allison","Heather","Eileen"],"index":8178,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9763364792,"difficulty":0.0236635208}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Mona knows whether Andre's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"David can now know whether Andre can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mona","David","Andre"],"index":221,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9784488678,"difficulty":0.0215511322}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Carl is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Michael can now know that Carl can know that Carl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Carl"],"index":9368,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9767642021,"difficulty":0.0232357979}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Latasha does not know whether or not everyone's forehead is muddy. It is publicly announced that Latasha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Dennis can now know that Latasha can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dennis","Latasha"],"index":3638,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9722716212,"difficulty":0.0277283788}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Joey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Ann","Joey"],"index":6754,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9763324261,"difficulty":0.0236675739}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ramon's card is shown to Kathleen. Kathleen's card is shown to Mary. Ramon's card is shown to Mary. Kathleen's card is shown to Ramon. Mary's card is shown to Ramon. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Ramon does not know whether Ramon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ramon can now know that Kathleen can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathleen","Mary","Ramon"],"index":8480,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.731810987,"difficulty":1.731810987}
-{"premise":"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 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) ] [ ! (Agenta knows whether 3) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Charles can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Randall","Betty","Arthur"],"index":6547,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9782877564,"difficulty":0.0217122436}
-{"premise":"There are two 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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Becky can now know whether Gabrielle can know that Gabrielle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Becky","Gabrielle"],"index":4467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7825962305,"difficulty":0.2174037695}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether Gerald's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Gerald can now know that Ryan can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ryan","Gerald"],"index":6368,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.954051435,"difficulty":0.045948565}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma's forehead is muddy. It is publicly announced that Andrea knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Michael can now know that Andrea can know whether Norma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Norma","Andrea"],"index":8300,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9646332264,"difficulty":0.0353667736}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Alberto. Gabriel's card is shown to Mildred. Mildred's card is shown to Gabriel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Alberto picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alberto","Mildred","Robert","Gabriel"],"index":557,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9788566828,"difficulty":0.0211433172}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Terry does not know whether Daryl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Terry can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daryl","Janice","Terry","Dennis"],"index":5703,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9759172797,"difficulty":0.0240827203}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy. It is publicly announced that Rebecca does not know whether Rebecca'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|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":"Rebecca can now know that Richard can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rebecca","Richard"],"index":4772,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9735162854,"difficulty":0.0264837146}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wesley's card is shown to Barbara. Barbara's card is shown to Cindi. Wesley's card is shown to Cindi. Barbara's card is shown to Wesley. Cindi's card is shown to Wesley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cindi can now know whether Cindi picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Cindi","Wesley"],"index":3936,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6462275982,"difficulty":1.6462275982}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mercedes can now know that Veronica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Joseph","Mercedes","Veronica"],"index":4588,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857246876,"difficulty":0.0142753124}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geneva's card is shown to Theodore. Lori's card is shown to Theodore. Geneva's card is shown to David. David's card is shown to Geneva. David's card is shown to Lori. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Theodore picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"David can now know that Lori picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Theodore","David","Geneva","Lori"],"index":6475,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9753206372,"difficulty":0.0246793628}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know whether Donna can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Donna","John"],"index":23,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9749343395,"difficulty":0.0250656605}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jamie is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Glen can now know whether Donna can know that Jamie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jamie","Glen","Donna"],"index":1518,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5843444467,"difficulty":0.4156555533}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"David can now know whether Marjorie can know whether Kristen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Kristen","Marjorie"],"index":3347,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9719402194,"difficulty":0.0280597806}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlotte's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Justin can now know that Charlotte can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charlotte","Justin"],"index":3955,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823414087,"difficulty":0.0176585913}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to John. Mary's card is shown to Elizabeth. Elizabeth's card is shown to Mary. Ruth's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Elizabeth picked a red card. It is publicly announced that Elizabeth does not know whether Elizabeth picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that John does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mary can now know whether Ruth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Elizabeth","Mary","Ruth"],"index":372,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7192521691,"difficulty":0.2807478309}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mike's card is shown to Alex. Alex's card is shown to Mike. Brent's card is shown to Mike. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mike can now know that Brent picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alex","Mike","Brent"],"index":7858,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9789616466,"difficulty":0.0210383534}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Patti can now know that Billy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gladys","Milagros","Billy","Patti"],"index":6985,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9818695188,"difficulty":0.0181304812}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to John. Donna's card is shown to Patricia. Patricia's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Monica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Patricia","Monica","Donna"],"index":1904,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786509275,"difficulty":0.0213490725}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Claudine is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Claudine can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Claudine","Georgia","Beth"],"index":1667,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9796856046,"difficulty":0.0203143954}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glenda's card is shown to Diana. Joyce's card is shown to Glenda. Jason's card is shown to Glenda. Diana's card is shown to Joyce. Joyce's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Diana can now know whether Joyce can know whether Diana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Diana","Glenda","Joyce","Jason"],"index":5435,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8604522347,"difficulty":0.1395477653}
-{"premise":"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 Antoine knows whether 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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Zachary can now know whether Antoine can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Zachary","Antoine"],"index":7603,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9724293351,"difficulty":0.0275706649}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Preston knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Preston can now know whether Walter can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Walter","Preston"],"index":5536,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8574821353,"difficulty":0.1425178647}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jonathan can now know whether Deborah can know that Jonathan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Jonathan","Deborah"],"index":1978,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9407576323,"difficulty":0.0592423677}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marcia can now know whether Joseph can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marcia","Joseph","Billie"],"index":285,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.97633636,"difficulty":0.02366364}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emma knows whether someone's forehead is muddy. It is publicly announced that Vernon knows whether Johnny's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Richard can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vernon","Johnny","Emma","Richard"],"index":2254,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9801124334,"difficulty":0.0198875666}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Gregory","Richard","Brian"],"index":7022,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.986405313,"difficulty":0.013594687}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Maria. Ricky's card is shown to Joy. Ricky's card is shown to Jennifer. Jennifer's card is shown to Ricky. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Jennifer picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ricky can now know that Ricky picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Joy","Jennifer","Ricky"],"index":1955,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9756439328,"difficulty":0.0243560672}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Lawrence. Lawrence's card is shown to Doris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lawrence can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lawrence","Doris","Joyce"],"index":3690,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9797791839,"difficulty":0.0202208161}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felecia's card is shown to Jeanette. Lois's card is shown to Jeanette. Jeanette's card is shown to Lois. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Felecia can now know whether Jeanette can know that Lois picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeanette","Felecia","Lois"],"index":664,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6649387479,"difficulty":1.6649387479}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Glenna can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brent","Deborah","Michael","Glenna"],"index":5822,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9767150283,"difficulty":0.0232849717}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy. It is publicly announced that Gina does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Suzanne can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Suzanne","Michael","Gina"],"index":9158,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9349691868,"difficulty":1.9349691868}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl knows whether Cheryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marilyn","Cheryl","Michael","John"],"index":7267,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8794503212,"difficulty":0.1205496788}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Olga. Wanda's card is shown to Robert. Omer's card is shown to Robert. Omer's card is shown to Wanda. Olga's card is shown to Omer. Wanda's card is shown to Omer. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Omer does not know whether Robert picked a red card. It is publicly announced that Olga does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Olga can now know whether Robert can know whether Wanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olga","Robert","Wanda","Omer"],"index":6398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8843906522,"difficulty":0.1156093478}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Mark. Mark's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eva can now know whether Carolyn can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Eva","Mark","Jennifer"],"index":1076,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8169010282,"difficulty":0.1830989718}
-{"premise":"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 Phyllis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Phyllis can now know whether Eric can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Phyllis","Eric"],"index":5788,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9396122098,"difficulty":0.0603877902}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walker does not know whether Walker's forehead is muddy. It is publicly announced that Katherine does not know whether Katherine's forehead is muddy. It is publicly announced that Katherine 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jeri can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katherine","Jeri","Walker"],"index":5958,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9523277879,"difficulty":0.0476722121}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Charlotte. Charlotte's card is shown to Daniel. William's card is shown to Daniel. Daniel's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlotte can now know whether Mary can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charlotte","Daniel","Mary","William"],"index":9539,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9734645486,"difficulty":0.0265354514}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paula knows whether Paula's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jon can now know that Vivian can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jon","Paula","Jayme","Vivian"],"index":9578,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9779592752,"difficulty":0.0220407248}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosalina knows whether Rosalina is thirsty. It is publicly announced that Robert does not know whether Gordon is thirsty. It is publicly announced that Rosalina is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Gordon can now know that Adam is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adam","Rosalina","Robert","Gordon"],"index":7449,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9735836387,"difficulty":0.0264163613}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Retha. Retha's card is shown to Troy. Troy's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Retha can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Retha","Troy","Mary"],"index":2862,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9726228118,"difficulty":0.0273771882}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Pamela can now know that Joseph can know that Pamela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Pilar","Pamela"],"index":227,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853720069,"difficulty":0.0146279931}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda knows whether Brenda is thirsty. It is publicly announced that Jorge is thirsty. It is publicly announced that Brenda is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] [ ! ~(1) ] (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] [ ! ~(1) ] 0","hypothesis":"Brenda can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brenda","Doris","Jorge","Wade"],"index":3029,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9777090549,"difficulty":0.0222909451}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cheryl does not know whether or not everyone is thirsty. It is publicly announced that Pamela is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] 0","hypothesis":"Cheryl can now know whether Pamela can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pamela","Cheryl","Giselle"],"index":1285,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8757525682,"difficulty":0.1242474318}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Velda can now know that Patricia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Velda","Earline","Patricia","Hilary"],"index":1755,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.977799654,"difficulty":0.022200346}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Tonya can now know that Tonya's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jacqueline","Kenneth","Tonya"],"index":2825,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.974820137,"difficulty":0.025179863}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Beatriz does not know whether Chris is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Beatriz can now know that Robert can know that Chris is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Beatriz","Betty","Robert","Chris"],"index":8603,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9554526806,"difficulty":0.0445473194}
-{"premise":"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)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Karen can now know that Maureen can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Maureen","David","Hannah"],"index":917,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9729657173,"difficulty":0.0270342827}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know whether Sofia can know that Ralph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Ralph","Leonardo","Sofia"],"index":8774,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5601300597,"difficulty":1.5601300597}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Virginia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 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) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","John","Joey","Virginia"],"index":8783,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9813935757,"difficulty":0.0186064243}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Catherine knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Pauline can now know whether Catherine can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Catherine","Jean","Pauline"],"index":8587,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9705770612,"difficulty":0.0294229388}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Enid's card is shown to Reuben. Enid's card is shown to Timothy. Reuben's card is shown to Enid. It is publicly announced that someone picked a red card. It is publicly announced that Enid does not know whether Timothy picked a red card. It is publicly announced that Reuben does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Reuben can now know that Enid can know whether Reuben picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Reuben","Timothy","Enid"],"index":1372,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6654075384,"difficulty":0.3345924616}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Diane can now know that Tanya can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tanya","Michael","Carl","Diane"],"index":2114,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8239498734,"difficulty":0.1760501266}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Janice knows whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Kathleen can now know that Jose can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Janice","Kathleen","Jose"],"index":544,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9851562977,"difficulty":0.0148437023}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmen's card is shown to Eugene. Eugene's card is shown to Carmen. Nathan's card is shown to Carmen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eugene can now know that Carmen can know whether Nathan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","Carmen","Nathan"],"index":7427,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7056857944,"difficulty":0.2943142056}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynn does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Michael can now know whether Robert can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lynn","Patricia","Michael","Robert"],"index":3500,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8967052102,"difficulty":0.1032947898}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Floyd can now know that Bradley can know that Betsy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betsy","Antonio","Floyd","Bradley"],"index":5836,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864778519,"difficulty":0.0135221481}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Howard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Howard","Jillian","William"],"index":4102,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9602473974,"difficulty":0.0397526026}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Emma can now know that Alexis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alexis","Caridad","Emma"],"index":146,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9776346684,"difficulty":0.0223653316}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bessie's card is shown to Jeremy. Jeremy's card is shown to Bessie. John's card is shown to Bessie. Jeremy's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Bessie picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Jeremy can now know that John can know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeremy","Bessie","John"],"index":6188,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9776591659,"difficulty":0.0223408341}
-{"premise":"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's forehead is muddy. It is publicly announced that Evette does not know whether Evette's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 1)","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":"Evette can now know whether Sandra can know that Evette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Evette","Sandra"],"index":159,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8761717677,"difficulty":1.8761717677}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Alfred can now know that Edward can know that Alfred is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alfred","Jose","Edward"],"index":8628,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9794175029,"difficulty":0.0205824971}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenn's forehead is muddy. It is publicly announced that Martha does not know whether Martha'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 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":"Martha can now know that Glenn can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Martha","Glenn"],"index":4208,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9787953496,"difficulty":0.0212046504}
-{"premise":"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&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Cortney can now know whether Lewis can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lewis","Cortney"],"index":8407,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9400817752,"difficulty":0.0599182248}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(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":"Donna can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Martha","Donna","Jesus"],"index":5383,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9694930911,"difficulty":0.0305069089}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Keith can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Keith","Michael","Robert"],"index":6351,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9112096429,"difficulty":0.0887903571}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aimee's card is shown to Carroll. Carroll's card is shown to Robin. It is publicly announced that someone picked a red card. It is publicly announced that Aimee picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Robin can now know that Aimee picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carroll","Robin","Aimee"],"index":89,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9787282944,"difficulty":1.9787282944}
-{"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 (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":"Carl can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Glenn","Allie","William","Carl"],"index":1889,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7670967579,"difficulty":0.2329032421}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah does not know whether Delilah is thirsty. It is publicly announced that Doris knows whether someone is thirsty. It is publicly announced that Thomas does not know whether or not everyone is thirsty. It is publicly announced that Thomas does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know that Delilah can know whether Sarah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Delilah","Sarah","Doris"],"index":2100,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6925461292,"difficulty":1.6925461292}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alma's card is shown to Margaret. Margaret's card is shown to Alma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Alma can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Margaret","Alma"],"index":2088,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9798693061,"difficulty":0.0201306939}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kaitlyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Clarissa can now know that Neva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kaitlyn","Clarissa","Bruce","Neva"],"index":6816,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860507846,"difficulty":0.0139492154}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wayne does not know whether Michael is thirsty. It is publicly announced that Jay knows whether someone is thirsty. It is publicly announced that Anthony does not know whether or not everyone is thirsty. It is publicly announced that Anthony does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jay can now know whether Anthony can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Michael","Wayne","Jay"],"index":4326,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9737042189,"difficulty":0.0262957811}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joshua's card is shown to Erika. Erika's card is shown to Joshua. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Erika can now know whether Erika picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erika","Joshua","Kelley"],"index":4302,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6548878551,"difficulty":1.6548878551}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ward knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Sidney can now know whether Barbara can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alma","Sidney","Barbara","Ward"],"index":6743,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9746615887,"difficulty":0.0253384113}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leona","John","Lisa"],"index":7588,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858437777,"difficulty":0.0141562223}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Teresa. George's card is shown to Teresa. Teresa's card is shown to Karen. George's card is shown to Karen. Teresa's card is shown to George. Karen's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"George can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Teresa","Karen","George"],"index":3576,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9776697755,"difficulty":0.0223302245}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Gordon. Gordon's card is shown to Barbara. Robert's card is shown to Barbara. Mattie's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Gordon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gordon","Barbara","Robert","Mattie"],"index":8182,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9784795642,"difficulty":0.0215204358}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neil does not know whether Neil's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Christine can now know whether Ruby can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Neil","Pierre","Ruby","Christine"],"index":3294,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6811753511,"difficulty":1.6811753511}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandy knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jill can now know whether Brandy can know whether Brandy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandy","Frank","Dennis","Jill"],"index":9505,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9701889753,"difficulty":0.0298110247}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ebony does not know whether Michael is thirsty. It is publicly announced that Ebony is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Frank can now know that Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frank","Michael","Ebony"],"index":3716,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9749612808,"difficulty":0.0250387192}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Edward can now know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Doris","Edward","Mark"],"index":8969,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9788681269,"difficulty":0.0211318731}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Frank. Connie's card is shown to Juan. Frank's card is shown to Connie. Juan's card is shown to Connie. It is publicly announced that someone picked a red card. It is publicly announced that Juan knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Connie can now know that Juan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frank","Juan","Connie"],"index":5467,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9718778133,"difficulty":0.0281221867}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Alethea's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Alethea can now know whether Alethea's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alethea","David","Pam","Herman"],"index":7378,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9659457207,"difficulty":0.0340542793}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that 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":"Lee can now know whether George can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Lee","George"],"index":831,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7491218448,"difficulty":0.2508781552}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Sammy. Sammy's card is shown to Carolyn. Brenda's card is shown to Carolyn. Sammy's card is shown to Brenda. Carolyn's card is shown to Brenda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sammy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sammy","Carolyn","Brenda"],"index":9551,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9191420674,"difficulty":0.0808579326}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"William can now know that Carl can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carl","William"],"index":2292,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9627865553,"difficulty":0.0372134447}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley knows whether someone's forehead is muddy. It is publicly announced that Mike knows whether Amy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Daniel can now know that Bradley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mike","Amy","Bradley","Daniel"],"index":8164,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9808835387,"difficulty":0.0191164613}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis does not know whether Francis's forehead is muddy. It is publicly announced that Francis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|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) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Francis can now know that Francis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Francis","Mary"],"index":3360,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9529594183,"difficulty":0.0470405817}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Rory can now know that Brandon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doyle","Jared","Rory","Brandon"],"index":4432,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9861075878,"difficulty":0.0138924122}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marjorie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Marta can now know that Marjorie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marta","Marjorie"],"index":8011,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9614627957,"difficulty":1.9614627957}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie knows whether Mary's forehead is muddy. It is publicly announced that Marie does not know whether Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows 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 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Stuart can now know that Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marie","Mary","Stuart"],"index":6633,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9760352373,"difficulty":0.0239647627}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bert's card is shown to Roseann. Billy's card is shown to Roseann. Roseann's card is shown to Billy. Bert's card is shown to Billy. It is publicly announced that someone picked a red card. It is publicly announced that Roseann does not know whether or not everyone picked a red card. It is publicly announced that Bert knows whether Roseann picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Roseann can now know that Bert can know that Roseann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roseann","Bert","Billy"],"index":5709,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9613081813,"difficulty":0.0386918187}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marcus can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Marcus","Lorraine","Wilma"],"index":5369,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858352542,"difficulty":0.0141647458}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Dusty can now know whether Bob can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lyle","Bob","Dorothy","Dusty"],"index":5170,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9792596102,"difficulty":0.0207403898}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jordan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jordan can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Ed","Jordan"],"index":7559,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8784247041,"difficulty":0.1215752959}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Danny can now know that Victoria can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danny","Lana","Victoria","Kevin"],"index":1288,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9698791504,"difficulty":0.0301208496}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fay knows whether or not nobody's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know whether Fay can know that Fay's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dianne","John","Mike","Fay"],"index":3403,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8420810103,"difficulty":0.1579189897}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Wendy can now know whether Wendy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Wendy","Jason"],"index":4076,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9550163746,"difficulty":0.0449836254}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Melvin does not know whether Ron is thirsty. It is publicly announced that Thomas does not know whether Ron is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Ron can now know whether Tiffany can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Ron","Tiffany","Melvin"],"index":1171,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9743551016,"difficulty":0.0256448984}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeffrey can now know whether Katherin can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katherin","Jeffrey","Billy"],"index":2394,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.974443078,"difficulty":0.025556922}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leola's card is shown to Dennis. Dennis's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Leola picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Dennis can now know that Dennis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Matthew","Leola"],"index":4381,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9790563583,"difficulty":0.0209436417}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Florence knows whether or not nobody is thirsty. It is publicly announced that Florence knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Florence can now know whether Jacqueline can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Florence","Jacqueline"],"index":179,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9689443111,"difficulty":0.0310556889}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Shawn 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":["Shawn","Mary"],"index":3491,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9701363444,"difficulty":0.0298636556}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that Juan can know whether Sara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Samantha","Juan","Sara"],"index":1743,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9622929692,"difficulty":0.0377070308}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 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":"Cynthia can now know that Robert can know whether Billie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","Billie","Cynthia","Robert"],"index":5272,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8840506673,"difficulty":0.1159493327}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Al's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows 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":"Michael can now know whether Louise can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Al","Louise","Michael"],"index":8022,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7863413692,"difficulty":1.7863413692}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Andrea. Maria's card is shown to Janet. Andrea's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrea can now know that Andrea picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrea","Janet","Charles","Maria"],"index":908,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9791870117,"difficulty":0.0208129883}
-{"premise":"There are two 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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Erin can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Franklin","Erin"],"index":5332,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9722058177,"difficulty":0.0277941823}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Virginia can now know that George can know that Catherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Catherine","Virginia"],"index":8753,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853169322,"difficulty":0.0146830678}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether 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 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marvin","Jennifer","Richard"],"index":6565,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9641805291,"difficulty":0.0358194709}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elmer can now know that Percy can know that Elmer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elmer","Percy","Sandra"],"index":1614,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864989519,"difficulty":0.0135010481}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karlyn can now know whether Debra can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karlyn","Ruth","Louise","Debra"],"index":4910,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9188432693,"difficulty":0.0811567307}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Jimmie is thirsty. It is publicly announced that Douglas does not know whether Jimmie is thirsty. It is publicly announced that Douglas does not know whether Louise is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Charles can now know whether Douglas can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louise","Jimmie","Charles","Douglas"],"index":738,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9751612544,"difficulty":0.0248387456}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Jan can now know that Stephen can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tyree","Erika","Stephen","Jan"],"index":9259,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9733048677,"difficulty":0.0266951323}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sylvia can now know that Laurence can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sylvia","Laurence","Jeniffer"],"index":5202,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859884381,"difficulty":0.0140115619}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to John. John's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether someone picked a red card. It is publicly announced that John picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(1) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Thomas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Thomas"],"index":6233,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9684676528,"difficulty":0.0315323472}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willis is not thirsty. It is publicly announced that Robert does not know whether Dennis is thirsty. It is publicly announced that Evelyn does not know whether Dennis is thirsty. It is publicly announced that Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] Agentc knows whether (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] 0","hypothesis":"Dennis can now know whether Willis can know whether Willis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willis","Robert","Dennis","Evelyn"],"index":332,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8948715329,"difficulty":0.1051284671}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joe can now know whether Patricia can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Joe","Mollie"],"index":1960,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9791275859,"difficulty":0.0208724141}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Earl. Earl's card is shown to Gail. Earl's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gail can now know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Earl","Gail","Joseph"],"index":3709,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6803585887,"difficulty":1.6803585887}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Amanda. Eric's card is shown to Amanda. Eric's card is shown to Eva. Amanda's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Amanda does not know whether Amanda picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows 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:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Eva can now know whether Eric can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Eva","Eric"],"index":2123,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9754256606,"difficulty":0.0245743394}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Nicole. Nicole's card is shown to Victoria. Nicole's card is shown to Larry. Kyle's card is shown to Larry. Nicole's card is shown to Kyle. Victoria's card is shown to Kyle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicole can now know whether Kyle can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicole","Victoria","Larry","Kyle"],"index":9438,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9753668904,"difficulty":0.0246331096}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Kelly. Kelly's card is shown to Mark. Eric's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kelly can now know whether Eric can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelly","Eric","Mark"],"index":877,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9639177322,"difficulty":0.0360822678}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Barbara can now know that James can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barbara","James"],"index":1408,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9709638357,"difficulty":0.0290361643}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beverly can now know whether Judith can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leroy","Gladys","Judith","Beverly"],"index":1019,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5361438394,"difficulty":0.4638561606}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myrna knows whether or not nobody is thirsty. It is publicly announced that Myrna knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Myrna can now know whether Elizabeth can know whether Elizabeth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Myrna","Elizabeth"],"index":3423,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.875299871,"difficulty":0.124700129}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maryellen knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Maryellen can now know whether Beverly can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Beverly","Maryellen"],"index":4735,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9723947048,"difficulty":0.0276052952}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether Diana's forehead is muddy. It is publicly announced that Diana does not know whether or not everyone's forehead is muddy. It is publicly announced that Diana does not know whether Diana's forehead 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 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentd knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Marcus can now know whether Andrew can know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ramon","Marcus","Diana","Andrew"],"index":6720,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8465875983,"difficulty":0.1534124017}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Cecelia can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Mary","Cecelia","Gary"],"index":8894,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9759386182,"difficulty":0.0240613818}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Carlos can now know that Keith can know that Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carlos","Keith"],"index":118,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9819945693,"difficulty":0.0180054307}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edwin does not know whether Edwin's forehead is muddy. It is publicly announced that Edwin knows whether or not nobody's forehead is muddy. It is publicly announced that Edwin 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) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Edwin can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edwin","Jennifer","Nathan"],"index":5738,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8464477062,"difficulty":1.8464477062}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Allison can now know that Angela is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Allison","Angela","Barbera"],"index":7844,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9805052876,"difficulty":0.0194947124}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Monica can now know whether Edith can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Edith","Monica"],"index":8981,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9705355763,"difficulty":0.0294644237}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paula does not know whether or not everyone's forehead is muddy. It is publicly announced that Russell knows whether someone's forehead is muddy. It is publicly announced that Paula does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Paula can now know that Russell can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paula","Russell"],"index":6856,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8645583987,"difficulty":0.1354416013}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William knows whether or not nobody is thirsty. It is publicly announced that William knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Richard can now know that William can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Richard"],"index":4339,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9767144918,"difficulty":0.0232855082}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura does not know whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jack can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Laura","Jack"],"index":1317,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9788803458,"difficulty":0.0211196542}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruby knows whether Kelly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kelly can now know whether Kelly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Scott","Ruby","Kelly"],"index":5846,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9654788375,"difficulty":0.0345211625}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew does not know whether Allan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Valerie can now know whether Allan can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Allan","Valerie"],"index":1707,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9563814402,"difficulty":0.0436185598}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeff knows whether Cedric's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Cedric can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Jeff","Cedric"],"index":5559,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856774807,"difficulty":0.0143225193}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilyn knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Marilyn can now know that Mary can know that Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marilyn","Mary"],"index":5258,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9765971303,"difficulty":0.0234028697}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vera's card is shown to Guadalupe. Vera's card is shown to Irene. It is publicly announced that someone picked a red card. It is publicly announced that Guadalupe does not know whether Guadalupe picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Guadalupe can now know whether Vera can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Guadalupe","Vera","Irene"],"index":7848,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.976090312,"difficulty":0.023909688}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gretchen's card is shown to Joseph. Joseph's card is shown to Dana. Gretchen's card is shown to Dana. Joseph's card is shown to Gretchen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gretchen can now know that Dana can know that Gretchen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Dana","Gretchen"],"index":8698,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9785041213,"difficulty":0.0214958787}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Jessie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Chad can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessie","Robert","Regina","Chad"],"index":6915,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6034634709,"difficulty":1.6034634709}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew does not know whether Brandi is thirsty. It is publicly announced that Brandi is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! (1|2) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Matthew can now know that Brandi is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Matthew","Brandi"],"index":4959,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9754709005,"difficulty":0.0245290995}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luisa knows whether someone's forehead is muddy. It is publicly announced that Norman knows whether Luisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentb knows whether 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)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Luisa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Luisa","Norman","Thomas"],"index":9033,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9772696495,"difficulty":0.0227303505}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jose can now know that Tanya can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tanya","Amy","Jose","Mellissa"],"index":1515,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9802986979,"difficulty":0.0197013021}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Davis. Davis's card is shown to Nicole. Daniel's card is shown to Nicole. Davis's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Nicole picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Davis can now know whether Daniel can know that Daniel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Davis","Nicole","Daniel"],"index":8931,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6710075736,"difficulty":1.6710075736}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Walter. Gregory's card is shown to Kendra. It is publicly announced that someone picked a red card. It is publicly announced that Walter picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Walter can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Gregory","Janice","Kendra"],"index":7403,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9790670276,"difficulty":0.0209329724}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Ted can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ted","Craig"],"index":1951,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857950211,"difficulty":0.0142049789}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether Patricia's forehead is muddy. It is publicly announced that Sarah knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Sarah can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Robert","Patricia"],"index":5116,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9647163153,"difficulty":0.0352836847}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Annie. Annie's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Annie picked a red card. It is publicly announced that Paul does not know whether or not everyone picked a red card. It is publicly announced that Paul does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Paul can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Annie","Paul"],"index":3946,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6818175316,"difficulty":0.3181824684}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Timmy. Timmy's card is shown to Richard. Richard's card is shown to Susie. Susie's card is shown to Jose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jose can now know that Richard can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timmy","Richard","Susie","Jose"],"index":4540,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9773853421,"difficulty":0.0226146579}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Garrett can now know whether Georgia can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Georgia","Garrett","Danielle"],"index":645,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9787839055,"difficulty":0.0212160945}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Linnie can now know whether Richelle can know that Sanford's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linnie","Sanford","Richelle"],"index":9359,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.943080008,"difficulty":0.056919992}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janis's card is shown to Joseph. Ursula's card is shown to Joseph. Joseph's card is shown to Janis. Joseph's card is shown to Ursula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ursula can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Janis","Ursula"],"index":3011,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9778580666,"difficulty":0.0221419334}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Pablo can now know that Joe can know that Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Pablo","Margaret","John"],"index":2401,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9602053165,"difficulty":1.9602053165}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Delma. Delma's card is shown to Cheryl. It is publicly announced that someone picked a red card. It is publicly announced that Cheryl does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows 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":"Delma can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Delma","Cheryl"],"index":1057,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7011461854,"difficulty":1.7011461854}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Phyllis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Phyllis can now know that Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Phyllis","Maria","Timothy"],"index":4228,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9794837236,"difficulty":0.0205162764}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aaron does not know whether Edward is thirsty. It is publicly announced that Aaron is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] 0","hypothesis":"Wayne can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edward","Wayne","Aaron"],"index":5075,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9095517993,"difficulty":0.0904482007}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Barry can now know that Jerry can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barry","Jerry"],"index":9102,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9821889997,"difficulty":0.0178110003}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antonio does not know whether Shannon is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Dane can now know that Shannon can know that Dane is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Antonio","Shannon","Dane"],"index":906,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9745800495,"difficulty":0.0254199505}
-{"premise":"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 Luke knows whether Joseph's forehead is muddy. It is publicly announced that Luke knows whether Dean's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Dean can now know whether Luke's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dean","Luke","Joseph"],"index":3943,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8795545101,"difficulty":0.1204454899}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"James can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","James","Brittany","John"],"index":2527,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858132005,"difficulty":0.0141867995}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Beatrice can now know whether Jean can know whether Beatrice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Willie","Beatrice","Jean"],"index":8144,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9706798196,"difficulty":0.0293201804}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to James. James's card is shown to Krista. Betty's card is shown to Krista. Betty's card is shown to Floyd. James's card is shown to Betty. Floyd's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card. It is publicly announced that Krista knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know that Betty picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Krista","Floyd","Betty"],"index":135,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9669473767,"difficulty":0.0330526233}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tijuana does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Tijuana can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tijuana","Robin"],"index":9148,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9587773085,"difficulty":0.0412226915}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nadine knows whether Nadine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Melba can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Heidi","Melba","Johnnie","Nadine"],"index":8112,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9770973921,"difficulty":0.0229026079}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Constance knows whether Gino's forehead is muddy. It is publicly announced that Constance'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 3) ] [ ! ~(2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Constance can now know whether Constance's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Constance","Gino"],"index":5031,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9097192883,"difficulty":0.0902807117}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie does not know whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Willie can now know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Willie","Marie","Dorothy"],"index":2894,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9570143819,"difficulty":0.0429856181}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] Agentb 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))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"James can now know that Edward can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","James","Samuel","Edward"],"index":7883,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9735065699,"difficulty":0.0264934301}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey does not know whether Jeffrey's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Scott can now know that Jeffrey can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kelly","Jeffrey","Scott","Robert"],"index":4433,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9705722332,"difficulty":0.0294277668}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvette does not know whether Yvette's forehead is muddy. It is publicly announced that Bret does not know whether Bret's forehead is muddy. It is publicly announced that Yvette'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 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Thomas can now know that Yvette's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bret","Yvette","Thomas"],"index":7024,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.977407515,"difficulty":0.022592485}
-{"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 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":"Ralph can now know that Tracy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Louis","Ralph","Tracy"],"index":809,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9825748801,"difficulty":0.0174251199}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Daniel. Daniel's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Daniel can now know whether Anthony can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daniel","Anthony"],"index":2338,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9763204455,"difficulty":0.0236795545}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gayle does not know whether or not everyone's forehead is muddy. It is publicly announced that Gayle does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (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":"Gayle can now know whether John can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Gayle"],"index":6849,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9328923225,"difficulty":1.9328923225}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Earnestine. Earnestine's card is shown to Richard. Donald's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Earnestine","Donald","Richard"],"index":2671,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6548560858,"difficulty":1.6548560858}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether or not everyone is thirsty. It is publicly announced that Jean does not know whether Anna is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Margaret can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anna","Margaret","Jean"],"index":7186,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9652696252,"difficulty":0.0347303748}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Russell's card is shown to Jose. Jose's card is shown to Roy. Russell's card is shown to Roy. Jose's card is shown to Russell. Roy's card is shown to Russell. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Russell can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jose","Roy","Russell"],"index":8713,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9784069657,"difficulty":0.0215930343}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zelma's card is shown to Michael. Michael's card is shown to Robert. Michael's card is shown to Christine. Michael's card is shown to Zelma. Robert's card is shown to Zelma. It is publicly announced that someone picked a red card. It is publicly announced that Christine does not know whether Christine picked a red card. It is publicly announced that Robert knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Zelma can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Robert","Christine","Zelma"],"index":5357,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9661003947,"difficulty":0.0338996053}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gilbert does not know whether Gilbert's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Gilbert'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 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Gilbert can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Gilbert","Patricia"],"index":7647,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9726170301,"difficulty":0.0273829699}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elva is not thirsty. It is publicly announced that Elva is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Andrew can now know whether Elva can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phillip","Elva","Andrew"],"index":840,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9575009346,"difficulty":0.0424990654}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Rebecca knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Destiny can now know that Doris can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doris","Rebecca","Thomas","Destiny"],"index":5657,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9787403941,"difficulty":0.0212596059}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Marla. Marla's card is shown to Carl. Edward's card is shown to James. Marla's card is shown to Edward. Carl's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Marla does not know whether James picked a red card. It is publicly announced that Marla does not know whether Carl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Marla can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marla","Carl","James","Edward"],"index":777,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9735706449,"difficulty":0.0264293551}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether Sarah's forehead is muddy. It is publicly announced that Maria knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Sarah can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","David","Sarah"],"index":4670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.963927269,"difficulty":0.036072731}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luanne knows whether Ralph's forehead is muddy. It is publicly announced that Ralph does not know whether or not everyone's forehead is muddy. It is publicly announced that Ralph does not know whether Ralph's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agenta knows that (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) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jake can now know that Lidia can know whether Lidia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jake","Lidia","Ralph","Luanne"],"index":5439,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8913092613,"difficulty":0.1086907387}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Toni knows whether Rosetta's forehead is muddy. It is publicly announced that Toni's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Toni can now know that Rosetta can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Verna","Toni","Rosetta"],"index":6158,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9782488346,"difficulty":0.0217511654}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynette's card is shown to Mavis. Mavis's card is shown to Lynette. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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":"Lynette can now know that Mavis can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mavis","Lynette"],"index":7947,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9741942286,"difficulty":0.0258057714}
-{"premise":"There are three 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.","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)","n_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":"William can now know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Marvin","Melvin"],"index":887,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8655882478,"difficulty":1.8655882478}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jeanne can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Jennifer","Jeanne","Mary"],"index":2226,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9748927355,"difficulty":0.0251072645}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heather can now know that Jesse is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stacey","Heather","Jesse","Sandra"],"index":4292,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9802273512,"difficulty":0.0197726488}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether Elizabeth's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Robin can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robin","Elizabeth"],"index":4673,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9786196351,"difficulty":0.0213803649}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Ricky can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Carol","Elizabeth","Ricky"],"index":8930,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9662284255,"difficulty":0.0337715745}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Kathleen is thirsty. It is publicly announced that Kathleen does not know whether or not everyone is thirsty. It is publicly announced that Kathleen does not know whether Brian is thirsty. It is publicly announced that Brian is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] Agentd knows that (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] 0","hypothesis":"Brian can now know that James can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","James","Kathleen","Brian"],"index":3674,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9552240968,"difficulty":0.0447759032}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luz does not know whether Nathan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Nathan can now know whether Duane can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Luz","Nathan","Kimberly","Duane"],"index":6114,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8603712916,"difficulty":0.1396287084}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tracey can now know whether James can know whether Jim's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Tracey","Jim","Ellen"],"index":6880,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9455927014,"difficulty":0.0544072986}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl does not know whether Cheryl's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that Elizabeth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"William can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","William","Cheryl"],"index":7434,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9532411695,"difficulty":0.0467588305}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Brett is thirsty. It is publicly announced that Lawrence does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Erma can now know whether Lawrence can know that Lawrence is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Erma","Lawrence","Brett"],"index":5210,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5064483285,"difficulty":1.5064483285}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rebecca does not know whether Delores is thirsty. It is publicly announced that Patricia does not know whether Delores is thirsty. It is publicly announced that Patricia does not know whether Maria is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Delores can now know whether Rebecca can know whether Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Delores","Rebecca","Patricia"],"index":2307,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8742634654,"difficulty":0.1257365346}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether Mildred is thirsty. It is publicly announced that Elizabeth knows whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mildred can now know whether Elizabeth can know whether Mildred is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mildred","Elizabeth"],"index":8461,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8831844926,"difficulty":0.1168155074}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Molly. Ruby's card is shown to Molly. Molly's card is shown to Douglas. Ruby's card is shown to Douglas. Molly's card is shown to Ruby. Douglas's card is shown to Ruby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ruby can now know whether Ruby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Molly","Douglas","Ruby"],"index":6485,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6659275889,"difficulty":1.6659275889}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Troy can now know that Audrey can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shalon","Troy","Jason","Audrey"],"index":9400,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9599705935,"difficulty":0.0400294065}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peggy knows whether Peggy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Wm can now know that Cedric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cedric","Carolyn","Wm","Peggy"],"index":123,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859418273,"difficulty":0.0140581727}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sean's card is shown to Candace. Candace's card is shown to Sean. It is publicly announced that someone picked a red card. It is publicly announced that Sean knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows 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":"Candace can now know whether Candace picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Candace","Sean"],"index":7529,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6314959526,"difficulty":0.3685040474}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Glenn. Glenn's card is shown to Betty. Richard's card is shown to Betty. Betty's card is shown to Richard. Kevin's card is shown to Richard. Betty's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Glenn","Betty","Richard","Kevin"],"index":7263,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9676437378,"difficulty":0.0323562622}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Earl can now know that Margaret is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earl","Jimmy","Melody","Margaret"],"index":7259,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.979528904,"difficulty":0.020471096}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Mary. Mary's card is shown to Neal. Susan's card is shown to Neal. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Susan can now know whether Mary can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Susan","Neal"],"index":9181,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9762217402,"difficulty":0.0237782598}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Burt can now know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Burt","Dorothy"],"index":4529,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.986418426,"difficulty":0.013581574}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nickolas does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Philip can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bobby","Nickolas","Philip"],"index":5297,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9774773717,"difficulty":0.0225226283}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tommie does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Luz can now know that John can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Luz","Leona","John","Tommie"],"index":8245,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9762400389,"difficulty":0.0237599611}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether Cecilia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Cecilia can now know that Rita can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cecilia","Rita","Jessica","Daniel"],"index":2916,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9778240919,"difficulty":0.0221759081}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Michael. Michael's card is shown to Joseph. Daniel's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that Joseph can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Daniel","Joseph","John"],"index":7395,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9787741303,"difficulty":0.0212258697}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Daniel can now know that Rudy can know that Rudy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","John","Rudy"],"index":2112,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9764208198,"difficulty":0.0235791802}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether Vincent's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Brian can now know that Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Roscoe","Doris","Vincent"],"index":5371,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9816323519,"difficulty":0.0183676481}
-{"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 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":"Cynthia can now know whether William can know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ahmad","Cynthia","Delbert","William"],"index":7258,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9358651638,"difficulty":0.0641348362}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Kari can now know that Maria can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kari","Maria"],"index":6494,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9818615913,"difficulty":0.0181384087}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that Dorothy can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Erich","Karen","Maria"],"index":1642,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.6465838552,"difficulty":0.3534161448}
-{"premise":"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 Miriam's forehead is muddy. It is publicly announced that Miriam does not know whether or not everyone's forehead is muddy. It is publicly announced that Miriam does not know whether Miriam's forehead 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 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Cathy can now know that Fleta can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fleta","Cathy","Miriam","Mary"],"index":3269,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9387502074,"difficulty":1.9387502074}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anibal's card is shown to Virginia. Virginia's card is shown to Eric. Virginia's card is shown to Anibal. Eric's card is shown to Anibal. It is publicly announced that someone picked a red card. It is publicly announced that Eric picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Virginia can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Virginia","Eric","Anibal"],"index":4669,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6902305484,"difficulty":0.3097694516}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dylan's card is shown to Stacy. Stacy's card is shown to Demarcus. Stacy's card is shown to Michelle. Dylan's card is shown to Michelle. Stacy's card is shown to Dylan. Demarcus's card is shown to Dylan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stacy can now know whether Demarcus can know whether Demarcus picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stacy","Demarcus","Michelle","Dylan"],"index":5669,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8916583061,"difficulty":0.1083416939}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Todd can now know that Maisie can know that Todd's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sean","Maisie","Todd","Wayne"],"index":8674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.986523807,"difficulty":0.013476193}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman knows whether Norman's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Brian can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josephine","Terry","Brian","Norman"],"index":5315,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9771476984,"difficulty":0.0228523016}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"George can now know that Anthony can know that Anthony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","George","Anthony"],"index":4879,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9764530063,"difficulty":0.0235469937}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Arthur can now know whether Teresa can know that Arthur is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arthur","Teresa"],"index":7525,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5979191065,"difficulty":1.5979191065}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Debra can now know whether Ethel can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Debra","Joshua","Ethel"],"index":7738,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8718217015,"difficulty":0.1281782985}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest knows whether Ted's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Ted can now know that Ted's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sherry","Ernest","Felton","Ted"],"index":3336,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9814389348,"difficulty":0.0185610652}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa knows whether Lisa is thirsty. It is publicly announced that Cynthia does not know whether Robert is thirsty. It is publicly announced that Lisa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Robert can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Lisa","Cynthia","Robert"],"index":6322,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9774215221,"difficulty":0.0225784779}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Gregory. George's card is shown to Gregory. Gregory's card is shown to Beulah. George's card is shown to Beulah. Gregory's card is shown to Raymond. Gregory's card is shown to George. Raymond's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that George does not know whether George picked a red card. It is publicly announced that Gregory does not know whether Beulah picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gregory can now know that George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Beulah","Raymond","George"],"index":3515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9741374254,"difficulty":0.0258625746}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pedro's card is shown to Sabrina. Pedro's card is shown to Freddie. Sabrina's card is shown to Pedro. Freddie's card is shown to Pedro. It is publicly announced that someone picked a red card. It is publicly announced that Freddie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Pedro can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sabrina","Freddie","Pedro"],"index":902,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.693783164,"difficulty":1.693783164}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Nathan can now know that Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Nathan","Craig"],"index":3878,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9861057997,"difficulty":0.0138942003}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Bryan can now know whether David can know that Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bryan","David"],"index":4270,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9307646751,"difficulty":0.0692353249}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"David can now know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Jerri","Deborah","Jennifer"],"index":1992,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6102164984,"difficulty":1.6102164984}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Susan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Jessie","Delores"],"index":8386,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9826840758,"difficulty":0.0173159242}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amy can now know whether James can know whether George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","James","Amy","George"],"index":193,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9720992446,"difficulty":0.0279007554}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Dana can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dana","Teri"],"index":572,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9852639437,"difficulty":0.0147360563}
-{"premise":"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 does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Thomas can now know that Danielle can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Joshua","Danielle","Kenneth"],"index":336,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9714289904,"difficulty":0.0285710096}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mathew can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sharon","Mathew","Stephanie","Rene"],"index":7462,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9782508612,"difficulty":0.0217491388}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 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":"Melvin can now know whether Sonia can know whether Sonia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melvin","Sonia","Stacy","Carmen"],"index":7569,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9410994053,"difficulty":1.9410994053}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Willie can now know that Vincent can know that Margie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vincent","Willie","Margie","Todd"],"index":4282,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858571291,"difficulty":0.0141428709}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know whether Kimberly can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Kimberly","Jewel"],"index":2997,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9451358318,"difficulty":0.0548641682}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Felix can now know that Carol can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carol","Felix"],"index":1229,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9795635343,"difficulty":1.9795635343}
-{"premise":"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 knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"David can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","David"],"index":6734,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7377693057,"difficulty":0.2622306943}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tonya can now know whether Pauline can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pauline","Tonya","Erica"],"index":1311,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9699932337,"difficulty":0.0300067663}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know whether Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tatiana","Linda","Steven","Sharyl"],"index":6287,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9579974413,"difficulty":0.0420025587}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myrtis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Josie can now know that Myrtis can know whether Brian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Myrtis","Brian","Josie","Abbie"],"index":3916,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5358308554,"difficulty":0.4641691446}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugenio's card is shown to Kevin. Eugenio's card is shown to Stefani. Stefani's card is shown to Eugenio. Kevin's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stefani can now know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Stefani","Eugenio","Joseph"],"index":3002,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6544311643,"difficulty":1.6544311643}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eugene does not know whether Joan is thirsty. It is publicly announced that Joan does not know whether or not everyone is thirsty. It is publicly announced that Joan does not know whether Eugene is thirsty. It is publicly announced that Eugene is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] Agenta knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] 0","hypothesis":"Rachel can now know that Mary can know that Rachel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachel","Mary","Joan","Eugene"],"index":7607,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.95639503,"difficulty":0.04360497}
-{"premise":"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 or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"George can now know that Patrick can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Dianne","Will","Patrick"],"index":371,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9743450284,"difficulty":0.0256549716}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tad knows whether Marshall's forehead is muddy. It is publicly announced that Marshall knows whether Marshall's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Marshall can now know whether Marshall's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tad","Marshall"],"index":7702,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.965519011,"difficulty":0.034480989}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Chet. Chet's card is shown to Jack. It is publicly announced that someone picked a red card. It is publicly announced that Chet does not know whether or not everyone picked a red card. It is publicly announced that Chet knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Jack can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Chet","Jack"],"index":4625,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8883801103,"difficulty":0.1116198897}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clara's card is shown to Bret. Bret's card is shown to Billy. Billy's card is shown to Clara. It is publicly announced that someone picked a red card. It is publicly announced that Goldie does not know whether Bret picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Goldie can now know that Bret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bret","Billy","Goldie","Clara"],"index":2854,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9759693742,"difficulty":0.0240306258}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura does not know whether William is thirsty. It is publicly announced that William is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] 0","hypothesis":"William can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["William","Laura"],"index":2016,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9702076316,"difficulty":0.0297923684}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that May knows whether May's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Henry can now know that May can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Henry","May"],"index":7491,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9854088426,"difficulty":0.0145911574}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gloria can now know whether Lourdes can know that Lourdes's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lourdes","Gloria","Dwayne","Shirley"],"index":582,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6804807186,"difficulty":1.6804807186}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to James. Milton's card is shown to Ruby. Ruby's card is shown to Milton. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Milton can now know whether James can know that Ruby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Ruby","Milton","Brian"],"index":2174,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6760907173,"difficulty":0.3239092827}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott knows whether Scott is thirsty. It is publicly announced that Mozell does not know whether Etta is thirsty. It is publicly announced that Scott is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Scott can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joe","Scott","Mozell","Etta"],"index":4094,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9730282426,"difficulty":0.0269717574}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Benjamin can now know that Josephine can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Josephine","Benjamin","Carlos"],"index":2968,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9798250794,"difficulty":0.0201749206}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Daniel can now know whether Adrienne can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daniel","Adrienne"],"index":4056,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.937680006,"difficulty":0.062319994}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Zachery knows whether Jeannine's forehead is muddy. It is publicly announced that Zachery does not know whether Zachery's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jeannine can now know that Jeannine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Zachery","Jeannine","Carmen"],"index":3308,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9743409753,"difficulty":0.0256590247}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edith's card is shown to Jack. Jack's card is shown to Edith. It is publicly announced that someone picked a red card. It is publicly announced that Edith does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Jack can now know that Edith can know whether Jack picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jack","Edith"],"index":1675,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6422840953,"difficulty":0.3577159047}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sierra knows whether Billy's forehead is muddy. It is publicly announced that Sierra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Sierra can now know that Mable can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mable","Sierra","Billy"],"index":4445,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9814887643,"difficulty":0.0185112357}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Danny knows whether Danny is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Doris can now know that Danny can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Doris","Danny"],"index":168,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9790599346,"difficulty":0.0209400654}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Diane can now know that April's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diane","Kevin","Herbert","April"],"index":7061,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860876203,"difficulty":0.0139123797}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vanessa's card is shown to Nicholas. Harold's card is shown to Nicholas. Nicholas's card is shown to Harold. Nicholas's card is shown to Kathleen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicholas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nicholas","Vanessa","Harold","Kathleen"],"index":7100,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9678243399,"difficulty":0.0321756601}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to John. John's card is shown to Scott. Melissa's card is shown to Scott. Scott's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Scott","Melissa"],"index":6725,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9784442782,"difficulty":0.0215557218}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Ellen can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ellen","Gabriela","Lisa"],"index":8039,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9779274464,"difficulty":0.0220725536}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Debra is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Michael can now know whether Debra can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Roland","Debra","Laura"],"index":1495,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9088516235,"difficulty":0.0911483765}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deanna can now know that Deanna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","Gladys","Deanna","Elmer"],"index":58,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9826450348,"difficulty":0.0173549652}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"David can now know that Alan can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alan","David","Patricia","John"],"index":6747,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856186509,"difficulty":0.0143813491}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Neville is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Joseph can now know that Seth can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Seth","Joseph","Marvin","Neville"],"index":4889,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9767002463,"difficulty":0.0232997537}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cynthia can now know whether Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cynthia","Kathleen","Douglas"],"index":7220,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9607622027,"difficulty":0.0392377973}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberley can now know that Corinne can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bertha","Celia","Kimberley","Corinne"],"index":3693,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9824359417,"difficulty":0.0175640583}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angel knows whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 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 4) ] 0","hypothesis":"Jennifer can now know whether Angel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Angel","Rafael","Deana","Jennifer"],"index":4743,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9072265029,"difficulty":0.0927734971}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jasmine knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Patrick can now know that Walter is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","Jasmine","Walter","Bobby"],"index":8015,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9673557281,"difficulty":0.0326442719}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Sarah's forehead is muddy. It is publicly announced that Sarah knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"James can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Sarah","Misty"],"index":5660,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9786256552,"difficulty":0.0213743448}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason does not know whether or not everyone is thirsty. It is publicly announced that Tracy knows whether Tracy is thirsty. It is publicly announced that Bernice does not know whether Tracy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jason can now know whether Tracy can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bernice","Jason","Tracy","Anthony"],"index":4053,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9742990732,"difficulty":0.0257009268}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Homer does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether 1)","n_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":"Homer can now know whether Ross can know whether Homer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Homer","Kate","Ross"],"index":182,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9306203127,"difficulty":0.0693796873}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Karl. Brian's card is shown to Brett. Brett's card is shown to Brian. Brett's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Brett does not know whether Scott picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Karl can now know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karl","Brett","Brian","Scott"],"index":8971,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7456307411,"difficulty":1.7456307411}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Richard. Richard's card is shown to Catherine. Peter's card is shown to Catherine. Peter's card is shown to Micheal. Richard's card is shown to Peter. Micheal's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Richard picked a red card. It is publicly announced that Catherine knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 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:4 Agentb:1,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Micheal can now know that Catherine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Catherine","Micheal","Peter"],"index":1392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9679203033,"difficulty":0.0320796967}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fern does not know whether Joyce is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Fern can now know whether Eva can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Fern","Eva","Joyce"],"index":3310,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9741361737,"difficulty":0.0258638263}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kyle can now know whether Daniel can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kyle","Daniel"],"index":7499,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9792979956,"difficulty":0.0207020044}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jose can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeri","Rose","Jennifer","Jose"],"index":6253,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.799651742,"difficulty":0.200348258}
-{"premise":"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 Jennifer's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 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)) ] [ ! ~(1) ] 0","hypothesis":"Tony can now know that Jennifer can know that Tony's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Tony"],"index":7450,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9808751345,"difficulty":1.9808751345}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Stephanie can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerald","Stephanie","Caleb","Lily"],"index":2162,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9768262506,"difficulty":0.0231737494}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Sue. Andrew's card is shown to Sue. Sue's card is shown to Michael. Sue's card is shown to Andrew. Michael's card is shown to Andrew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Andrew can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sue","Michael","Andrew"],"index":705,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9781945348,"difficulty":0.0218054652}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 1)","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":"Dorothy can now know whether Kenneth can know whether Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Kenneth"],"index":6328,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9494060278,"difficulty":0.0505939722}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristina knows whether Robin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (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:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Robin can now know that Angelo can know that Kristina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robin","Kristina","Charlie","Angelo"],"index":7428,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858093858,"difficulty":0.0141906142}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Ruth. Jesse's card is shown to Ruth. Ruth's card is shown to Joy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Joy","Mary","Jesse"],"index":7724,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9199562073,"difficulty":0.0800437927}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louise does not know whether Martha is thirsty. It is publicly announced that Martha is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Rosario does not know whether Louise is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Martha can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martha","Jennifer","Rosario","Louise"],"index":5868,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5456041098,"difficulty":1.5456041098}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nova can now know whether Dale can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dale","Patricia","Nova","Charles"],"index":6169,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9728434086,"difficulty":0.0271565914}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barb knows whether Barb's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Hilda can now know that Virginia can know whether Virginia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Hilda","Barb","Virginia"],"index":2905,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9623642564,"difficulty":0.0376357436}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antonio's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Josephine can now know that Antonio can know whether Antonio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Antonio","Josephine","Joshua"],"index":2811,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9609283805,"difficulty":0.0390716195}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Andrew. Andrew's card is shown to Angela. Daniel's card is shown to Angela. Angela's card is shown to Daniel. James's card is shown to Daniel. Angela's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Angela","Daniel","James"],"index":1147,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9776158929,"difficulty":0.0223841071}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Steven. Sonny's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether Sonny picked a red card. It is publicly announced that Mary does not know whether Steven picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Steven can now know that Mary can know whether Sonny picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Mary","Sonny"],"index":8660,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8055371046,"difficulty":0.1944628954}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Gerardo. Gerardo's card is shown to Barbara. Barbara's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Ivy does not know whether Gerardo picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Gerardo can now know whether Ivy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gerardo","Barbara","Ivy","Michael"],"index":5294,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7295367122,"difficulty":1.7295367122}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Aaron. Jaime's card is shown to Aaron. Laura's card is shown to Aaron. Jaime's card is shown to Ashley. Laura's card is shown to Ashley. Aaron's card is shown to Jaime. Laura's card is shown to Jaime. Ashley's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Jaime does not know whether Ashley picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jaime can now know whether Laura can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aaron","Ashley","Jaime","Laura"],"index":4528,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9432351589,"difficulty":0.0567648411}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Jessica can now know whether Lawrence can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Lindsay","Lawrence"],"index":1842,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9736055732,"difficulty":0.0263944268}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clara 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 Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Clara can now know that Patrica can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Donna","Patrica","Clara"],"index":8588,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8587706089,"difficulty":0.1412293911}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lizzie's card is shown to Charles. Martha's card is shown to Charles. Charles's card is shown to Lizzie. Martha's card is shown to Lizzie. Charles's card is shown to Martha. It is publicly announced that someone picked a red card. It is publicly announced that Martha does not know whether Lizzie picked a red card. It is publicly announced that Martha knows whether Charles picked a red card. It is publicly announced that Charles does not know whether Charles picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (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 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Charles can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Lizzie","Martha"],"index":3362,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8953344822,"difficulty":0.1046655178}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Regina can now know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Steven","Regina"],"index":6439,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9765120745,"difficulty":0.0234879255}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Robert is thirsty. It is publicly announced that Robert does not know whether Elizabeth is thirsty. It is publicly announced that Michael is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Elizabeth can now know that Michael can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","Michael","Juana","Robert"],"index":9614,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9739684463,"difficulty":0.0260315537}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joshua can now know whether Joshua's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joshua","David","Nancy","Victoria"],"index":783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9557955265,"difficulty":0.0442044735}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Tamatha. Jana's card is shown to Darrel. Tamatha's card is shown to Jana. Darrel's card is shown to Jana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tamatha can now know whether Darrel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tamatha","Darrel","Ronald","Jana"],"index":3628,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.660443604,"difficulty":1.660443604}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Buddy can now know that Patrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Buddy","Richard","Patrick"],"index":6995,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860084653,"difficulty":0.0139915347}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lewis's card is shown to Thomas. Thomas's card is shown to Lewis. It is publicly announced that someone picked a red card. It is publicly announced that Thomas does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that 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":"Thomas can now know that Lewis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thomas","Lewis"],"index":4627,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9607305527,"difficulty":1.9607305527}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether Rebecca's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 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) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Larry can now know that Rita can know that Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rebecca","Angela","Larry","Rita"],"index":5565,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9809113741,"difficulty":0.0190886259}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Peggy. Anthony's card is shown to Stacey. Kathy's card is shown to Stacey. Stacey's card is shown to Kathy. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Anthony can now know whether Stacey can know whether Stacey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Peggy","Stacey","Kathy"],"index":9502,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8708259463,"difficulty":0.1291740537}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet does not know whether Janet's forehead is muddy. It is publicly announced that Sarah 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) ] [ ! (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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jennifer can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janet","Sarah","Jennifer"],"index":6406,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9633153677,"difficulty":0.0366846323}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Carl can now know whether Mary can know whether Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Reginald","Carl","Mary","Helen"],"index":5245,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9696587324,"difficulty":0.0303412676}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristie does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Patricia can now know that Kristie can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kristie","Patricia"],"index":1208,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9770794511,"difficulty":0.0229205489}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leroy's card is shown to Charlie. Fred's card is shown to Nicholas. Nicholas's card is shown to Fred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlie can now know that Nicholas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlie","Nicholas","Leroy","Fred"],"index":4744,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9787909985,"difficulty":0.0212090015}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Juan. Juan's card is shown to Daniel. Brenda's card is shown to Daniel. Daniel's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juan can now know that Daniel can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juan","Daniel","David","Brenda"],"index":2634,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9736507535,"difficulty":0.0263492465}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Mildred can now know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Linda","Mildred","Barbara"],"index":1247,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860571623,"difficulty":0.0139428377}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Curtis knows whether Donald's forehead is muddy. It is publicly announced that Philip's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] Agentb knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Curtis can now know whether Philip can know that Curtis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Curtis","Donald","Philip"],"index":6293,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8656349778,"difficulty":1.8656349778}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alberto knows whether Jacinta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Jacinta can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Denise","Alberto","Ashly","Jacinta"],"index":7051,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.978181541,"difficulty":0.021818459}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lawrence can now know that Marion can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marion","Howard","Lawrence"],"index":8202,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9803025723,"difficulty":0.0196974277}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Marian. Marian's card is shown to Gregory. Michael's card is shown to Gregory. Marian's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Gregory picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know whether Gregory can know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marian","Gregory","Michael"],"index":1676,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6749658585,"difficulty":0.3250341415}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley knows whether Stanley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Raymond can now know that Stanley can know that Glenn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Stanley","Raymond","Glenn"],"index":5264,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858621359,"difficulty":0.0141378641}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bethany can now know that Mavis can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mavis","Haley","Bethany","Titus"],"index":4266,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860509038,"difficulty":0.0139490962}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 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":"Sheila can now know that Juliet can know that Sheila's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sheila","Juliet","Ryan"],"index":4364,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9825105071,"difficulty":0.0174894929}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephanie's card is shown to Johanna. Johanna's card is shown to Stephanie. It is publicly announced that someone picked a red card. It is publicly announced that Stephanie does not know whether or not everyone picked a red card. It is publicly announced that Johanna knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Stephanie can now know that Johanna can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Johanna","Stephanie"],"index":7571,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8673589826,"difficulty":0.1326410174}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sybil can now know that Dennis can know that Sybil's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sybil","John","Gladys","Dennis"],"index":3246,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865378141,"difficulty":0.0134621859}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Marisa can now know whether Angelina can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marisa","Angelina"],"index":2071,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9732355475,"difficulty":0.0267644525}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Casey's forehead is muddy.","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":"Janine can now know that Michael can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Casey","Janine","Michael"],"index":6655,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9822618961,"difficulty":0.0177381039}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Rose can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rose","Philip","Evette","Kenneth"],"index":4608,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859669805,"difficulty":0.0140330195}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacy knows whether Christine's forehead is muddy. It is publicly announced that Christine does not know whether or not everyone's forehead is muddy. It is publicly announced that Christine does not know whether Christine's forehead 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 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sandi can now know that Stacy can know that Ramon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandi","Ramon","Christine","Stacy"],"index":6762,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9429196119,"difficulty":1.9429196119}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know whether Janet can know that Kay is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janet","Margaret","Tracy","Kay"],"index":1373,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5327510834,"difficulty":1.5327510834}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Raymond can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sonya","Louise","Ruth","Raymond"],"index":6323,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859198332,"difficulty":0.0140801668}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kim knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentc knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"William can now know that Kim can know whether Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Derrick","William","Kim"],"index":731,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9640949965,"difficulty":0.0359050035}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Wanda can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Margarita","Wanda"],"index":8075,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860629439,"difficulty":0.0139370561}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Stephanie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eugene","Barbara","Stephanie"],"index":3389,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9828748703,"difficulty":0.0171251297}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Richard can now know that Rosita can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Rosita"],"index":5301,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9803752303,"difficulty":0.0196247697}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether or not everyone is thirsty. It is publicly announced that Antoinette is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Antoinette can now know whether Mary can know that Arthur is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Arthur","Mary","Antoinette"],"index":4984,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5274925232,"difficulty":1.5274925232}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmelita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_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":"Barry can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barry","Carmelita","Robert"],"index":6448,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.982159555,"difficulty":0.017840445}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara is not thirsty. It is publicly announced that Edward is not thirsty. It is publicly announced that Barbara does not know whether Allison is thirsty. It is publicly announced that Allison knows whether Allison is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Edward can now know whether Barbara can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leslie","Barbara","Edward","Allison"],"index":8654,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9747716784,"difficulty":0.0252283216}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pearl does not know whether Lester is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Lester can now know that Lester is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lester","Pearl","Mary"],"index":802,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9757876396,"difficulty":1.9757876396}
-{"premise":"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 Julie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Julie can now know that Sergio can know that Julie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Julie","Sergio"],"index":2844,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9731696844,"difficulty":0.0268303156}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maurice is thirsty. It is publicly announced that Cindy knows whether someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Deborah does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Cindy can now know that Maurice can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cindy","Deborah","Maurice"],"index":4395,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9493127465,"difficulty":0.0506872535}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Justin can now know that Donna can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marlene","Donna","Justin"],"index":2589,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9785914421,"difficulty":0.0214085579}
-{"premise":"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 knows whether or not nobody's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 2) ] (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))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Edward","Charles"],"index":2688,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9724784493,"difficulty":0.0275215507}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward does not know whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Domingo can now know that Edward can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Domingo","Christopher","Edward"],"index":8317,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9711100459,"difficulty":0.0288899541}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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 Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Matthew","James","Melissa","Robert"],"index":3938,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7170938253,"difficulty":1.7170938253}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicholas does not know whether Mae is thirsty. It is publicly announced that Kieth does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Nicholas can now know that Kieth can know that Mae is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kieth","Nicholas","Mae","Elizabeth"],"index":2533,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9747228622,"difficulty":0.0252771378}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Verna does not know whether Verna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Willie can now know that Verna can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Verna","Willie"],"index":8191,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.977817893,"difficulty":0.022182107}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows 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":"Bonita can now know that Richard can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Alicia","Richard","Bonita"],"index":7595,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8255543709,"difficulty":0.1744456291}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether Ida's forehead is muddy. It is publicly announced that George knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jonathan can now know that Jonathan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Jonathan","Ida"],"index":9037,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9632414579,"difficulty":0.0367585421}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathan's card is shown to Latoria. Nathan's card is shown to Judith. Latoria's card is shown to Nathan. Latoria's card is shown to Rudolph. Judith's card is shown to Rudolph. It is publicly announced that someone picked a red card. It is publicly announced that Rudolph does not know whether Nathan picked a red card. It is publicly announced that Nathan does not know whether Nathan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nathan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Latoria","Judith","Nathan","Rudolph"],"index":4134,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8948922157,"difficulty":0.1051077843}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Douglas can now know whether Meta can know whether Juan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Meta","Juan","Douglas"],"index":7109,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9721713662,"difficulty":0.0278286338}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Timothy. Timothy's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Lisa knows whether Timothy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Timothy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Timothy","Lisa"],"index":8111,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9776458144,"difficulty":0.0223541856}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fred's card is shown to Donna. Donna's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Donna knows whether someone picked a red card. It is publicly announced that Donna knows whether someone picked a red card. It is publicly announced that Donna does not know whether Donna picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 1) ] 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)) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Donna can now know whether Fred can know whether Donna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donna","Fred"],"index":7696,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9154865742,"difficulty":0.0845134258}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peggy does not know whether or not everyone's forehead is muddy. It is publicly announced that Peggy 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) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Peggy"],"index":8238,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9681621194,"difficulty":0.0318378806}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmie's card is shown to Peter. Miguel's card is shown to Peter. Peter's card is shown to Jimmie. Miguel's card is shown to Jimmie. Peter's card is shown to Miguel. It is publicly announced that someone picked a red card. It is publicly announced that Miguel does not know whether Jimmie picked a red card. It is publicly announced that Miguel knows whether Peter picked a red card. It is publicly announced that Peter does not know whether Peter picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jimmie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peter","Jimmie","Miguel"],"index":9197,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9724487066,"difficulty":0.0275512934}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lori can now know whether Patricia can know whether Sara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lori","Sara","Patricia","Margaret"],"index":4052,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.971639514,"difficulty":0.028360486}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony does not know whether Tony's forehead is muddy. It is publicly announced that Willie knows whether Irene's forehead is muddy. It is publicly announced that John's forehead is not muddy. It is publicly announced that Willie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Irene can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tony","Willie","John","Irene"],"index":8805,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5656962991,"difficulty":0.4343037009}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Wallace can now know that Dwayne can know that Wallace's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sherrie","Wallace","Dwayne"],"index":5773,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864943027,"difficulty":0.0135056973}
-{"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 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":"Mary can now know that Alice can know whether Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Brenda","Alice","Patricia"],"index":4592,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8720470667,"difficulty":0.1279529333}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angelia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Laura can now know whether Mike is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Angelia","Kara","Mike"],"index":7962,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5098950267,"difficulty":0.4901049733}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karl does not know whether or not everyone's forehead is muddy. It is publicly announced that Karl does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Karl can now know that Robert can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Karl"],"index":207,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.977789402,"difficulty":0.022210598}
-{"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 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":"Patrick can now know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Kelly","Kenneth"],"index":6491,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8707988262,"difficulty":0.1292011738}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Karen can now know that Ellen can know that Ellen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ellen","Karen","Tomasa"],"index":5440,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.980140388,"difficulty":0.019859612}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ricardo does not know whether Irene is thirsty. It is publicly announced that Irene does not know whether Joe is thirsty. It is publicly announced that Ricardo is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] Agentc knows whether (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Blanche can now know whether Irene can know that Ricardo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Ricardo","Blanche","Irene"],"index":1061,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6719647646,"difficulty":0.3280352354}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Jared. Raymond's card is shown to Reba. Jared's card is shown to Ellen. Reba's card is shown to Ellen. Raymond's card is shown to Ellen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Reba can now know that Jared can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jared","Reba","Raymond","Ellen"],"index":9024,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9776275158,"difficulty":0.0223724842}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Carol. Carol's card is shown to Peter. Antonette's card is shown to Peter. Peter's card is shown to Antonette. Karen's card is shown to Antonette. Peter's card is shown to Karen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Antonette can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Peter","Antonette","Karen"],"index":4128,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9774517417,"difficulty":0.0225482583}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jonathon does not know whether Ben is thirsty. It is publicly announced that Jonathon does not know whether Ben is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Maxine can now know that Ben can know whether Maxine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ben","Maxine","Valerie","Jonathon"],"index":1981,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.605838716,"difficulty":1.605838716}
-{"premise":"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's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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":"Eric can now know that Barbara can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Eric","Roy","Barbara"],"index":7297,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9822773337,"difficulty":0.0177226663}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Lillie. Julie's card is shown to Robert. Ronald's card is shown to Robert. Ronald's card is shown to Julie. Lillie's card is shown to Ronald. Julie's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Ronald does not know whether Robert picked a red card. It is publicly announced that Lillie does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Robert can now know whether Julie can know that Lillie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lillie","Robert","Julie","Ronald"],"index":48,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6653839946,"difficulty":0.3346160054}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Derrick. Derrick's card is shown to Clayton. Derrick's card is shown to Ida. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Paul can now know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Derrick","Paul","Clayton","Ida"],"index":1751,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7036812305,"difficulty":1.7036812305}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jose can now know that Lori can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jose","Ernest","Lori"],"index":6522,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.6335983872,"difficulty":0.3664016128}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Yer can now know that Kenneth can know that Melba is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melba","Kenneth","Yer"],"index":1341,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9800133109,"difficulty":0.0199866891}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Mattie. Ruby's card is shown to Mary. Ruby's card is shown to Justin. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ruby can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruby","Mattie","Mary","Justin"],"index":872,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8886595964,"difficulty":0.1113404036}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cornelius can now know whether Joseph can know whether Allison's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ernest","Joseph","Allison","Cornelius"],"index":5713,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9724165797,"difficulty":0.0275834203}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Keith. Keith's card is shown to Andres. Joseph's card is shown to Andres. Andres's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Andres does not know whether Andres picked a red card. It is publicly announced that Andres knows whether someone picked a red card. It is publicly announced that Keith does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Keith","Andres","Joseph"],"index":2940,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.935199976,"difficulty":1.935199976}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Miguel does not know whether Carmelo is thirsty. It is publicly announced that Jessica is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Miguel can now know whether Carmelo can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Miguel","Carmelo"],"index":8859,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9725774527,"difficulty":0.0274225473}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Olivia does not know whether Steven is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Virginia can now know whether Virginia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Virginia","Daniel","Steven","Olivia"],"index":4767,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5642618537,"difficulty":0.4357381463}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Gloria can now know that Charlie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gloria","Charlie"],"index":233,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9746927023,"difficulty":0.0253072977}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Johnnie can now know whether Herbert can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Johnnie","Herbert"],"index":7342,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9789248705,"difficulty":0.0210751295}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Thelma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Christopher can now know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Christopher","Thelma"],"index":4312,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857960939,"difficulty":0.0142039061}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edgar's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jason can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lloyd","Jason","Edgar"],"index":8024,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.980941236,"difficulty":0.019058764}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcus knows whether Debbie's forehead is muddy. It is publicly announced that Marcus 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) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Debbie can now know whether Marcus's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debbie","Marcus"],"index":9057,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8752979636,"difficulty":0.1247020364}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Debra can now know that Ellis can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debra","William","Ellis"],"index":8156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9850880504,"difficulty":0.0149119496}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danny's card is shown to Lizette. Lizette's card is shown to Brenda. Lizette's card is shown to Danny. Brenda's card is shown to Danny. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lizette can now know whether Danny can know that Lizette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lizette","Brenda","Danny"],"index":5969,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6520918012,"difficulty":1.6520918012}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stanley is not thirsty. It is publicly announced that Stanley knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Martha can now know whether Naomi can know whether Martha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Martha","Stanley","Cynthia","Naomi"],"index":7553,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8718485236,"difficulty":0.1281514764}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alison's card is shown to Theresa. Theresa's card is shown to Samuel. Samuel's card is shown to Alison. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Theresa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Theresa","Samuel","Jane","Alison"],"index":5971,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9789291024,"difficulty":0.0210708976}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darla's card is shown to Stephanie. Stephanie's card is shown to Darla. It is publicly announced that someone picked a red card. It is publicly announced that Darla knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Stephanie can now know that Darla can know that Stephanie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stephanie","Darla"],"index":1528,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.961899817,"difficulty":0.038100183}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Carol can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carol","Barbara","Jessica","Robert"],"index":6853,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8751743436,"difficulty":0.1248256564}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Andrea. Jeffery's card is shown to Andrea. Andrea's card is shown to Jeffery. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know that Andrea can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Andrea","Jeffery"],"index":8767,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7143364549,"difficulty":1.7143364549}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know whether Marvin can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Marvin","Angela","Kenneth"],"index":8912,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9750096798,"difficulty":0.0249903202}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Mary. Mary's card is shown to Todd. It is publicly announced that someone picked a red card. It is publicly announced that Todd picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Todd can now know whether Mary can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Todd"],"index":5613,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9035106897,"difficulty":0.0964893103}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Greta. Dale's card is shown to Howard. Howard's card is shown to Dale. It is publicly announced that someone picked a red card. It is publicly announced that Greta picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Howard can now know that Greta can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Greta","Howard","Dale"],"index":6660,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9092151523,"difficulty":1.9092151523}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Margaret. Gracie's card is shown to John. John's card is shown to Gracie. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether someone picked a red card. It is publicly announced that Gracie does not know whether or not everyone picked a red card. It is publicly announced that Gracie knows whether or not nobody picked a red card. It is publicly announced that Gracie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"John can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","John","Gracie"],"index":6218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9309051633,"difficulty":0.0690948367}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to James. Violet's card is shown to James. Ruth's card is shown to Willie. Ruth's card is shown to Violet. James's card is shown to Ruth. Violet's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Willie does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"James can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Willie","Violet","Ruth"],"index":2235,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8953812122,"difficulty":0.1046187878}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roy does not know whether Angela is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Roy can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Roy","Angela"],"index":6648,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9760756493,"difficulty":0.0239243507}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Matthew can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["June","Barbara","Matthew","Elsie"],"index":1460,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9782831669,"difficulty":0.0217168331}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Sarah. Sarah's card is shown to Donald. Donald's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sarah can now know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Donald","Patricia"],"index":239,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6642483473,"difficulty":1.6642483473}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori knows whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Michelle can now know that Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michelle","Lori"],"index":2787,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9815996289,"difficulty":0.0184003711}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 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":"Bonnie can now know whether Michael can know that Jill's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Jill","Tina","Bonnie"],"index":8003,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7685502768,"difficulty":0.2314497232}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Tina can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Herman","Tina","John"],"index":1929,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853878617,"difficulty":0.0146121383}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Peter is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether Peter can know that Denise is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Peter","Denise"],"index":7198,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7184482813,"difficulty":0.2815517187}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jill's card is shown to Roger. Roger's card is shown to Jill. It is publicly announced that someone picked a red card. It is publicly announced that Jill knows whether or not nobody picked a red card. It is publicly announced that Roger does not know whether Roger picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jill can now know that Roger can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Roger","Jill"],"index":8253,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7247275114,"difficulty":0.2752724886}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Samuel can now know whether Bobby can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorris","Samuel","Bobby"],"index":5676,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9788013101,"difficulty":0.0211986899}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jerry can now know that Melba can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Jerry","Melba"],"index":9521,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9599631429,"difficulty":0.0400368571}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marilyn does not know whether Howard is thirsty. It is publicly announced that Howard does not know whether June is thirsty. It is publicly announced that Marilyn is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"June can now know that Marilyn can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["June","Marilyn","Lena","Howard"],"index":8645,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9072744846,"difficulty":1.9072744846}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Colleen's card is shown to Elizabeth. Angela's card is shown to Colleen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Colleen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Colleen","Angela"],"index":6195,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9797155857,"difficulty":0.0202844143}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua knows whether Joshua is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Benito can now know that Joshua can know that Benito is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Benito","Joshua"],"index":3577,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9792935252,"difficulty":0.0207064748}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vance's card is shown to Catherine. Kenneth's card is shown to Vance. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Catherine can now know that Vance can know that Catherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Vance","Kenneth","Robert"],"index":2249,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9793992043,"difficulty":0.0206007957}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy. It is publicly announced that Eugene 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 whether (1&2)) ] [ ! (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) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Susan can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Eugene","Susan"],"index":1387,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9775415063,"difficulty":0.0224584937}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to John. John's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that William can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","William"],"index":330,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9761421084,"difficulty":0.0238578916}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Peter can now know that David can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronda","David","Peter"],"index":230,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9774048924,"difficulty":0.0225951076}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know that Roberta can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Rita","Roberta","Stephen"],"index":8344,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.982778728,"difficulty":0.017221272}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dan does not know whether Alan is thirsty. It is publicly announced that Dan is not thirsty. It is publicly announced that Alan knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Alan can now know whether Shannon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dan","Alan","Shannon"],"index":6606,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.533378005,"difficulty":1.533378005}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kevin can now know that Joel can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joel","Kevin","Heather"],"index":7030,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859393835,"difficulty":0.0140606165}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Trevor's card is shown to Tammy. Sabrina's card is shown to Steven. Steven's card is shown to Sabrina. Steven's card is shown to Trevor. It is publicly announced that someone picked a red card. It is publicly announced that Steven does not know whether Trevor picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Steven can now know whether Steven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tammy","Steven","Sabrina","Trevor"],"index":8404,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7483765483,"difficulty":1.7483765483}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Florencio can now know that Shane can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charlie","Shane","Florencio"],"index":3490,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859803915,"difficulty":0.0140196085}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Michael can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Michael","Mary"],"index":1112,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9622686505,"difficulty":0.0377313495}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tyler knows whether or not everyone's forehead is muddy. It is publicly announced that Billie knows whether Billie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Billie can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tyler","Billie"],"index":3167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.972622931,"difficulty":0.027377069}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Kelvin knows whether Kelvin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Kelvin"],"index":537,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9710183144,"difficulty":0.0289816856}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice does not know whether Janice's forehead is muddy. It is publicly announced that Janice knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|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":"Kenneth can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Janice","Kenneth"],"index":6685,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9593801498,"difficulty":0.0406198502}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Margaret. Melvin's card is shown to Abbey. Melvin's card is shown to Doris. Doris's card is shown to Melvin. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Melvin can now know whether Margaret can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Abbey","Doris","Melvin"],"index":4055,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9729539156,"difficulty":0.0270460844}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chasity does not know whether Catherine is thirsty. It is publicly announced that Catherine does not know whether or not everyone is thirsty. It is publicly announced that Catherine does not know whether Chasity is thirsty. It is publicly announced that Chasity is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] Agentc knows that (Agentd knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] 0","hypothesis":"Catherine can now know that Chasity can know whether Ella is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ella","Daryl","Catherine","Chasity"],"index":5324,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5798968673,"difficulty":1.5798968673}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heather can now know whether Donnie can know whether Heather is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","Donnie","Adrian","Lorraine"],"index":6567,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.808445394,"difficulty":0.191554606}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derek's card is shown to Miranda. Derek's card is shown to Julie. David's card is shown to Julie. David's card is shown to Derek. Miranda's card is shown to David. Derek's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that David does not know whether Julie picked a red card. It is publicly announced that Miranda does not know whether Julie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Julie can now know that David can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Miranda","Julie","Derek","David"],"index":3823,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7419080138,"difficulty":1.7419080138}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Yvonne can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clarissa","Ann","Yvonne","Donna"],"index":1891,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9674980044,"difficulty":0.0325019956}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanna's card is shown to Ruth. Ruth's card is shown to Shaun. Megan's card is shown to Shaun. Shaun's card is shown to Megan. Joanna's card is shown to Megan. Shaun's card is shown to Joanna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joanna can now know whether Joanna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Shaun","Megan","Joanna"],"index":5392,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6417099237,"difficulty":1.6417099237}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathan's card is shown to Susan. Nathan's card is shown to Mark. Mark's card is shown to Nathan. It is publicly announced that someone picked a red card. It is publicly announced that Nathan does not know whether Nathan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nathan can now know whether Mark can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Mark","Nathan"],"index":4997,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9751614332,"difficulty":0.0248385668}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rose can now know that Willie can know that Rose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dolores","Rose","George","Willie"],"index":8694,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865119457,"difficulty":0.0134880543}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Linda. Shane's card is shown to Linda. Cynthia's card is shown to Linda. Linda's card is shown to Mary. Shane's card is shown to Mary. Cynthia's card is shown to Mary. Linda's card is shown to Shane. Cynthia's card is shown to Shane. Shane's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Linda picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agentd knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Cynthia can now know that Shane can know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Mary","Shane","Cynthia"],"index":5453,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7606312037,"difficulty":0.2393687963}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lowell does not know whether Emma is thirsty. It is publicly announced that Geraldine does not know whether Nathan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Lowell can now know that Emma can know whether Emma is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geraldine","Lowell","Emma","Nathan"],"index":986,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6843864918,"difficulty":0.3156135082}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jose can now know whether Jean can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Jean","Bradley","Michelle"],"index":653,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8977308273,"difficulty":0.1022691727}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Wanda can now know whether Margaret can know that Brenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Brenda","Wanda","Kristi"],"index":2284,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9402028322,"difficulty":0.0597971678}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jade knows whether Joan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Joan can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jade","Florence","Joan","Alyssa"],"index":1916,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9729748964,"difficulty":0.0270251036}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gregory","Joseph","Martha"],"index":2431,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5648750663,"difficulty":1.5648750663}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tom does not know whether Edward is thirsty. It is publicly announced that Tom does not know whether Edward is thirsty. It is publicly announced that Edward does not know whether Kathi is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Kathi can now know that Edward can know whether Kathi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edward","Kathi","Tom"],"index":3233,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7048069239,"difficulty":1.7048069239}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Lea. Cheryl's card is shown to Margaret. Lea's card is shown to Cheryl. Sara's card is shown to Cheryl. Lea's card is shown to Sara. Cheryl's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lea can now know whether Cheryl can know whether Cheryl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lea","Margaret","Cheryl","Sara"],"index":4747,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8973865509,"difficulty":0.1026134491}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Mary. Mary's card is shown to Leana. Henry's card is shown to Leana. Leana's card is shown to Henry. William's card is shown to Henry. Leana's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Leana picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Leana","Henry","William"],"index":4898,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9772313833,"difficulty":0.0227686167}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelia's card is shown to Edith. Marvin's card is shown to Shelia. It is publicly announced that someone picked a red card. It is publicly announced that Edith does not know whether or not everyone picked a red card. It is publicly announced that Edith knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Marvin can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edith","Marvin","Shelia"],"index":8736,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9771952033,"difficulty":0.0228047967}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maryann's card is shown to Fran. Fran's card is shown to Patricia. Maryann's card is shown to Patricia. Luanne's card is shown to Maryann. Fran's card is shown to Luanne. Patricia's card is shown to Luanne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Luanne can now know that Maryann picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fran","Patricia","Maryann","Luanne"],"index":3457,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9777799845,"difficulty":0.0222200155}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Earl can now know whether Melissa can know that Melissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melissa","Earl"],"index":559,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9511343241,"difficulty":0.0488656759}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Deanna. John's card is shown to Deanna. Deanna's card is shown to Rosa. John's card is shown to Rosa. Rosa's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deanna can now know that John can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Deanna","Rosa","John"],"index":753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9781603217,"difficulty":0.0218396783}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Denise does not know whether Laura is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Laura can now know that Rhonda can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Rhonda","Laura","Denise"],"index":450,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9765555263,"difficulty":0.0234444737}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Antonia. Eula's card is shown to Judy. Jason's card is shown to Judy. Antonia's card is shown to Eula. Eula's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Antonia can now know that Jason can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antonia","Judy","Eula","Jason"],"index":4477,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9657503366,"difficulty":0.0342496634}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether or not everyone is thirsty. It is publicly announced that Jack is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] 0","hypothesis":"Sarah can now know that Eric can know that Sarah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jack","Eric","Sarah"],"index":7320,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9635613561,"difficulty":0.0364386439}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monique's card is shown to Liza. Monique's card is shown to Samuel. Samuel's card is shown to Gerald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Samuel can now know whether Gerald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Liza","Samuel","Monique","Gerald"],"index":6942,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.650251925,"difficulty":1.650251925}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Ryan. Jeffrey's card is shown to Daisy. Ryan's card is shown to Christina. Daisy's card is shown to Christina. Jeffrey's card is shown to Christina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daisy can now know whether Jeffrey can know whether Ryan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ryan","Daisy","Jeffrey","Christina"],"index":354,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8951054811,"difficulty":0.1048945189}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pauline knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Helen can now know that Pauline can know that Pauline's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","Christopher","Pauline"],"index":2200,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9746194482,"difficulty":0.0253805518}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rose knows whether Rose is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Richard can now know whether Rose can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Rose"],"index":8814,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8629583716,"difficulty":0.1370416284}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Theresa can now know whether Robert can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Theresa","Robert"],"index":658,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9787997007,"difficulty":0.0212002993}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerry knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kenneth can now know whether Danny is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danny","Jerry","Jaime","Kenneth"],"index":4459,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5899056196,"difficulty":1.5899056196}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Blanche's forehead is muddy. It is publicly announced that Barbara knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Barbara can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Amy","Blanche"],"index":13,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9770897627,"difficulty":0.0229102373}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kellie does not know whether or not everyone is thirsty. It is publicly announced that Gail does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Gail can now know that Gail is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kellie","Gail","Karyn","John"],"index":4172,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9601374865,"difficulty":0.0398625135}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Amanda can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Amanda"],"index":2463,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860172868,"difficulty":0.0139827132}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ernest can now know whether Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ernest","Walter","Jessie","Jarod"],"index":8553,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9612269998,"difficulty":0.0387730002}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darnell does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Darnell can now know whether James can know that Oscar's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Catherine","James","Darnell","Oscar"],"index":4560,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8294833302,"difficulty":0.1705166698}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows 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":"Richard can now know whether Kevin can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Marlene","Richard","Susan"],"index":880,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9189914465,"difficulty":0.0810085535}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clifton's card is shown to Harold. Harold's card is shown to Clifton. It is publicly announced that someone picked a red card. It is publicly announced that Harold knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb 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":"Clifton can now know whether Harold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harold","Clifton"],"index":1909,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8182938099,"difficulty":0.1817061901}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corey's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Lindsey can now know whether Corey can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Corey","Lindsey"],"index":7217,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9737591743,"difficulty":0.0262408257}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Julie can now know whether Julie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffrey","Gerald","Julie"],"index":327,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8640004396,"difficulty":1.8640004396}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agentb knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Alana can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marlene","Alana"],"index":8889,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857646823,"difficulty":0.0142353177}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bobbie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bobbie","Rosanne","Mark"],"index":6036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7703773975,"difficulty":0.2296226025}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alba knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"George can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["George","Alba"],"index":447,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9777202606,"difficulty":0.0222797394}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether John is thirsty. It is publicly announced that John is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] 0","hypothesis":"Barbara can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Barbara"],"index":1180,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9762455821,"difficulty":0.0237544179}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Keith does not know whether Tommy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lucille can now know whether Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Keith","Mary","Tommy","Lucille"],"index":8030,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5837106705,"difficulty":1.5837106705}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brittny can now know that Nicole can know that Nicole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nicole","Elena","Brittny","Amy"],"index":723,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864401221,"difficulty":0.0135598779}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristina's card is shown to Ruth. Ruth's card is shown to Nancy. Kristina's card is shown to Nancy. Ruth's card is shown to Kristina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nancy can now know that Kristina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ruth","Nancy","Kristina"],"index":8,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786786437,"difficulty":0.0213213563}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (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":"Elizabeth can now know whether Charles can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Christine","Nicole","Charles"],"index":7309,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9142733812,"difficulty":0.0857266188}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know that Megan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Jon","Megan","Delores"],"index":4710,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858912826,"difficulty":0.0141087174}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Patricia can now know whether Maxine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maxine","Doretha","Patricia","Pamela"],"index":7102,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9758213162,"difficulty":0.0241786838}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darla can now know that Michael can know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Shawn","Darla","Mary"],"index":7347,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9620385766,"difficulty":0.0379614234}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Orlando's card is shown to Loretta. Loretta's card is shown to Orlando. It is publicly announced that someone picked a red card. It is publicly announced that Loretta does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 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":"Orlando can now know that Loretta can know that Orlando picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Loretta","Orlando"],"index":1479,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9660280347,"difficulty":1.9660280347}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathleen knows whether or not everyone is thirsty. It is publicly announced that Marion is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Marion can now know whether Opal can know whether Opal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Opal","Kathleen","Marion"],"index":2909,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8263251781,"difficulty":0.1736748219}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Merlin can now know that Bridget can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Merlin","Sara","Bridget"],"index":2818,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860149622,"difficulty":0.0139850378}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Shellie can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Natasha","Shellie","Desmond"],"index":6381,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9197344184,"difficulty":1.9197344184}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that 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) ] [ ! 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":"Pamela can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pamela","Jerry","John"],"index":5389,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6376885772,"difficulty":0.3623114228}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dale is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Dale can now know that Doris can know whether Denise is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Dale","Denise","Ann"],"index":8415,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.510608077,"difficulty":1.510608077}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lori does not know whether Tyrone is thirsty. It is publicly announced that Lori does not know whether Tyrone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Erin can now know whether Tyrone can know whether Abigail is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tyrone","Erin","Abigail","Lori"],"index":1855,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8702327609,"difficulty":0.1297672391}
-{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Christopher can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Frank"],"index":5983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5421406031,"difficulty":0.4578593969}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Cheryl. Cheryl's card is shown to Dale. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Cheryl can now know that Cheryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cheryl","Dale"],"index":3911,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9787920713,"difficulty":0.0212079287}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruby does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Maureen can now know whether Maureen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ruby","Stacy","Maureen"],"index":6722,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.600954175,"difficulty":1.600954175}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carlos can now know that Jason can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Jason","Carlos"],"index":6514,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9828372002,"difficulty":0.0171627998}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Elizabeth can now know whether Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Harry","Jennifer","Robert"],"index":451,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9568090439,"difficulty":0.0431909561}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Matthew can now know whether Orpha can know that Orpha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Orpha","Matthew"],"index":6711,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9288334846,"difficulty":0.0711665154}
-{"premise":"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 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 Jerry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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)) ] [ ! ~(1) ] Agentb knows that (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Kathryn can now know that Carl can know that Carl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerry","Kathryn","Katie","Carl"],"index":209,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9729376435,"difficulty":0.0270623565}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Betty. Betty's card is shown to Jennifer. Elizabeth's card is shown to Jennifer. Jennifer's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know that Betty can know whether Betty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Jennifer","Elizabeth"],"index":3609,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6841756701,"difficulty":1.6841756701}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Hugh can now know that Annie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hugh","Annie","Darrell"],"index":6875,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9813829064,"difficulty":0.0186170936}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aletha does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Aletha can now know whether Helen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Aletha","John"],"index":1971,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8473610878,"difficulty":0.1526389122}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Ethel. Joseph's card is shown to Kathleen. Ethel's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathleen can now know that Joseph can know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ethel","Kathleen","Joseph"],"index":6945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786581993,"difficulty":0.0213418007}
-{"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 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":"Ivan can now know that David can know whether Tom's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alida","David","Tom","Ivan"],"index":316,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8677176237,"difficulty":0.1322823763}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Isabel can now know whether Isabel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Isabel","Otis","Deborah","Willie"],"index":7790,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9556974769,"difficulty":0.0443025231}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katie does not know whether or not everyone is thirsty. It is publicly announced that Tori does not know whether Bernard is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Katie can now know that Bernard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katie","Tori","Bernard"],"index":1573,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9604266286,"difficulty":0.0395733714}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sue knows whether Naomi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Sue can now know whether Erik can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sue","Erik","Naomi","Dennis"],"index":2466,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9762517214,"difficulty":0.0237482786}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sharon can now know that Melanie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Sharon","Jennifer","Melanie"],"index":3985,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857597947,"difficulty":0.0142402053}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy. It is publicly announced that Julio knows whether someone's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Charles can now know whether Julio can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Julio"],"index":1220,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8467799425,"difficulty":0.1532200575}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know whether Amy can know whether Christine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Amy","David","Christine"],"index":5225,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8067586422,"difficulty":0.1932413578}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Douglas can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Martha","Matthew","Douglas","Ellen"],"index":3130,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860175252,"difficulty":0.0139824748}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephanie's card is shown to Adam. Adam's card is shown to Gladys. Stephanie's card is shown to Gladys. Adam's card is shown to Stephanie. Gladys's card is shown to Stephanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Adam can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adam","Gladys","Stephanie"],"index":2028,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9780805111,"difficulty":0.0219194889}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether Norma's forehead is muddy. It is publicly announced that 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 2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Norma can now know whether Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Norma"],"index":713,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8001955152,"difficulty":0.1998044848}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Raymond. Sandra's card is shown to Helen. Victoria's card is shown to Helen. Raymond's card is shown to Sandra. Sandra's card is shown to Victoria. It is publicly announced that someone picked a red card. It is publicly announced that Victoria does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Raymond can now know that Victoria can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Helen","Sandra","Victoria"],"index":6744,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9768120646,"difficulty":0.0231879354}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Brian can now know that Roy can know that Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roy","Ron","Gerald","Brian"],"index":6525,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858745933,"difficulty":0.0141254067}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Misha is thirsty. It is publicly announced that Travis knows whether or not nobody is thirsty. It is publicly announced that Charles does not know whether Travis is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Charles","Misha","Travis"],"index":7855,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9394525886,"difficulty":0.0605474114}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jason can now know whether Daniel can know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Jason","Ilene","Rebecca"],"index":8044,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9428964257,"difficulty":0.0571035743}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dawn can now know that Susan can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Michael","Dawn"],"index":4576,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8663321733,"difficulty":0.1336678267}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Rick. Cynthia's card is shown to Rick. Rick's card is shown to Dixie. Cynthia's card is shown to Dixie. Rick's card is shown to Irene. Rick's card is shown to Cynthia. Irene's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether Cynthia picked a red card. It is publicly announced that Rick does not know whether Dixie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Irene can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rick","Dixie","Irene","Cynthia"],"index":7177,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9707431197,"difficulty":0.0292568803}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Edwin knows whether Corie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Corie can now know whether Pauline can know that Corie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edwin","Pauline","Corie"],"index":5957,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9580023885,"difficulty":0.0419976115}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paul can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Terry","Allison","Nina"],"index":5040,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858312607,"difficulty":0.0141687393}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to David. Melinda's card is shown to David. David's card is shown to Dorothy. Melinda's card is shown to Dorothy. David's card is shown to Melinda. Dorothy's card is shown to Melinda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Dorothy","Melinda"],"index":4086,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9775231481,"difficulty":0.0224768519}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecilia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (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":"Jess can now know whether Willie can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jess","Willie","Cecilia"],"index":8028,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9729269147,"difficulty":0.0270730853}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lauren knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Lauren can now know that Laverne can know that Laverne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lauren","Laverne"],"index":4441,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9765209556,"difficulty":0.0234790444}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theresa does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joshua can now know that Theresa can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Theresa","Joshua","Ted","Jared"],"index":6659,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9690872431,"difficulty":0.0309127569}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacob does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Michael can now know whether Tiffany is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacob","Michael","Pasquale","Tiffany"],"index":2540,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6037173867,"difficulty":1.6037173867}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Omar's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Rhonda can now know that Deborah's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Omar","Deborah","Jessica","Rhonda"],"index":436,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.981744945,"difficulty":0.018255055}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"James can now know whether David can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","David","James"],"index":7528,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9694463015,"difficulty":0.0305536985}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fernando does not know whether Molly is thirsty. It is publicly announced that Fernando knows whether Fernando is thirsty. It is publicly announced that Darren does not know whether Molly is thirsty. It is publicly announced that Darren knows whether Darren is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Darren can now know that Molly can know that Darren is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darren","Fernando","Molly"],"index":1617,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9734606147,"difficulty":0.0265393853}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Grady does not know whether Grady's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Shirley can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Shirley","Grady"],"index":1660,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.979049325,"difficulty":0.020950675}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether Hector is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Hector can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Hector"],"index":5761,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9774823785,"difficulty":0.0225176215}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Nathan. Nathan's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Nathan does not know whether or not everyone picked a red card. It is publicly announced that Nathan knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Nathan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nathan","Joseph"],"index":1995,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9771026373,"difficulty":0.0228973627}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Arnold. Arnold's card is shown to Laurie. Arnold's card is shown to Chad. Rosa's card is shown to Chad. Arnold's card is shown to Rosa. Laurie's card is shown to Rosa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laurie can now know that Chad can know whether Laurie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arnold","Laurie","Chad","Rosa"],"index":3687,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.697170496,"difficulty":1.697170496}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Jorge is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Ronald can now know that Julie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Jorge","Julie"],"index":2555,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9070661664,"difficulty":0.0929338336}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know whether Cristi can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anna","Anthony","Robert","Cristi"],"index":7805,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9786835313,"difficulty":0.0213164687}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Maria is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Joseph can now know that Michael can know whether Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Floyd","Maria","Michael"],"index":3131,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6108374596,"difficulty":1.6108374596}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Miguel. Miguel's card is shown to Ralph. Ralph's card is shown to Steven. It is publicly announced that someone picked a red card. It is publicly announced that Steven does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Steven can now know whether Miguel can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Miguel","Ralph","Steven"],"index":4686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8963992596,"difficulty":0.1036007404}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Glen's forehead is muddy. It is publicly announced that Glen knows whether Glen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Glen"],"index":9094,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9806932807,"difficulty":0.0193067193}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosanna knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Christopher can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Rosanna","Mary","Christopher"],"index":4239,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9783987403,"difficulty":0.0216012597}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Adrianne is thirsty. It is publicly announced that Michael does not know whether Adrianne is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Meagan can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Rebecca","Adrianne","Meagan"],"index":6315,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9728438854,"difficulty":0.0271561146}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Mary. Mary's card is shown to Tammy. Mary's card is shown to William. Tammy's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that William can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Tammy","William"],"index":444,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9783118367,"difficulty":0.0216881633}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Holli","Holly","Robert","Shirley"],"index":7682,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856193066,"difficulty":0.0143806934}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothy can now know whether James can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Dorothy","Rodney"],"index":5966,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9753682613,"difficulty":0.0246317387}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mary can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Mary","Donald"],"index":3104,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9769462943,"difficulty":0.0230537057}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy is not thirsty. It is publicly announced that Bernice does not know whether Sherrie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Sherrie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Sherrie","Steven","Bernice"],"index":1747,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.97390908,"difficulty":0.02609092}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyler's card is shown to Ryan. Ryan's card is shown to Tyler. Ryan's card is shown to Ruby. Tyler's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ryan can now know whether Tyler can know that Ruby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ryan","Tyler","Ruby"],"index":1157,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5807269812,"difficulty":0.4192730188}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Steven can now know that Steven is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dale","Steven","Charissa","James"],"index":7231,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9786206484,"difficulty":0.0213793516}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terry can now know whether Jim is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Anita","Terry","Jim"],"index":4,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5816769004,"difficulty":0.4183230996}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theodore knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Scott can now know whether Selena can know that Selena's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Theodore","Rick","Scott","Selena"],"index":4422,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9567872286,"difficulty":0.0432127714}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Audrey's card is shown to Marvin. Marvin's card is shown to Audrey. Michael's card is shown to Audrey. Audrey's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marvin can now know whether Audrey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marvin","Audrey","Michael"],"index":9513,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.654394567,"difficulty":0.345605433}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"William can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Colleen","William"],"index":6104,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9860764742,"difficulty":1.9860764742}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Helena is thirsty. It is publicly announced that Helena knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Helena can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Helena","David"],"index":951,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9649091959,"difficulty":0.0350908041}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwina's card is shown to David. David's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Edwina picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"David can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Walter","Edwina"],"index":1006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.978975594,"difficulty":0.021024406}
-{"premise":"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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Johnny can now know that Michael can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Johnny","Tristan","Michael","Nicholas"],"index":6073,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8362560868,"difficulty":1.8362560868}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gayle knows whether Marvin's forehead is muddy. It is publicly announced that Gayle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentc knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Marvin can now know whether Jeffrey can know whether Marvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeffrey","Gayle","Marvin"],"index":6975,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.949180007,"difficulty":0.050819993}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Rhonda. Alberta's card is shown to Vera. Rhonda's card is shown to Michael. Alberta's card is shown to Michael. Vera's card is shown to Alberta. Michael's card is shown to Alberta. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Alberta can now know whether Rhonda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rhonda","Vera","Michael","Alberta"],"index":8504,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6684257984,"difficulty":1.6684257984}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joshua can now know whether Helen can know whether Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mattie","Helen","Doris","Joshua"],"index":6864,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.970985949,"difficulty":0.029014051}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Donald. Mary's card is shown to Kathe. Donald's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Donald can know that Kathe picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Kathe","Mary"],"index":5667,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9784895182,"difficulty":0.0215104818}
-{"premise":"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 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) ] [ ! (Agenta knows whether 3) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Brandon can now know that Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Phyllis","Anthony","Brandon"],"index":9391,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9812895656,"difficulty":0.0187104344}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen knows whether Alan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Gregory can now know whether Carmen can know whether Alan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alan","Carmen","Shirley","Gregory"],"index":7151,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9709212184,"difficulty":0.0290787816}
-{"premise":"There are two 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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Carol can now know whether Katherine can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Katherine","Carol"],"index":8107,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9354917407,"difficulty":0.0645082593}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Elizabeth","Susan","Paul"],"index":4001,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.958496809,"difficulty":0.041503191}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows 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":"Mary can now know that Scott can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Jennifer","Mary","Jacqueline"],"index":1067,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8284164667,"difficulty":0.1715835333}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Genevieve. Genevieve's card is shown to Shirley. It is publicly announced that someone picked a red card. It is publicly announced that Genevieve picked a black card. It is publicly announced that Genevieve knows whether Shirley picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Genevieve can now know whether Shirley can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Genevieve","Shirley"],"index":1456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9737678766,"difficulty":0.0262321234}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina knows whether Louise's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Glenda can now know that Louise can know that Glenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Louise","Glenda","Christina","Terrence"],"index":5564,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858826399,"difficulty":0.0141173601}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know that Julianna can know that Kathryn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathryn","John","Julianna","Brandon"],"index":6587,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859199524,"difficulty":0.0140800476}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Javier does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Cherly can now know whether Javier can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Javier","Cherly"],"index":1959,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9718691707,"difficulty":0.0281308293}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Lisa can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Lydia","Lisa"],"index":433,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9771813154,"difficulty":0.0228186846}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy. It is publicly announced that Charlie knows whether Charlie'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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Olympia can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charlie","Olympia","Richard"],"index":3922,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9539367557,"difficulty":0.0460632443}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth is not thirsty. It is publicly announced that Elizabeth knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Elizabeth can now know that William can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Elizabeth","Susan","William"],"index":6814,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9764297009,"difficulty":0.0235702991}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wayne does not know whether Robbie is thirsty. It is publicly announced that Robbie does not know whether Iris is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Robbie can now know that Wayne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wayne","Robbie","Iris"],"index":1225,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9754689932,"difficulty":0.0245310068}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jose can now know that Steven can know whether Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jose","Steven"],"index":8870,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9141950607,"difficulty":1.9141950607}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Elizabeth. Jeffrey's card is shown to Joanne. Trevor's card is shown to Joanne. Joanne's card is shown to Trevor. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Trevor picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Jeffrey can now know that Joanne can know whether Joanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","Joanne","Jeffrey","Trevor"],"index":5973,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7579763532,"difficulty":1.7579763532}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Thomas can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kennith","Thomas"],"index":864,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9584821463,"difficulty":0.0415178537}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eliza knows whether Ashley's forehead is muddy. It is publicly announced that Eliza knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ashley can now know whether Ashley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eliza","Racheal","Ashley"],"index":1574,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9616552591,"difficulty":0.0383447409}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Mathew. Eugene's card is shown to Wanda. Wanda's card is shown to Eugene. It is publicly announced that someone picked a red card. It is publicly announced that Wanda knows whether someone picked a red card. It is publicly announced that Eugene does not know whether or not everyone picked a red card. It is publicly announced that Eugene knows whether or not nobody picked a red card. It is publicly announced that Eugene does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Wanda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mathew","Wanda","Eugene"],"index":120,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6231020093,"difficulty":0.3768979907}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tiffany can now know that George can know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tiffany","George","Patricia","Kevin"],"index":7171,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9759685993,"difficulty":0.0240314007}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Robert. Ann's card is shown to Robert. William's card is shown to Robert. Robert's card is shown to John. Ann's card is shown to John. William's card is shown to John. Robert's card is shown to Ann. William's card is shown to Ann. Ann's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Robert can now know whether Ann can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","John","Ann","William"],"index":4573,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9745566249,"difficulty":0.0254433751}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether Everett is thirsty. It is publicly announced that Melissa does not know whether Everett is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Melissa can now know whether Everett can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Everett","Melissa"],"index":6909,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9301315546,"difficulty":0.0698684454}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Jason. Eden's card is shown to Jason. Jason's card is shown to Craig. Eden's card is shown to Craig. Jason's card is shown to Eden. It is publicly announced that someone picked a red card. It is publicly announced that Eden does not know whether Craig picked a red card. It is publicly announced that Eden knows whether Jason picked a red card. It is publicly announced that Jason does not know whether Jason picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Craig can now know whether Craig picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Craig","Eden"],"index":8085,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7785724401,"difficulty":1.7785724401}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Frank can now know that Shannon can know that Shannon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dana","Tiffany","Shannon","Frank"],"index":5310,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9614003301,"difficulty":0.0385996699}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ella knows whether someone is thirsty. It is publicly announced that Ella knows whether Mike is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ella can now know whether Mike can know that Ella is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mike","Ella"],"index":5176,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7053807974,"difficulty":0.2946192026}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Alex is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Robert can now know whether Alex is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Alex","Robert"],"index":6817,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6705758572,"difficulty":1.6705758572}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice knows whether Billy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Billy can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Janice","Billy"],"index":2122,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9796395898,"difficulty":0.0203604102}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that James can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Chris","Joseph"],"index":6350,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6549688578,"difficulty":1.6549688578}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Kimberley","Jeffrey","Theodore"],"index":2492,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9679480791,"difficulty":0.0320519209}
-{"premise":"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 knows whether Randall's forehead is muddy. It is publicly announced that Gloria knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Gloria can now know that Randall can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gloria","Randall"],"index":863,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9682193398,"difficulty":0.0317806602}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelby's card is shown to Clark. Clark's card is shown to Shelby. It is publicly announced that someone picked a red card. It is publicly announced that Shelby does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (~(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":"Shelby can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Clark","Shelby"],"index":2305,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9699636102,"difficulty":0.0300363898}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha does not know whether Chris is thirsty. It is publicly announced that Martha knows whether or not everyone is thirsty. It is publicly announced that Ramona knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Chris can now know whether Chris is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Chris","Ramona","Martha"],"index":8630,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7546585798,"difficulty":0.2453414202}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Robert. Robert's card is shown to Patricia. Robert's card is shown to Gertude. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 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 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Bruce","Patricia","Gertude"],"index":9124,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9716575146,"difficulty":0.0283424854}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know that Christopher can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tom","Marty","Christopher","Keith"],"index":1079,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858663678,"difficulty":0.0141336322}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonas's card is shown to Anamaria. Gia's card is shown to Anamaria. Anamaria's card is shown to Jonas. Gia's card is shown to Jonas. Anamaria's card is shown to Gia. It is publicly announced that someone picked a red card. It is publicly announced that Gia does not know whether Jonas picked a red card. It is publicly announced that Gia knows whether Anamaria picked a red card. It is publicly announced that Anamaria does not know whether Anamaria picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Anamaria can now know that Gia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anamaria","Jonas","Gia"],"index":5038,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9732434154,"difficulty":0.0267565846}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kate knows whether John's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kate can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kate","John"],"index":273,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9838559628,"difficulty":0.0161440372}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Devon does not know whether or not everyone is thirsty. It is publicly announced that Thomas does not know whether or not everyone is thirsty. It is publicly announced that Christopher does not know whether Bonnie is thirsty. It is publicly announced that Devon does not know whether Bonnie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Bonnie can now know whether Devon can know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Devon","Christopher","Thomas","Bonnie"],"index":1252,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8384523988,"difficulty":0.1615476012}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Joseph can now know whether Catherine can know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Catherine","Joseph"],"index":6962,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.87046206,"difficulty":1.87046206}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adam does not know whether Margret is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Steven can now know whether Adam can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margret","Steven","Adam"],"index":2332,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8979510069,"difficulty":0.1020489931}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hilda's card is shown to Johnny. Johnny's card is shown to James. Hilda's card is shown to Jeremy. Johnny's card is shown to Hilda. James's card is shown to Hilda. It is publicly announced that someone picked a red card. It is publicly announced that Johnny does not know whether Jeremy picked a red card. It is publicly announced that Johnny does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Johnny can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","James","Jeremy","Hilda"],"index":3524,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9743552208,"difficulty":0.0256447792}
-{"premise":"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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Mary can now know that James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Mary"],"index":7791,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9808949828,"difficulty":0.0191050172}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Nancy can now know whether Glenn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bill","Glenn","Nancy","Virginia"],"index":7503,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9598415494,"difficulty":0.0401584506}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria's forehead is muddy. It is publicly announced that Esther knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Esther can now know that Terri can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Terri","Maria","Esther"],"index":6115,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9802873731,"difficulty":0.0197126269}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Leah can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Octavio","Leah","John","Hubert"],"index":7550,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859396219,"difficulty":0.0140603781}
-{"premise":"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)) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Sylvia can now know that Harold can know that Sylvia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Sarah","Clarence","Sylvia"],"index":1504,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.961094439,"difficulty":1.961094439}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Philip knows whether or not everyone's forehead is muddy. It is publicly announced that Janice knows whether Janice'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 (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Philip can now know whether Janice can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Philip","Janice"],"index":1729,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9366113544,"difficulty":0.0633886456}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tanner knows whether or not nobody's forehead is muddy. It is publicly announced that Tyrone does not know whether Tyrone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Kendra can now know whether Tanner can know whether Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Tyrone","Kendra","Tanner"],"index":4903,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9488262534,"difficulty":0.0511737466}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Pamela can now know that Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jean","Pamela","Richard"],"index":1867,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9814423919,"difficulty":1.9814423919}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Raymond can now know whether Maria can know whether Nicholas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Raymond","Allan","Nicholas"],"index":2582,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9430718422,"difficulty":0.0569281578}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know that Avis can know whether Billy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Avis","Dorothy","Alma","Billy"],"index":8418,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9632242322,"difficulty":0.0367757678}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Armando's card is shown to Peggy. Marlene's card is shown to Armando. It is publicly announced that someone picked a red card. It is publicly announced that Willis does not know whether Peggy picked a red card. It is publicly announced that Peggy picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Peggy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Willis","Peggy","Armando","Marlene"],"index":1513,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9693844318,"difficulty":0.0306155682}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Robert can now know that Helen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Helen","Robert"],"index":5641,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9614137411,"difficulty":0.0385862589}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Zachary can now know whether Sonya can know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Patricia","Zachary","Sonya"],"index":5849,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7829412818,"difficulty":0.2170587182}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Joyce can now know that Steven can know that Marshall's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Marshall","Mark","Steven"],"index":7401,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856418967,"difficulty":0.0143581033}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Jack. Ronald's card is shown to Jack. Ronald's card is shown to Dennise. It is publicly announced that someone picked a red card. It is publicly announced that Jack does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jack can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jerry","Jack","Ronald","Dennise"],"index":6363,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9690992236,"difficulty":0.0309007764}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amos's card is shown to Dale. Dale's card is shown to Amos. It is publicly announced that someone picked a red card. It is publicly announced that Amos does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Dale can now know whether Amos can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dale","Amos"],"index":2020,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6274555922,"difficulty":0.3725444078}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Alexander. Alexander's card is shown to Patrick. Alexander's card is shown to John. Alexander's card is shown to Helen. Patrick's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card. It is publicly announced that Patrick knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Alexander can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alexander","Patrick","John","Helen"],"index":4111,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6540333629,"difficulty":1.6540333629}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Wendy. Sidney's card is shown to Wendy. Wendy's card is shown to Robin. Sidney's card is shown to Robin. Wendy's card is shown to Sidney. It is publicly announced that someone picked a red card. It is publicly announced that Sidney does not know whether Robin picked a red card. It is publicly announced that Sidney knows whether Wendy picked a red card. It is publicly announced that Wendy does not know whether Wendy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sidney can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wendy","Robin","Sidney"],"index":2032,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9720511436,"difficulty":0.0279488564}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gabriel's card is shown to Michelle. Michelle's card is shown to Gregory. Gabriel's card is shown to Judy. Judy's card is shown to Gabriel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd: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:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know whether Judy can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Gregory","Judy","Gabriel"],"index":3675,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9636100531,"difficulty":0.0363899469}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Karin can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alexander","Tammy","Karin","Michael"],"index":9385,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9226967692,"difficulty":0.0773032308}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hanh's card is shown to Angela. Hanh's card is shown to Roy. Angela's card is shown to Hanh. Angela's card is shown to Aletha. Roy's card is shown to Aletha. It is publicly announced that someone picked a red card. It is publicly announced that Aletha does not know whether Hanh picked a red card. It is publicly announced that Hanh does not know whether Hanh picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Aletha can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Roy","Hanh","Aletha"],"index":9375,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8935461044,"difficulty":0.1064538956}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Rachel can now know that Rachel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rachel","Chantell"],"index":2607,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9855008721,"difficulty":0.0144991279}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracy's card is shown to Magen. Tracy's card is shown to Myra. Myra's card is shown to Tracy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Myra can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Magen","Myra","Tracy"],"index":4354,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9681692123,"difficulty":0.0318307877}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Helen. Jonathan's card is shown to Maureen. It is publicly announced that someone picked a red card. It is publicly announced that Helen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 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 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Jonathan can now know that Jonathan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Jonathan","Ira","Maureen"],"index":2546,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9788172841,"difficulty":0.0211827159}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Ross's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ross can now know that Dennise can know that Dennise's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ross","Teressa","John","Dennise"],"index":1179,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858973026,"difficulty":0.0141026974}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Brian can now know that Carol can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carol","Donald","Brian"],"index":1532,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9639734626,"difficulty":0.0360265374}
-{"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":"John can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clinton","John","Robert","Terry"],"index":7778,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9395204782,"difficulty":1.9395204782}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Princess can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Ruth","Princess"],"index":6148,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9579790831,"difficulty":0.0420209169}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randolph does not know whether Gerald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Robert can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Randolph","Gerald","Thomas"],"index":398,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9701883197,"difficulty":0.0298116803}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Shanice is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Mallie can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shanice","John","Mallie"],"index":9530,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9701664448,"difficulty":0.0298335552}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether Dion is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Paul can now know whether Mark can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","Paul","Mark","Dion"],"index":7234,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9704182744,"difficulty":0.0295817256}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas knows whether someone is thirsty. It is publicly announced that Christopher knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Thomas can now know that Mary can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Mary","Christopher"],"index":7845,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9625980854,"difficulty":0.0374019146}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher does not know whether Harry is thirsty. It is publicly announced that Christopher does not know whether Harry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Christopher can now know that Christopher is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Josie","Harry","Alice"],"index":521,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9745545387,"difficulty":0.0254454613}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mabel's card is shown to Raymond. Hugo's card is shown to Raymond. Raymond's card is shown to Hugo. Raymond's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Hugo can now know whether Hugo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Mabel","Hugo","Robert"],"index":8751,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6431470513,"difficulty":1.6431470513}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy does not know whether Timothy's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Kimberly can now know that Timothy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kimberly","Timothy"],"index":9607,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8126074076,"difficulty":1.8126074076}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Martin can now know whether Nicholas can know whether Martin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicholas","Martin","Alton","Gail"],"index":7684,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8086926937,"difficulty":0.1913073063}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Linda can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","James","Jessica","Christopher"],"index":7616,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858196974,"difficulty":0.0141803026}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to William. Elizabeth's card is shown to William. William's card is shown to Marcella. Andrew's card is shown to Marcella. William's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marcella can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Andrew","Marcella","Elizabeth"],"index":8019,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6651751995,"difficulty":0.3348248005}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Harold. Harold's card is shown to Matha. Edward's card is shown to Elaine. Elaine's card is shown to Edward. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harold can now know that Elaine can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Matha","Elaine","Edward"],"index":6834,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9778376222,"difficulty":0.0221623778}
-{"premise":"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)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Donald can now know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Frank","Jolene","Ann"],"index":8246,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.96033746,"difficulty":0.03966254}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rodney can now know whether Michael can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rodney","Michael","Timothy"],"index":7629,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9526529908,"difficulty":0.0473470092}
-{"premise":"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 does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"David can now know that Patrick can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phillip","Patrick","Dana","David"],"index":7008,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9774583578,"difficulty":0.0225416422}
-{"premise":"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 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) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Rhonda can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rhonda","Jason","Joseph","Linda"],"index":8734,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9783220887,"difficulty":0.0216779113}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Patricia. Patricia's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patricia","Michael"],"index":9066,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8827363253,"difficulty":1.8827363253}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vera can now know that Gerald can know that Gerald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gerald","David","Vera"],"index":9,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865147471,"difficulty":0.0134852529}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald is not thirsty. It is publicly announced that Lisa is not thirsty. It is publicly announced that Donald does not know whether Maria is thirsty. It is publicly announced that Maria knows whether Maria is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Maria can now know whether Lisa can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nikki","Donald","Lisa","Maria"],"index":2706,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9700869918,"difficulty":0.0299130082}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Christina is thirsty. It is publicly announced that Kevin knows whether or not everyone is thirsty. It is publicly announced that Edward knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Christina can now know whether Edward is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christina","Edward","Kevin"],"index":1217,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6684778929,"difficulty":1.6684778929}
-{"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 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":"James can now know whether Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Ronald","Greta","James"],"index":328,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8556312323,"difficulty":0.1443687677}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know that Donald can know that Rose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Rose","Donald"],"index":8590,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864170551,"difficulty":0.0135829449}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angel's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Angel can now know whether Melissa can know whether Angel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Angel","Melissa"],"index":3415,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9443462491,"difficulty":0.0556537509}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Tina. Tina's card is shown to Joanne. It is publicly announced that someone picked a red card. It is publicly announced that Tina does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (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":"Tina can now know whether Tina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tina","Joanne"],"index":2189,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6040764451,"difficulty":1.6040764451}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobbie's card is shown to Sonia. Felipe's card is shown to Sonia. Wayne's card is shown to Sonia. Sonia's card is shown to Felipe. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sonia can now know whether Felipe picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bobbie","Sonia","Felipe","Wayne"],"index":3658,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6551628113,"difficulty":1.6551628113}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Autumn knows whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Melissa can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debora","Autumn","Melissa","Jason"],"index":7566,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6311348081,"difficulty":0.3688651919}
-{"premise":"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 knows whether Reginald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Albert can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Albert","Reginald","Patricia"],"index":2665,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9816821218,"difficulty":0.0183178782}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows 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":"Rosa can now know whether Harold can know that Rosa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harold","Rosa","Shannon"],"index":8143,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7090215087,"difficulty":1.7090215087}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Howard does not know whether Jim is thirsty. It is publicly announced that Howard is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Howard can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Margaret","Jim","Howard"],"index":5159,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9087074399,"difficulty":1.9087074399}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald does not know whether Margaret is thirsty. It is publicly announced that Allan knows whether or not nobody is thirsty. It is publicly announced that Donald does not know whether Allan is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agentd knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Allan can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Donald","Margaret","Allan"],"index":3657,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9677731395,"difficulty":0.0322268605}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Shannon. Shannon's card is shown to Aliza. Scott's card is shown to Aliza. Anthony's card is shown to Scott. Shannon's card is shown to Anthony. Aliza's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Aliza can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shannon","Aliza","Scott","Anthony"],"index":2245,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9774923921,"difficulty":0.0225076079}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Courtney's card is shown to Floyd. Helen's card is shown to Floyd. Alice's card is shown to Courtney. Floyd's card is shown to Helen. Floyd's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Floyd knows whether or not everyone picked a red card. It is publicly announced that Alice knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Courtney can now know that Helen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Floyd","Courtney","Helen","Alice"],"index":4186,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9503729939,"difficulty":0.0496270061}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tom does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Tom can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sandra","Tom","Virginia","Sean"],"index":4340,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9676182866,"difficulty":0.0323817134}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jennifer can now know that Curtis can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jennifer","Curtis"],"index":27,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9762011766,"difficulty":0.0237988234}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Paulette. Sandra's card is shown to Paulette. Paulette's card is shown to Sandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know that Paulette can know that Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paulette","Kevin","Kelly","Sandra"],"index":116,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.978864789,"difficulty":0.021135211}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michelle does not know whether Ruby is thirsty. It is publicly announced that Bruce is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Bruce can now know that Michelle can know whether Michelle is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bruce","Michelle","Ruby"],"index":9307,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6745992303,"difficulty":0.3254007697}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alicia's card is shown to Willie. Patricia's card is shown to Alicia. Willie's card is shown to Patricia. Alicia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Willie can now know that Willie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Willie","Alicia","Patricia"],"index":1693,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.978574872,"difficulty":0.021425128}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know whether Linda can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clarissa","Christopher","Sarah","Linda"],"index":9457,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9792765379,"difficulty":0.0207234621}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Peggy can now know that Kimberly can know that Peggy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kimberly","Peggy"],"index":83,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865797162,"difficulty":0.0134202838}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lance does not know whether or not everyone's forehead is muddy. It is publicly announced that Lance does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 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":"Mary can now know that Lance can know that Lance's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Lance"],"index":2173,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9645440578,"difficulty":0.0354559422}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terrie knows whether or not everyone's forehead is muddy. It is publicly announced that Brett knows whether Brett'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 that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Terrie can now know that Brett can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Terrie","Brett"],"index":1822,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9723810554,"difficulty":0.0276189446}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Charlene. Charlene's card is shown to Christine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Charlene can now know whether Christine can know whether Christine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charlene","Christine"],"index":2991,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9044832587,"difficulty":1.9044832587}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bryce can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eileen","George","Bryce","Edith"],"index":3817,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858996272,"difficulty":0.0141003728}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marcellus can now know that Miguel can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marcellus","Michelle","Miguel","Edward"],"index":1974,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9825338721,"difficulty":0.0174661279}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Richard can now know that Bambi can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Kathy","Bambi","Zulema"],"index":4453,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7048813701,"difficulty":0.2951186299}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Betty. Amy's card is shown to Judy. Amy's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Judy does not know whether Judy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Amy can now know that Betty picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amy","Betty","Judy","Richard"],"index":7885,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9759317636,"difficulty":0.0240682364}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Tiffany can now know whether Jared can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jared","Tiffany","Shirley"],"index":7586,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7138824463,"difficulty":1.7138824463}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Buddy can now know that Dwayne can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Buddy","Alex","Dwayne","Donna"],"index":3569,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9775030017,"difficulty":0.0224969983}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Shelia. Ann's card is shown to Shelia. Shelia's card is shown to Darrell. It is publicly announced that someone picked a red card. It is publicly announced that Darrell does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 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 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Darrell can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shelia","Darrell","Ann"],"index":7015,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9691292048,"difficulty":0.0308707952}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Charles can now know whether Melvin can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melvin","Charles"],"index":4113,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9431902766,"difficulty":0.0568097234}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marty's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Irene can now know that Marty can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Irene","Marty"],"index":9040,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.696231842,"difficulty":1.696231842}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Larry. Gladys's card is shown to Jerry. Larry's card is shown to Gladys. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know whether Gladys can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Jerry","Gladys"],"index":3787,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9633114934,"difficulty":0.0366885066}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Desiree is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Cameron","Denise","Desiree"],"index":163,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9801627398,"difficulty":0.0198372602}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Morris does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Morris can now know whether Linda can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Jeremy","Morris","Linda"],"index":2233,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9754624367,"difficulty":0.0245375633}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mabel's card is shown to Fannie. Mabel's card is shown to Joshua. Joshua's card is shown to Chris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fannie can now know whether Mabel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Fannie","Joshua","Mabel","Chris"],"index":1178,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6581867337,"difficulty":0.3418132663}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Judith knows whether Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Judith can now know that Sarah can know whether Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Judith","Edith","Sarah"],"index":3723,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9643902779,"difficulty":0.0356097221}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terry can now know whether Nita can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nita","Terry","Jason","Anthony"],"index":2923,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9749658108,"difficulty":0.0250341892}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Tyler. Kimberly's card is shown to Tyler. Virginia's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tyler can now know whether Virginia can know whether Tyler picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Virginia","Tyler","Kimberly"],"index":2222,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8991789818,"difficulty":1.8991789818}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurie does not know whether Laurie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know that Anthony can know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Anthony","Laurie","Odis"],"index":3810,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8921740055,"difficulty":1.8921740055}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joyce does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brenda can now know that Joyce can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joyce","Brenda","Leland"],"index":7004,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9661926031,"difficulty":0.0338073969}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wendy's card is shown to Christopher. Christopher's card is shown to Wendy. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Wendy knows whether Christopher picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (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) ] 0","hypothesis":"Christopher can now know that Wendy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Wendy"],"index":2074,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9775997996,"difficulty":0.0224002004}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobbie's forehead 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 3)","n_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":"Bobbie can now know whether Sammie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bonnie","Bobbie","Sammie"],"index":8509,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.894143343,"difficulty":0.105856657}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorenzo's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Lorenzo can now know that Johnnie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Johnnie","Lorenzo"],"index":9093,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823096395,"difficulty":0.0176903605}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Frances can now know whether Eric can know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Frances","Eric"],"index":1424,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.945547998,"difficulty":0.054452002}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Cynthia can now know that Keith can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jamie","Timothy","Keith","Cynthia"],"index":1979,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7624712586,"difficulty":1.7624712586}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to Gregory. Gregory's card is shown to Edward. Gregory's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Edward can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gregory","Edward","Janice"],"index":3472,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9679710269,"difficulty":0.0320289731}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elaine can now know whether Barbara can know whether Jesus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesus","Elaine","Barbara","Kathy"],"index":3312,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.950748384,"difficulty":0.049251616}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lorna does not know whether Mia is thirsty. It is publicly announced that Mia does not know whether or not everyone is thirsty. It is publicly announced that Mia does not know whether Lorna is thirsty. It is publicly announced that Lorna is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] 0","hypothesis":"Lorna can now know that Mia can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Marc","Mia","Lorna"],"index":6810,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9528334141,"difficulty":0.0471665859}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ron does not know whether Karen is thirsty. It is publicly announced that Ron does not know whether Karen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Dustin can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ron","India","Karen","Dustin"],"index":1986,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9086633325,"difficulty":0.0913366675}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Teresa. Paul's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Teresa can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Teresa","Mary"],"index":2642,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9150425792,"difficulty":0.0849574208}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Janie. Jeremy's card is shown to Shirley. Janie's card is shown to Jeremy. Louise's card is shown to Jeremy. It is publicly announced that someone picked a red card. It is publicly announced that Louise does not know whether or not everyone picked a red card. It is publicly announced that Louise does not know whether Louise picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Shirley can now know that Janie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janie","Louise","Shirley","Jeremy"],"index":2972,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9637928605,"difficulty":0.0362071395}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Lora. Lora's card is shown to Paula. Louise's card is shown to Paula. It is publicly announced that someone picked a red card. It is publicly announced that Paula picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Lora can now know that Paula can know whether Paula picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lora","Paula","Louise"],"index":8594,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.72979182,"difficulty":0.27020818}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Paul can now know that Janet can know whether Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Paul","Meredith","Janet"],"index":3338,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9645200372,"difficulty":0.0354799628}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois knows whether Ebony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Ebony can now know that Lois can know that Crystal's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Crystal","Lois","Ebony"],"index":6015,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858859777,"difficulty":0.0141140223}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee knows whether Ruben'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 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":"Lee can now know that Lee's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ruben","Lee"],"index":9053,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9818831682,"difficulty":0.0181168318}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melanie's card is shown to Edith. Edith's card is shown to Melanie. It is publicly announced that someone picked a red card. It is publicly announced that Edith knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb 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":"Edith can now know that Melanie can know whether Edith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edith","Melanie"],"index":3889,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7977882624,"difficulty":0.2022117376}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Selma does not know whether Alicia is thirsty. It is publicly announced that Dominique does not know whether Alicia is thirsty. It is publicly announced that Dominique does not know whether Brent is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agenta knows that (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Brent can now know that Alicia can know whether Selma is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brent","Alicia","Selma","Dominique"],"index":5534,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6521372199,"difficulty":1.6521372199}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Neil does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Maria can now know that Neil can know whether Ronald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Brian","Neil","Maria"],"index":9577,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6258895397,"difficulty":0.3741104603}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Jerome can now know that John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lois","John","Keith","Jerome"],"index":9070,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9786487222,"difficulty":0.0213512778}
-{"premise":"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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Joe can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joe","Robert","Ofelia","Edna"],"index":8852,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8355306387,"difficulty":1.8355306387}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that John knows whether Thomas's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"John can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Thomas"],"index":1367,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.976813674,"difficulty":0.023186326}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Megan does not know whether Michael is thirsty. It is publicly announced that Megan does not know whether Michael is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Megan can now know that Michael can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Megan"],"index":8376,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9748966098,"difficulty":1.9748966098}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether or not everyone's forehead is muddy.","smcdel_problem":"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":"Jennifer can now know that Hazel can know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hazel","Jennifer","Terry"],"index":4163,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8628877401,"difficulty":0.1371122599}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shauna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"James can now know that Shauna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Shauna"],"index":8212,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9860603809,"difficulty":1.9860603809}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander knows whether Joseph's forehead is muddy. It is publicly announced that Alexander does not know whether Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Alexander can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alexander","Joseph","Norman"],"index":1135,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9747055173,"difficulty":0.0252944827}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita does not know whether James is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"James can now know that Anita can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anita","James"],"index":6717,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6575663686,"difficulty":1.6575663686}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emma does not know whether or not everyone's forehead is muddy. It is publicly announced that Erma knows whether Erma'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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"John can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Erma","John","Emma"],"index":3483,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9702736139,"difficulty":0.0297263861}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"James can now know whether Pauline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Pauline"],"index":3481,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9621107578,"difficulty":0.0378892422}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl knows whether Juanita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Daniel can now know whether Juanita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Cheryl","Juanita","Troy"],"index":4391,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9104207754,"difficulty":0.0895792246}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane does not know whether Diane's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|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) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Mike can now know that Diane's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Diane","Mike"],"index":5355,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9546868205,"difficulty":0.0453131795}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Lois is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lois can now know whether William can know that Lois is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Lois"],"index":9277,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6237784028,"difficulty":0.3762215972}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Micheal does not know whether Hollis is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Hollis can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hollis","Micheal","Richard"],"index":6599,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.963525176,"difficulty":0.036474824}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Silvia can now know whether Randall is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Silvia","Melissa","Randall","Mary"],"index":2489,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5200992227,"difficulty":1.5200992227}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Jeremy. Deirdre's card is shown to Jeremy. Jeremy's card is shown to Jose. Deirdre's card is shown to Jose. Jeremy's card is shown to Deirdre. Jose's card is shown to Deirdre. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jose can now know that Jose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeremy","Jose","Deirdre"],"index":7599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9781056643,"difficulty":0.0218943357}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jill does not know whether Judith is thirsty. It is publicly announced that Jill knows whether or not everyone is thirsty. It is publicly announced that Paul knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Judith can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judith","Paul","Jill"],"index":9454,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9490776658,"difficulty":0.0509223342}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Heather can now know that Jeanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arthur","Heather","Jeanne","Jose"],"index":2896,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860554934,"difficulty":0.0139445066}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Israel can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Israel","John","Michael","Victor"],"index":2947,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858539701,"difficulty":0.0141460299}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Linda can now know whether Robert can know that Linda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Leroy","Linda","Glenda"],"index":3299,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6087464094,"difficulty":1.6087464094}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Marian. Derek's card is shown to Gregory. Fred's card is shown to Gregory. Marian's card is shown to Derek. Derek's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Fred does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Derek can now know whether Gregory can know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marian","Gregory","Derek","Fred"],"index":6380,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8696823716,"difficulty":0.1303176284}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Lessie. Gregory's card is shown to Paula. Lessie's card is shown to Gregory. Paula's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Paula knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lessie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lessie","Paula","Gregory"],"index":8302,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9707087874,"difficulty":0.0292912126}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karissa can now know that Blanche is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Briana","Elaine","Karissa","Blanche"],"index":8437,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9801867604,"difficulty":0.0198132396}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Daniel can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pamela","Delia","James","Daniel"],"index":1619,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9784042239,"difficulty":0.0215957761}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Richard. Joan's card is shown to Richard. Richard's card is shown to Brandy. Albert's card is shown to Brandy. Richard's card is shown to Joan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Albert","Brandy","Joan"],"index":837,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.977801621,"difficulty":0.022198379}
-{"premise":"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's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Floyd can now know that Carlos can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Floyd","John","Charlie","Carlos"],"index":7512,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9737340808,"difficulty":0.0262659192}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William is thirsty. It is publicly announced that William does not know whether Joy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Joy can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joy","William"],"index":1940,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9062306285,"difficulty":1.9062306285}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Jacqueline can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacqueline","Mary","Judy","Elizabeth"],"index":6539,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9208932519,"difficulty":0.0791067481}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether Shante is thirsty. It is publicly announced that Elizabeth does not know whether Shante is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Stephen can now know whether Shante can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shante","Stephen","Timothy","Elizabeth"],"index":1812,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9254819155,"difficulty":0.0745180845}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin is thirsty. It is publicly announced that Justin does not know whether Kimberly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Richard can now know whether William can know whether Kimberly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Kimberly","Justin","William"],"index":6637,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8739566207,"difficulty":0.1260433793}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lola knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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 that Rosemary can know that Lola's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tracy","Rosemary","Robert","Lola"],"index":2344,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9737504721,"difficulty":0.0262495279}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mia's card is shown to Lucille. Lucille's card is shown to Mia. It is publicly announced that someone picked a red card. It is publicly announced that Mia knows whether Mia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (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":"Lucille can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lucille","Mia"],"index":5346,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9734645486,"difficulty":0.0265354514}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Marlene. Alonzo's card is shown to Marlene. Alonzo's card is shown to Elizabeth. Elizabeth's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marlene can now know whether William can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marlene","Elizabeth","William","Alonzo"],"index":594,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9758089781,"difficulty":0.0241910219}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Timothy. Timothy's card is shown to Courtney. Timothy's card is shown to Michael. Courtney's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Courtney does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know whether Timothy can know that Timothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Courtney","Michael"],"index":5575,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5651738644,"difficulty":0.4348261356}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Carla. Carla's card is shown to John. Ruby's card is shown to John. John's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card. It is publicly announced that John knows whether someone picked a red card. It is publicly announced that Carla does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carla","John","Ruby"],"index":3329,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7205466628,"difficulty":1.7205466628}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 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:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"James can now know that Joan can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jenine","Joan","James"],"index":1139,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9755790234,"difficulty":0.0244209766}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roderick knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Ryan can now know whether Roderick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jodi","Ryan","Roderick","Michael"],"index":9376,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9018067122,"difficulty":0.0981932878}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bethann knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Adina can now know that Bethann can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Bethann","Bobbie","Adina"],"index":874,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9788205028,"difficulty":0.0211794972}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Edward can now know that Becky's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edward","Becky"],"index":4829,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9854215384,"difficulty":0.0145784616}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glenn's card is shown to Melvin. Madge's card is shown to Melvin. Melvin's card is shown to Glenn. Melvin's card is shown to Madge. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Madge can now know that Glenn can know that Melvin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melvin","Glenn","Madge"],"index":4835,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9783187509,"difficulty":0.0216812491}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Travis's card is shown to Joyce. Jeffery's card is shown to Travis. Joyce's card is shown to Stanley. Travis's card is shown to Jeffery. It is publicly announced that someone picked a red card. It is publicly announced that Stanley does not know whether Jeffery picked a red card. It is publicly announced that Joyce picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Jeffery can now know that Travis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Travis","Stanley","Jeffery"],"index":4361,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9755383134,"difficulty":0.0244616866}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Terrance is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Susan can now know that Terrance can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","Donna","Judy","Terrance"],"index":375,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9791617393,"difficulty":0.0208382607}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanna's card is shown to Sarah. Sarah's card is shown to Joanna. Joanna's card is shown to Leslie. Leslie's card is shown to Cleveland. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know that Cleveland can know that Cleveland picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","Joanna","Leslie","Cleveland"],"index":2879,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786524773,"difficulty":0.0213475227}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Oswaldo can now know that Lawrence can know that Lawrence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lawrence","Oswaldo","Catherine"],"index":3962,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865521789,"difficulty":0.0134478211}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tai's card is shown to Sarah. Sarah's card is shown to Tai. Andrea's card is shown to Tai. Sarah's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Tai picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Tai can now know whether Andrea can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Tai","Andrea"],"index":8875,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9755282998,"difficulty":0.0244717002}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Marshall. Marshall's card is shown to Sharon. Yvonne's card is shown to Sharon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sharon can now know whether Yvonne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marshall","Sharon","Yvonne"],"index":3691,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6514585018,"difficulty":0.3485414982}
-{"premise":"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 Mike knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Joe can now know whether Mike can know that Mike's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mike","Joe"],"index":8716,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8592682481,"difficulty":1.8592682481}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Marsha can now know that Vanessa can know whether Harriet is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marsha","Harriet","Vanessa"],"index":8601,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.656219542,"difficulty":0.343780458}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether Samantha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows 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":"Ruth can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ruth","Nicole","Samantha"],"index":3991,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9816434979,"difficulty":0.0183565021}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Judith can now know that Stefanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Judith","Stefanie"],"index":6147,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860898256,"difficulty":0.0139101744}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Lewis. George's card is shown to Lewis. George's card is shown to Jessica. Jessica's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Jessica picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Lewis can now know that George can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lewis","Jessica","George"],"index":6758,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9777647853,"difficulty":0.0222352147}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Dolores can now know whether Enrique can know that Enrique's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Enrique","Dolores","Steven","Cassie"],"index":1136,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8092215061,"difficulty":1.8092215061}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juan can now know whether Leroy can know that Doris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juan","Leroy","Amber","Doris"],"index":5903,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9475431442,"difficulty":0.0524568558}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shelley can now know that Faith can know whether Faith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Shelley","Faith","Gregory"],"index":1114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9512447715,"difficulty":0.0487552285}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ervin knows whether Virgina's forehead is muddy. It is publicly announced that Ervin does not know whether Ervin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows 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 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Robert can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ervin","Virgina","Robert"],"index":8735,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.975456059,"difficulty":0.024543941}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ashley can now know that Gladys's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gladys","Robert","Ashley","Margaret"],"index":1128,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858629107,"difficulty":0.0141370893}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Patricia can now know that Laura can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Percy","Randy","Laura"],"index":4663,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9777255058,"difficulty":0.0222744942}
-{"premise":"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 Salvador's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Salvador can now know that Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Thomas","Salvador","Robert"],"index":860,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9782002568,"difficulty":0.0217997432}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ethel knows whether Antonio's forehead is muddy. It is publicly announced that Ethel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Ethel can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Antonio","Ethel"],"index":6039,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9687758684,"difficulty":0.0312241316}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa does not know whether Erica is thirsty. It is publicly announced that Lisa does not know whether Erica is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lisa can now know that Erica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Carolyn","Erica","David"],"index":3523,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.975014925,"difficulty":0.024985075}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sharon can now know whether Olivia can know that Olivia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sharon","Reba","Tom","Olivia"],"index":9128,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7049180865,"difficulty":1.7049180865}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Pamela. Pamela's card is shown to Nettie. It is publicly announced that someone picked a red card. It is publicly announced that Rosemary knows whether someone picked a red card. It is publicly announced that Pamela picked a red card. It is publicly announced that Rosemary does not know whether Rosemary picked a red card. It is publicly announced that Rosemary does not know whether Rosemary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Rosemary can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pamela","Rosemary","Nettie"],"index":8849,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9671729207,"difficulty":0.0328270793}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Florence's card is shown to Racheal. Racheal's card is shown to Madeline. Racheal's card is shown to Florence. Madeline's card is shown to Florence. It is publicly announced that someone picked a red card. It is publicly announced that Madeline does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Racheal can now know whether Madeline can know that Racheal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Racheal","Madeline","Florence"],"index":2009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5650855303,"difficulty":0.4349144697}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Rachel. Rachel's card is shown to Michelle. It is publicly announced that someone picked a red card. It is publicly announced that Rachel does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Michelle can now know that Rachel can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rachel","Michelle"],"index":5062,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9660408497,"difficulty":0.0339591503}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether Liliana's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Nicolas can now know that Liliana can know whether Liliana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicolas","Anna","Donna","Liliana"],"index":7106,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9635083079,"difficulty":0.0364916921}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amy can now know that Victor can know that Rosanna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victor","Rosanna","Jacqueline","Amy"],"index":7605,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864475727,"difficulty":0.0135524273}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sonja's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Kristen can now know that Sonja can know whether Sonja's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irwin","Sonja","Kristen","Robert"],"index":8113,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8998555541,"difficulty":0.1001444459}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramona knows whether Morton's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Morton can now know whether Morton's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ramona","Ruby","Morton","Tiffany"],"index":4609,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9083694816,"difficulty":1.9083694816}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee does not know whether Lee's forehead is muddy. It is publicly announced that Charles knows whether Janie's forehead is muddy. It is publicly announced that John's forehead is not muddy. It is publicly announced that Charles's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"John can now know whether Lee's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lee","Charles","John","Janie"],"index":6393,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8961320519,"difficulty":0.1038679481}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tessa can now know whether Stephen can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annie","Stephen","Tessa","James"],"index":4475,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9470121264,"difficulty":0.0529878736}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Marion. Marion's card is shown to Ruth. Theresa's card is shown to Ruth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ruth can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marion","Ruth","Theresa"],"index":7800,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9677730203,"difficulty":0.0322269797}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Dean. Dean's card is shown to Christopher. Jeffrey's card is shown to Jermaine. Jermaine's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that Jermaine can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dean","Christopher","Jermaine","Jeffrey"],"index":3142,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.921746254,"difficulty":0.078253746}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Mitchell. Freddie's card is shown to Mitchell. Mitchell's card is shown to Carl. Freddie's card is shown to Shirley. Mitchell's card is shown to Freddie. Shirley's card is shown to Freddie. It is publicly announced that someone picked a red card. It is publicly announced that Mitchell knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Carl can now know whether Freddie can know whether Mitchell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mitchell","Carl","Shirley","Freddie"],"index":853,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8993957043,"difficulty":0.1006042957}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Peter can now know that Todd's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angel","Todd","Peter"],"index":1503,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9779242873,"difficulty":0.0220757127}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryn's card is shown to Rhonda. Micki's card is shown to Rhonda. Rhonda's card is shown to Micki. Rhonda's card is shown to Oma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kathryn can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rhonda","Kathryn","Micki","Oma"],"index":5073,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9778990746,"difficulty":0.0221009254}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beckie's card is shown to Kate. Bonnie's card is shown to Kate. Kate's card is shown to Beckie. Bonnie's card is shown to Beckie. Kate's card is shown to Erik. Kate's card is shown to Bonnie. It is publicly announced that someone picked a red card. It is publicly announced that Erik does not know whether Erik picked a red card. It is publicly announced that Bonnie does not know whether or not everyone picked a red card. It is publicly announced that Beckie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(2) ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"Bonnie can now know that Kate picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kate","Beckie","Erik","Bonnie"],"index":3257,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9629070163,"difficulty":1.9629070163}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Tanya can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tanya","Charles","Thomas"],"index":7325,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.6751272082,"difficulty":0.3248727918}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allen's card is shown to Larry. Allen's card is shown to Timothy. Larry's card is shown to William. Timothy's card is shown to William. Allen's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Allen can now know that Timothy can know whether William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Timothy","Allen","William"],"index":4184,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6709389091,"difficulty":1.6709389091}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Cathrine can now know that Tony can know that Rachel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cathrine","Tony","Rachel"],"index":6388,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9781726599,"difficulty":1.9781726599}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether or not nobody's forehead is muddy. It is publicly announced that Cynthia does not know whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Cynthia can now know whether Bernard can know whether Maxine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maxine","Cynthia","Bernard","Matthew"],"index":5004,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9471397996,"difficulty":0.0528602004}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fidel can now know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Isaac","Albert","Fidel"],"index":3124,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864355922,"difficulty":0.0135644078}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heather can now know that Deborah can know that Heather's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roy","Heather","Deborah","Melanie"],"index":5631,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865554571,"difficulty":0.0134445429}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph knows whether Joseph is thirsty. It is publicly announced that Pamela does not know whether Julie is thirsty. It is publicly announced that Joseph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Frederick can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frederick","Joseph","Pamela","Julie"],"index":1593,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9722632766,"difficulty":0.0277367234}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clay's card is shown to Laura. Laura's card is shown to Clay. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Laura can now know that Clay can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Laura","Clay"],"index":739,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9776776433,"difficulty":0.0223223567}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Linda. Karan's card is shown to Linda. Linda's card is shown to Brenda. Joel's card is shown to Brenda. Linda's card is shown to Karan. Brenda's card is shown to Karan. Linda's card is shown to Joel. Brenda's card is shown to Joel. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joel picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Karan can now know whether Linda can know whether Joel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Brenda","Karan","Joel"],"index":9464,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8921115398,"difficulty":0.1078884602}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Matthew can now know that Gloria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gloria","Matthew","Laurence","Roy"],"index":2213,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.98607409,"difficulty":0.01392591}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Juliette can now know whether James can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Juliette"],"index":2159,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5870816112,"difficulty":1.5870816112}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jewel can now know whether Renee can know that Renee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Renee","Jewel","Angela"],"index":8135,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9478412271,"difficulty":0.0521587729}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steve knows whether Sherman's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Omar can now know whether Patricia can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Omar","Patricia","Steve","Sherman"],"index":6461,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9395183325,"difficulty":0.0604816675}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristina's card is shown to Robert. Robert's card is shown to Cristina. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Cristina knows whether Robert picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Cristina can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Cristina"],"index":2031,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9770773649,"difficulty":0.0229226351}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heather can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Heather","Irene","Barbara","Mildred"],"index":6035,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9808681607,"difficulty":0.0191318393}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosemary knows whether Aisha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Thomas can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rosemary","Gary","Aisha","Thomas"],"index":6882,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9815118909,"difficulty":0.0184881091}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 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":"Mabel can now know whether Charles can know that Dale's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mabel","Allen","Dale","Charles"],"index":2286,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7662679553,"difficulty":0.2337320447}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Jeff can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","Jeff","Michael","Paula"],"index":2596,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9622601867,"difficulty":0.0377398133}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Cesar can now know that Stanford is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stanford","Lydia","Cesar","Javier"],"index":7382,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.979621768,"difficulty":0.020378232}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to George. Matthew's card is shown to Ed. George's card is shown to Matthew. George's card is shown to Julian. Ed's card is shown to Julian. It is publicly announced that someone picked a red card. It is publicly announced that Julian does not know whether Matthew picked a red card. It is publicly announced that Matthew does not know whether Matthew picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"George can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Ed","Matthew","Julian"],"index":9082,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.973856926,"difficulty":0.026143074}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mike can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Raphael","Mike","Bernice"],"index":4713,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858048558,"difficulty":0.0141951442}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Jason can now know that Marilyn can know whether Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marilyn","Jason"],"index":7010,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9519889951,"difficulty":0.0480110049}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Sarah can now know that Kenneth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Sarah","Tona","Vivian"],"index":759,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9796152711,"difficulty":0.0203847289}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nestor's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Nestor can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Orlando","Jose","Nestor"],"index":9059,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.985973835,"difficulty":0.014026165}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Brian. Diane's card is shown to John. Brian's card is shown to Diane. It is publicly announced that someone picked a red card. It is publicly announced that Diane does not know whether John picked a red card. It is publicly announced that Brian does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brian can now know that Diane can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","John","Diane"],"index":2519,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9627837539,"difficulty":0.0372162461}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"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":"Karla can now know that Billy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Karla","Billy"],"index":4031,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9777116776,"difficulty":0.0222883224}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Ronald can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Beverley","Ronald","Jay"],"index":7711,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9401772022,"difficulty":0.0598227978}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shaun can now know that Timothy can know that Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Julia","James","Shaun"],"index":1138,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864987135,"difficulty":0.0135012865}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jake does not know whether Jake's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy. It is publicly announced that Jon does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jon can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jake","Joyce","Richard","Jon"],"index":9543,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9669472575,"difficulty":0.0330527425}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gerri can now know whether Rosita can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosita","Gerri","Paul","Alice"],"index":3622,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9787205458,"difficulty":0.0212794542}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Newton's forehead is muddy. It is publicly announced that Gregory's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Gary can now know that Gregory can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bryan","Gary","Newton","Gregory"],"index":5144,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9809220433,"difficulty":0.0190779567}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Gregory can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eleanor","Bradley","Matthew","Gregory"],"index":8198,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9624577165,"difficulty":0.0375422835}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wesley does not know whether Rachel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Carmen can now know that Rachel can know that Rachel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wesley","Rachel","Carmen","William"],"index":2409,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9765821099,"difficulty":0.0234178901}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Terrance's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Harvey can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Terrance","Jose","Calvin","Harvey"],"index":2426,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9784786701,"difficulty":0.0215213299}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Milton can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Milton","Clay"],"index":9055,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9811252356,"difficulty":0.0188747644}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Marilyn can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gilbert","Marilyn","Stephanie"],"index":6900,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857847095,"difficulty":0.0142152905}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Etsuko can now know whether Jennifer can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sophia","Jennifer","Etsuko"],"index":3278,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9791930914,"difficulty":0.0208069086}
-{"premise":"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 Kimberley's forehead is muddy. It is publicly announced that Kimberley does not know whether or not everyone's forehead is muddy. It is publicly announced that Kimberley does not know whether Kimberley's forehead 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 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kimberley can now know that William can know whether Kimberley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lacy","Melissa","Kimberley","William"],"index":7567,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9014709592,"difficulty":0.0985290408}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denise's card is shown to William. Randa's card is shown to William. Denise's card is shown to Randa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Denise","William","Randa"],"index":603,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6581169963,"difficulty":0.3418830037}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Lucretia. Nancy's card is shown to Lucretia. Lucretia's card is shown to Bonnie. Nancy's card is shown to Bonnie. Bonnie's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Nancy does not know whether Lucretia picked a red card. It is publicly announced that Lucretia knows whether Nancy picked a red card. It is publicly announced that Nancy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bonnie can now know whether Bonnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lucretia","Bonnie","Nancy"],"index":5487,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6446390748,"difficulty":0.3553609252}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale does not know whether Dale's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dale can now know that Dale's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dale","Jaclyn"],"index":453,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.979802072,"difficulty":0.020197928}
-{"premise":"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 Paul knows whether or not everyone's forehead is muddy. It is publicly announced that Paul does not know whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Christine can now know that Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tara","Paul","Christine"],"index":6925,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9654391408,"difficulty":0.0345608592}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 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":"Jerry can now know whether Jerry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Helen","Jerry","Patrick"],"index":6893,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8251108527,"difficulty":0.1748891473}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cathy knows whether or not nobody is thirsty. It is publicly announced that Cathy knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Anna can now know whether Cathy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cathy","Anna"],"index":3365,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9147996902,"difficulty":0.0852003098}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ricky does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Velma can now know that Ricky can know that Joni is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ricky","Velma","Joni","Debbie"],"index":7488,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9620753527,"difficulty":0.0379246473}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Holly knows whether Jerome's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Liz can now know that Holly can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eugene","Liz","Holly","Jerome"],"index":3585,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9855654836,"difficulty":0.0144345164}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amber's card is shown to Shawna. Shawna's card is shown to Tanesha. Shawna's card is shown to Amber. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tanesha can now know whether Shawna can know that Shawna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shawna","Tanesha","Amber"],"index":8811,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6792292595,"difficulty":0.3207707405}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Lisa. Lisa's card is shown to Nancy. Lisa's card is shown to Stephen. Nancy's card is shown to Stephen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephen can now know whether Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Nancy","Stephen"],"index":3972,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6604964733,"difficulty":0.3395035267}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Carl can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carl","Renee","Daniel"],"index":8548,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9801751971,"difficulty":0.0198248029}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Olen","Robert","William","Theresa"],"index":2624,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.982578218,"difficulty":0.017421782}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to John. John's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Willie knows whether or not nobody picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Willie can now know whether John can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Willie"],"index":7798,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9357403517,"difficulty":0.0642596483}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Frances. Frances's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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":"Frances can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Frances","Timothy"],"index":6316,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8968200088,"difficulty":1.8968200088}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Elizabeth. Elizabeth's card is shown to Gary. Sylvia's card is shown to Gary. Gary's card is shown to Sylvia. Kelly's card is shown to Sylvia. Gary's card is shown to Kelly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kelly can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Gary","Sylvia","Kelly"],"index":571,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9184473753,"difficulty":0.0815526247}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Bennie can now know that Bennie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bennie","David","Amanda"],"index":1519,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860998988,"difficulty":0.0139001012}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"James can now know that Joe can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Joe","Vicki","James"],"index":7874,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9792078137,"difficulty":0.0207921863}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith knows whether Keith's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Laura can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Keith","Laura"],"index":604,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9771795869,"difficulty":0.0228204131}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Glenn. Gloria's card is shown to Ann. Glenn's card is shown to Gloria. Ann's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that Ann knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Gloria can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glenn","Ann","Gloria"],"index":314,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9716157913,"difficulty":0.0283842087}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marisol's forehead 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 3)","n_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":"George can now know whether Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Marisol","Christopher"],"index":8768,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8829733729,"difficulty":0.1170266271}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Alfred can now know whether Tracey can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alfred","Mildred","Tracey"],"index":2651,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9709223509,"difficulty":0.0290776491}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mollie knows whether Mollie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lorna can now know whether Antonio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Mollie","Lorna","Antonio"],"index":2669,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9666166902,"difficulty":0.0333833098}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 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":"Luis can now know that Jaime can know that Denise's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Luis","William","Jaime","Denise"],"index":9027,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823854566,"difficulty":0.0176145434}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (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":"Jean can now know whether Linda can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Lester","Jean"],"index":7239,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9762855768,"difficulty":0.0237144232}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"George can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Steven","George"],"index":1950,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9800963998,"difficulty":0.0199036002}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willa knows whether someone's forehead is muddy. It is publicly announced that Leah knows whether Juan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Robert can now know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leah","Juan","Willa","Robert"],"index":380,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.962511003,"difficulty":0.037488997}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Vernon can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Steve","Vernon"],"index":3986,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858967662,"difficulty":0.0141032338}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Elizabeth. Gregory's card is shown to Pauline. Elizabeth's card is shown to Pauline. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Pauline picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Elizabeth can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregory","Elizabeth","Pauline"],"index":8261,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9759952426,"difficulty":0.0240047574}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joyce can now know whether Brenda can know that Joyce is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bobby","Joyce","Brenda","Joel"],"index":3371,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5477160215,"difficulty":1.5477160215}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thelma can now know whether David can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosa","David","Thelma","Felton"],"index":3640,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9449697733,"difficulty":0.0550302267}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucas's card is shown to Christopher. Lucas's card is shown to James. James's card is shown to Lucas. Christopher's card is shown to Adrian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lucas can now know that Adrian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","James","Lucas","Adrian"],"index":8401,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9787515998,"difficulty":0.0212484002}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paula can now know that Yvone can know that Yvone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Yvone","Paula","Joseph"],"index":152,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9822291136,"difficulty":0.0177708864}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Charles. Charles's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"William can now know that Charles can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charles","William"],"index":2097,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9630883336,"difficulty":0.0369116664}
-{"premise":"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 Junior knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Amanda can now know that Junior can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Junior","Amanda"],"index":6228,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9731997252,"difficulty":0.0268002748}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amanda","Mary","Patricia"],"index":41,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864451289,"difficulty":0.0135548711}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Krystal can now know whether Joel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Krystal","John","Joel"],"index":509,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9706483483,"difficulty":0.0293516517}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maurice does not know whether Maurice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jesse can now know whether Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maurice","Jesse","Manuel","Margaret"],"index":1769,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8986061811,"difficulty":0.1013938189}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether Jon's forehead is muddy. It is publicly announced that Jon knows whether Jon's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jon can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jacqueline","Jon"],"index":9364,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9837865233,"difficulty":0.0162134767}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julio's card is shown to David. David's card is shown to Linda. Roy's card is shown to Julio. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Roy picked a red card. It is publicly announced that Roy knows whether or not nobody picked a red card. It is publicly announced that David does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Roy can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Roy","Linda","Julio"],"index":6824,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9710167646,"difficulty":0.0289832354}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alexander does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Michael can now know that Mary can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Alexander","Mike","Mary"],"index":2966,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9765377641,"difficulty":0.0234622359}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bertha's card is shown to Patricia. Laura's card is shown to Patricia. Laura's card is shown to Bertha. Bertha's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bertha can now know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Patricia","Bertha","Laura"],"index":1320,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6389656663,"difficulty":1.6389656663}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harriet is not thirsty. It is publicly announced that Tabitha is not thirsty. It is publicly announced that Harriet does not know whether Lynda is thirsty. It is publicly announced that Lynda knows whether Lynda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Harriet can now know that Tabitha can know whether Tabitha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bernard","Harriet","Tabitha","Lynda"],"index":1661,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7681893706,"difficulty":0.2318106294}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Jeffrey can now know whether Marcia can know that Marcia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marcia","Jaime","Jeffrey"],"index":468,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8577576876,"difficulty":1.8577576876}
-{"premise":"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 Kathleen knows whether or not everyone's forehead is muddy. It is publicly announced that Kathleen does not know whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Amy can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amy","Kathleen","William"],"index":6787,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8369253278,"difficulty":0.1630746722}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Richard can now know whether Harold can know whether Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Harold","Richard"],"index":555,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9702433944,"difficulty":0.0297566056}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Christopher. Andrea's card is shown to Willis. Andrea's card is shown to Douglas. Douglas's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Willis knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Willis can now know that Christopher can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Willis","Douglas","Andrea"],"index":7706,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9721634388,"difficulty":0.0278365612}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lori does not know whether Patrick is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Lori can now know whether Edith can know whether Lori is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patrick","Edith","Lori"],"index":4041,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8494950533,"difficulty":0.1505049467}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara knows whether Deborah's forehead is muddy. It is publicly announced that Deborah knows whether Tamara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Flora can now know that Tamara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tamara","Deborah","Flora"],"index":8806,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9843988419,"difficulty":0.0156011581}
-{"premise":"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 Jennifer does not know whether Jennifer's forehead is muddy. It is publicly announced that Edward'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 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Jennifer can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Edward","Catherine"],"index":6149,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9782552123,"difficulty":0.0217447877}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anita's card is shown to Ronnie. Ronnie's card is shown to Anita. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows 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":"Ronnie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ronnie","Anita"],"index":467,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9779134393,"difficulty":0.0220865607}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mollie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ramon can now know whether Mollie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lien","Ramon","Roosevelt","Mollie"],"index":2659,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9700869918,"difficulty":0.0299130082}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Scott is thirsty. It is publicly announced that Scott is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Jennifer can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jennifer","Scott"],"index":1026,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.975682199,"difficulty":0.024317801}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Juan is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Michael can now know that Juan can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Juan"],"index":3954,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9770182371,"difficulty":0.0229817629}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Edward is thirsty. It is publicly announced that Edward knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Mary can now know that Edward is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edward","Mary"],"index":7366,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9378162622,"difficulty":0.0621837378}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Richard can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debra","Richard","Howard"],"index":5285,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9809877872,"difficulty":0.0190122128}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carlos can now know whether Karl can know whether Rae is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rae","Willard","Karl","Carlos"],"index":3108,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8097859025,"difficulty":0.1902140975}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Ronald. Ronald's card is shown to Kathleen. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 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":"Ronald can now know that Kathleen can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronald","Kathleen"],"index":4182,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9772924185,"difficulty":0.0227075815}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donna can now know that Pamela can know that Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Barry","Donna"],"index":353,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865369797,"difficulty":0.0134630203}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Curtis knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Garland can now know that Dana can know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Curtis","Garland","Dana"],"index":8370,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856648445,"difficulty":0.0143351555}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lilly's card is shown to Aubrey. Walter's card is shown to Aubrey. Aubrey's card is shown to Lilly. It is publicly announced that someone picked a red card. It is publicly announced that Lilly does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lilly can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Aubrey","Lilly","Walter"],"index":8994,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9651776552,"difficulty":0.0348223448}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell does not know whether Darrell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Darrell can now know that Kevin can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Brett","Darrell","Kevin"],"index":1846,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9792128205,"difficulty":0.0207871795}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Scott can now know whether Michael can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Michael","Glenda"],"index":1269,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8666590452,"difficulty":0.1333409548}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sergio can now know whether Monique can know that Aaron's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lenore","Sergio","Monique","Aaron"],"index":2732,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.952822268,"difficulty":0.047177732}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patti knows whether someone is thirsty. It is publicly announced that Patti knows whether Adam is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Adam can now know whether Patti can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Adam","Patti"],"index":6159,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9704167247,"difficulty":0.0295832753}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martin does not know whether Dennis is thirsty. It is publicly announced that Dennis knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Martin can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dennis","Martin"],"index":6234,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9647915959,"difficulty":0.0352084041}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","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":"Steven can now know whether Scott can know that Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steven","Scott","Claire"],"index":1717,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7247690558,"difficulty":1.7247690558}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Paula can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jan","Kelly","Christopher","Paula"],"index":3008,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9681789279,"difficulty":0.0318210721}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"William can now know that Shane can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Jose","Shane"],"index":5759,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9265822172,"difficulty":1.9265822172}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Johnny can now know that April can know whether Gisela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gisela","April","Johnny","Joel"],"index":7598,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6024553776,"difficulty":0.3975446224}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Irma can now know whether Jimmy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irma","Larry","Jimmy","Jessica"],"index":6793,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9715230465,"difficulty":0.0284769535}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen does not know whether Pamela is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Benjamin can now know that Martin can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pamela","Karen","Benjamin","Martin"],"index":1853,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9637208581,"difficulty":0.0362791419}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Courtney's card is shown to Arthur. Sandra's card is shown to Arthur. Arthur's card is shown to Courtney. Sandra's card is shown to Courtney. Courtney's card is shown to Sandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Courtney can now know that Arthur picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arthur","Courtney","Sandra"],"index":7923,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786321521,"difficulty":0.0213678479}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Michelle. Michelle's card is shown to Rosemary. It is publicly announced that someone picked a red card. It is publicly announced that Michelle knows whether someone picked a red card. It is publicly announced that Michelle knows whether someone picked a red card. It is publicly announced that Michelle does not know whether Michelle picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rosemary can now know whether Michelle can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michelle","Rosemary"],"index":5596,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9744880199,"difficulty":0.0255119801}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Robert. Robert's card is shown to Glen. Robert's card is shown to Paul. Robert's card is shown to Eric. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Glen can now know whether Glen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Glen","Paul","Eric"],"index":4139,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6263700128,"difficulty":1.6263700128}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura does not know whether Michelle is thirsty. It is publicly announced that Laura is not thirsty. It is publicly announced that Michelle knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Laura can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Laura","Michelle","Edna"],"index":139,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9681376815,"difficulty":0.0318623185}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Roy can now know that Jeff can know that Jeff's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeff","Roy"],"index":5113,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865484834,"difficulty":0.0134515166}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Monty can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Monty","Janell","Michael","Karen"],"index":2579,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8324187398,"difficulty":0.1675812602}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlie does not know whether Erica is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Charlie can now know whether Charlie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Erica","Charlie"],"index":3706,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5849629045,"difficulty":0.4150370955}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrea can now know whether Katrina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katrina","Amy","Michael","Andrea"],"index":4656,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9610869288,"difficulty":0.0389130712}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alec is not thirsty. It is publicly announced that Alec knows whether or not nobody is thirsty. It is publicly announced that Kara knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Kara can now know that Alec is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alec","Kara"],"index":4944,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9579460621,"difficulty":0.0420539379}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Lester. Lester's card is shown to Beverly. It is publicly announced that someone picked a red card. It is publicly announced that Lester knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether 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":"Lester can now know whether Beverly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lester","Beverly"],"index":4201,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7612390518,"difficulty":0.2387609482}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura is not thirsty. It is publicly announced that Rachel does not know whether Eva is thirsty. It is publicly announced that Alec does not know whether Eva is thirsty. It is publicly announced that Rachel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] Agentd knows that (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] 0","hypothesis":"Alec can now know that Eva can know that Laura is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Rachel","Eva","Alec"],"index":8086,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9744377136,"difficulty":0.0255622864}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elias does not know whether Lori is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lori can now know that Elias can know that Terry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elias","Claire","Lori","Terry"],"index":8995,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9763569236,"difficulty":0.0236430764}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosendo's card is shown to Juanita. Juanita's card is shown to Rosendo. It is publicly announced that someone picked a red card. It is publicly announced that Rosendo knows whether Juanita picked a red card.","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":"Juanita can now know that Rosendo can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Juanita","Rosendo"],"index":3420,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9782147408,"difficulty":0.0217852592}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter does not know whether Peter's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Angela can now know whether Peter's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Peter","Angela","Olga","Carol"],"index":7501,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8963950872,"difficulty":0.1036049128}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Joseph is thirsty. It is publicly announced that Daniel knows whether Daniel is thirsty. It is publicly announced that Richard does not know whether Joseph is thirsty. It is publicly announced that Richard knows whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Richard can now know whether Joseph can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Daniel","Joseph"],"index":4213,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9740265608,"difficulty":0.0259734392}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosemary knows whether or not nobody is thirsty. It is publicly announced that Rosemary is thirsty. It is publicly announced that Michelle does not know whether Billy is thirsty. It is publicly announced that Michelle does not know whether Billy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Michelle can now know whether Billy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Billy","Michelle","Rosemary"],"index":8809,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7550899386,"difficulty":1.7550899386}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Willie can now know that Randy can know whether Julie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Julie","Donald","Willie"],"index":2475,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9626522064,"difficulty":0.0373477936}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Autumn can now know that Lillian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lillian","Robert","Eula","Autumn"],"index":6410,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9826037288,"difficulty":0.0173962712}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Kelly can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Brenda","Sharon","Kelly"],"index":9556,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859423041,"difficulty":0.0140576959}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Asuncion's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Asuncion can now know that Bruce's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Asuncion","Bruce","Ronald","Sherry"],"index":1476,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860112667,"difficulty":0.0139887333}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"John can now know that David can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","John"],"index":6,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9691194892,"difficulty":0.0308805108}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marie can now know whether Steven can know whether Caryn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Steven","Caryn","Henry"],"index":7483,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8045457006,"difficulty":0.1954542994}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether Debra's forehead is muddy. It is publicly announced that Raymond does not know whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Debra can now know whether Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Raymond","Debra","Robert"],"index":8337,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9039946198,"difficulty":0.0960053802}
-{"premise":"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 Edna knows whether someone's forehead is muddy. It is publicly announced that Janice does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Linda can now know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Daniel","Edna","Janice"],"index":8605,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8952779174,"difficulty":0.1047220826}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Steven can now know that Arthur's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Arthur","Steven"],"index":2890,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9750077724,"difficulty":0.0249922276}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Tyrone can now know that Peter can know that Tyrone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Peter","Tyrone"],"index":3503,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9817506671,"difficulty":0.0182493329}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Derrick can now know that Sherrie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sherrie","John","Derrick","Marilyn"],"index":9125,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864761233,"difficulty":0.0135238767}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Christopher. Christopher's card is shown to Elizabeth. James's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know whether Christopher can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Elizabeth","James"],"index":383,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9761560559,"difficulty":0.0238439441}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daisy's card is shown to Jimmy. Jimmy's card is shown to Daisy. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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":"Daisy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jimmy","Daisy"],"index":6509,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9784116745,"difficulty":0.0215883255}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peggy's card is shown to Merle. Peggy's card is shown to Joseph. Merle's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Merle can now know whether Merle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Peggy","Merle","Joseph"],"index":3866,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6590746045,"difficulty":0.3409253955}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Russell can now know that Colette is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Colette","Russell"],"index":4222,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9809615016,"difficulty":0.0190384984}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lyle can now know whether Jason can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Russell","Lyle","Jason"],"index":5521,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9199000597,"difficulty":0.0800999403}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vanessa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Vanessa can now know whether Hazel can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vanessa","Hazel","Ernest"],"index":7787,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9441164732,"difficulty":0.0558835268}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"John can now know that Susan can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Susan"],"index":1300,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853357673,"difficulty":0.0146642327}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Loretta knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Loretta can now know that Roger can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roger","Mario","Betty","Loretta"],"index":8319,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9697269201,"difficulty":0.0302730799}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hilda does not know whether Hilda's forehead is muddy. It is publicly announced that Juliette does not know whether Juliette's forehead is muddy. It is publicly announced that Juliette 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jonathan can now know whether Juliette's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Juliette","Jonathan","Hilda"],"index":9575,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8587019444,"difficulty":0.1412980556}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Richard can now know that Sharon can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Gordon","Sharon","Esther"],"index":1011,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9782652855,"difficulty":0.0217347145}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Basil can now know that Rose can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rose","Michael","Basil"],"index":422,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9694458246,"difficulty":0.0305541754}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Don is not thirsty. It is publicly announced that Donald is not thirsty. It is publicly announced that Don does not know whether Joseph is thirsty. It is publicly announced that Joseph knows whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] Agenta knows that (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Crystal can now know that Donald can know that Don is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Crystal","Don","Donald","Joseph"],"index":2461,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.968724966,"difficulty":0.031275034}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marvin can now know that Patrica can know that Patrica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","James","Brenda","Patrica"],"index":5464,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864956737,"difficulty":0.0135043263}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juanita knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know whether Juanita can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Juanita","John"],"index":1583,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9786314964,"difficulty":0.0213685036}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Matthew. Matthew's card is shown to Laura. Donald's card is shown to Ashley. Matthew's card is shown to Donald. Laura's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Matthew does not know whether Ashley picked a red card. It is publicly announced that Matthew does not know whether Laura picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Matthew can now know that Ashley picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Laura","Ashley","Donald"],"index":8134,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9743773937,"difficulty":0.0256226063}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Scott can now know whether James can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","James","Scott","Stephen"],"index":7854,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.979116261,"difficulty":0.020883739}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula does not know whether Kaitlin is thirsty. It is publicly announced that Paula does not know whether Kaitlin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Kaitlin can now know that Paula can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kaitlin","Maria","Marilyn","Paula"],"index":1431,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9153910875,"difficulty":0.0846089125}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","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":"Gordon can now know that Karl can know whether Gordon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gordon","Karl","Lisa"],"index":8826,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8308029175,"difficulty":0.1691970825}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Howard does not know whether Antonio is thirsty. It is publicly announced that Howard does not know whether Antonio is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] Agentc knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"David can now know whether Howard can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Antonio","Ellen","David","Howard"],"index":2628,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5920543075,"difficulty":0.4079456925}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Earnestine's forehead is muddy. It is publicly announced that Kevin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Earnestine can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Earnestine","Kevin"],"index":6183,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8444046378,"difficulty":0.1555953622}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Clara. Melvin's card is shown to Doris. Doris's card is shown to Melvin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Doris can now know whether Doris picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clara","Doris","Melvin"],"index":7948,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6746385098,"difficulty":1.6746385098}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randolph does not know whether Randolph's forehead is muddy. It is publicly announced that Patricia's forehead is not muddy. It is publicly announced that Randolph's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] [ ! ~(2) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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) ] [ ! ~(2) ] 0","hypothesis":"Randolph can now know whether Patricia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Randolph","Donna","Patricia"],"index":5461,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.830735147,"difficulty":0.169264853}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eddie can now know whether Alvin can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eddie","Alvin","Pat"],"index":6427,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5215799212,"difficulty":0.4784200788}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janie does not know whether Emily is thirsty. It is publicly announced that Emily does not know whether Janie is thirsty. It is publicly announced that Janie does not know whether Carrie is thirsty. It is publicly announced that Janie does not know whether Jeanne is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Emily can now know that Carrie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janie","Emily","Jeanne","Carrie"],"index":3825,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9080109,"difficulty":0.0919891}
-{"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":"Elaine can now know that Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Claude","Ann","Kim","Elaine"],"index":7364,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9826015234,"difficulty":0.0173984766}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Jennifer. Johnny's card is shown to Weldon. Johnny's card is shown to Jason. Jason's card is shown to Johnny. It is publicly announced that someone picked a red card. It is publicly announced that Weldon knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Weldon can now know that Johnny can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Weldon","Jason","Johnny"],"index":3851,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9771680832,"difficulty":0.0228319168}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laurie does not know whether Amy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Amy can now know that Corinne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Corinne","Amy","Laurie"],"index":7664,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9766686559,"difficulty":0.0233313441}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mamie does not know whether or not everyone's forehead is muddy. It is publicly announced that Mamie does not know whether or not everyone's forehead is muddy. It is publicly announced that Cornelia 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 whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Mamie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cornelia","Mamie"],"index":2571,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8579732776,"difficulty":1.8579732776}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 1)","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":"Adam can now know that Doris can know whether Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Bethany","Adam","Wanda"],"index":6294,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8463027477,"difficulty":1.8463027477}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (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":"Patrick can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patrick","Ellis","John"],"index":3281,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9790412784,"difficulty":0.0209587216}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Rolando can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rolando","Anthony"],"index":6361,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9771015048,"difficulty":0.0228984952}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that June's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Thomas can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Laurie","June","Ryan"],"index":9508,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859349728,"difficulty":0.0140650272}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian knows whether or not everyone is thirsty. It is publicly announced that Tracy is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Tracy can now know whether Brian can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Brian","Tracy"],"index":1435,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9743306637,"difficulty":0.0256693363}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacob does not know whether Jacob's forehead is muddy. It is publicly announced that Jacob knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Jacob can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jacob","James"],"index":7477,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9543491602,"difficulty":1.9543491602}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Louis. Jeffery's card is shown to Louis. Louis's card is shown to Frances. Jeffery's card is shown to Caleb. Louis's card is shown to Jeffery. Caleb's card is shown to Jeffery. It is publicly announced that someone picked a red card. It is publicly announced that Louis knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Frances can now know that Caleb can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Frances","Caleb","Jeffery"],"index":890,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.711435914,"difficulty":1.711435914}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that Grady can know that Frank's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Grady","Frank","Kirk"],"index":4427,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865267873,"difficulty":0.0134732127}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clifford's card is shown to Juan. Catharine's card is shown to Juan. Juan's card is shown to Jeffery. Catharine's card is shown to Jeffery. Juan's card is shown to Clifford. Juan's card is shown to Catharine. Clifford's card is shown to Catharine. It is publicly announced that someone picked a red card. It is publicly announced that Catharine does not know whether Catharine picked a red card. It is publicly announced that Juan does not know whether Jeffery picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Clifford can now know whether Juan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Jeffery","Clifford","Catharine"],"index":591,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7571770549,"difficulty":0.2428229451}
-{"premise":"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 Desiree knows whether someone's forehead is muddy. It is publicly announced that Peggy does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Dorothy can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dorothy","Pedro","Desiree","Peggy"],"index":2132,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.970708549,"difficulty":0.029291451}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Ernest can now know that Ernest's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephen","Joseph","Ernest"],"index":811,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9782409668,"difficulty":0.0217590332}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 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) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know that Juanita can know that Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Juanita","James","Evelyn"],"index":2586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.979113996,"difficulty":0.020886004}
-{"premise":"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 Adrian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Irma can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Irma","Patrick","Adrian","Ruth"],"index":8121,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9730963111,"difficulty":0.0269036889}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicki can now know that Jesus can know whether Jesus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jesus","Laticia","Trevor","Nicki"],"index":130,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.843626678,"difficulty":1.843626678}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lori's card is shown to Evelyn. Cheryl's card is shown to Lori. Randy's card is shown to Lori. Evelyn's card is shown to Cheryl. Cheryl's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that Randy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Lori can now know whether Cheryl can know that Randy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Evelyn","Lori","Cheryl","Randy"],"index":8284,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5688265562,"difficulty":0.4311734438}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kamala can now know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kamala","Edward","Sandra","Dean"],"index":7794,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9814280272,"difficulty":0.0185719728}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Rosalee's forehead is muddy. It is publicly announced that Steven knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Rosalee can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","William","Rosalee"],"index":617,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9659261703,"difficulty":0.0340738297}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Darrell can now know that Joan can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","Darrell","Joan"],"index":6634,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9359110594,"difficulty":0.0640889406}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know that Maria can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jenny","Larry","Ronald","Maria"],"index":6764,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9359514713,"difficulty":0.0640485287}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Melvin knows whether Oda's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Oda can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Melvin","Oda"],"index":4952,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9809730053,"difficulty":0.0190269947}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rita is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Rita can now know that Ingrid can know that Jeffrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rita","Jeffrey","Ingrid"],"index":115,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9789453149,"difficulty":0.0210546851}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"David can now know that Eddy can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joe","Mary","David","Eddy"],"index":486,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9774463773,"difficulty":0.0225536227}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Olivia can now know that William can know whether Emilio's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Olivia","Emilio"],"index":6032,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8710389733,"difficulty":0.1289610267}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (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":"Lillian can now know whether Shawn can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arthur","Lillian","Eric","Shawn"],"index":3486,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9172110558,"difficulty":0.0827889442}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mildred is not thirsty. It is publicly announced that Eusebia does not know whether Matthew is thirsty. It is publicly announced that Glenn does not know whether Matthew is thirsty. It is publicly announced that Eusebia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] Agentd knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] 0","hypothesis":"Glenn can now know that Mildred can know that Mildred is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Eusebia","Matthew","Glenn"],"index":38,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9726821184,"difficulty":0.0273178816}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steve knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Kathleen can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Steve","Kathleen"],"index":9418,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9708163738,"difficulty":0.0291836262}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bill's card is shown to Phyllis. Phyllis's card is shown to James. Bill's card is shown to William. William's card is shown to Bill. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Phyllis can now know whether Bill can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phyllis","James","William","Bill"],"index":4679,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9339993,"difficulty":0.0660007}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Tori is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"James can now know whether Micheal is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tori","Leon","James","Micheal"],"index":5585,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5893416405,"difficulty":1.5893416405}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesse knows whether David's forehead is muddy. It is publicly announced that Jesse's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Jesse can now know that David can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Jesse","David"],"index":7980,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9815545082,"difficulty":0.0184454918}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether or not everyone is thirsty. It is publicly announced that Kendra is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] 0","hypothesis":"Nancy can now know whether Kendra can know whether Kendra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kendra","Nancy","Rachel"],"index":5064,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8297224641,"difficulty":0.1702775359}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to Kathy. Kathy's card is shown to Robert. Martha's card is shown to Robert. Jacqueline's card is shown to Robert. Kathy's card is shown to Martha. Robert's card is shown to Jacqueline. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Martha can now know that Jacqueline can know whether Jacqueline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathy","Robert","Martha","Jacqueline"],"index":8771,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6897192597,"difficulty":1.6897192597}
-{"premise":"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 knows whether Pei's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Charlie can now know that Pei's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harold","Charlie","Pei"],"index":3478,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9814807773,"difficulty":0.0185192227}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Lisa. Lisa's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Lisa does not know whether Alfredo picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alfredo can now know whether Alfredo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alfredo","Lisa","George"],"index":876,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7690117955,"difficulty":1.7690117955}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christina can now know whether Terrance is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terrance","Christina","Penny","Robert"],"index":6152,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5751230717,"difficulty":0.4248769283}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darlene's card is shown to Audrie. Audrie's card is shown to Albert. Claude's card is shown to Albert. Albert's card is shown to Darlene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Audrie can now know that Darlene can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Audrie","Albert","Darlene","Claude"],"index":2406,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9777390361,"difficulty":0.0222609639}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Glory is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Nancy can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glory","Nancy","Rosa"],"index":535,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9795701504,"difficulty":0.0204298496}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Kenneth. Kenneth's card is shown to Jane. Kenneth's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kenneth","Jane","Robert"],"index":6855,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9684002995,"difficulty":0.0315997005}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edwin can now know whether Victoria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edwin","Jennifer","Linda","Victoria"],"index":5071,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8583903909,"difficulty":0.1416096091}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Lashonda. Carol's card is shown to Scott. Scott's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lashonda can now know whether Chad picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lashonda","Scott","Carol","Chad"],"index":3754,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6462275982,"difficulty":1.6462275982}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jan can now know that Ada's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jan","Ted","Ada","Marjorie"],"index":3699,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859626889,"difficulty":0.0140373111}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peggy does not know whether or not everyone is thirsty. It is publicly announced that Charles does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Joseph can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peggy","Charles","Beverly","Joseph"],"index":3906,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.712400794,"difficulty":0.287599206}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Kathryn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Shannon can now know whether Kathryn can know that Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Shannon","Kathryn","Charles"],"index":8535,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5791489482,"difficulty":0.4208510518}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doris can now know that Anita can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Percy","Al","Anita","Doris"],"index":6309,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9825063944,"difficulty":0.0174936056}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Desiree's card is shown to Clinton. Lee's card is shown to Desiree. Clinton's card is shown to Lee. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Desiree can now know that Clinton can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clinton","Desiree","Lee"],"index":2072,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.970108211,"difficulty":0.029891789}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Julia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gene","Jane","Julia"],"index":9034,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860175252,"difficulty":0.0139824748}
-{"premise":"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.","smcdel_problem":"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":"John can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Danielle","John","Tiffany"],"index":4299,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9720163345,"difficulty":0.0279836655}
-{"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 (~(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 or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carlos","Stephanie","Henry","John"],"index":7097,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9640262127,"difficulty":0.0359737873}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Erma. Erma's card is shown to Roland. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Erma can now know that Roland can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Erma","Roland"],"index":6027,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9177395105,"difficulty":0.0822604895}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betsy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Carlos can now know whether Betsy can know that Carlos is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carlos","Betsy"],"index":8810,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6127843857,"difficulty":1.6127843857}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Haydee's card is shown to Joseph. Joseph's card is shown to Haydee. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Joseph can now know that Haydee can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joseph","Haydee"],"index":171,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9632971287,"difficulty":0.0367028713}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Antonio. Antonio's card is shown to Seth. Antonio's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Seth can now know whether Seth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Antonio","Seth","Joseph"],"index":4868,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7505415678,"difficulty":1.7505415678}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kurt can now know that Matthew can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kurt","Matthew","John"],"index":4967,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8304985762,"difficulty":0.1695014238}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Marjorie. Kathy's card is shown to Marjorie. Marjorie's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marjorie","Robert","Kathy"],"index":6960,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6600799561,"difficulty":1.6600799561}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Cecelia. Richard's card is shown to Elaine. Richard's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Cecelia does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Elaine can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cecelia","Elaine","Donna","Richard"],"index":4155,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9746667743,"difficulty":0.0253332257}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Robert can now know whether Daniel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daniel","Robert"],"index":73,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9714077115,"difficulty":0.0285922885}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ray can now know that Migdalia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ray","Migdalia","Samuel","Susan"],"index":8890,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9775760174,"difficulty":0.0224239826}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alfred's card is shown to Robert. Robert's card is shown to Alfred. Alfred's card is shown to Rocco. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Robert can now know that Rocco picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Alfred","Rocco"],"index":3482,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.977740407,"difficulty":0.022259593}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jo does not know whether Jo's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jo can now know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jo","Richard"],"index":2798,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9797651172,"difficulty":1.9797651172}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that Regina can know that Jerrell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Jerrell","Regina","David"],"index":6318,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864994287,"difficulty":0.0135005713}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Orlando can now know whether Sarita can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarita","Norma","Orlando"],"index":1820,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9750934243,"difficulty":0.0249065757}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Michael can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Andrew","Michael"],"index":3990,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9826891422,"difficulty":0.0173108578}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mae does not know whether Mike is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Carla can now know whether Raymond is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mike","Carla","Mae","Raymond"],"index":9157,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6235641837,"difficulty":1.6235641837}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether Tiffany is thirsty. It is publicly announced that Tiffany knows whether someone is thirsty. It is publicly announced that Kimberly does not know whether Tiffany is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Tiffany can now know that Jesus can know that Tiffany is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jesus","Kimberly","Tiffany"],"index":8636,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9519757032,"difficulty":0.0480242968}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Marget can now know that Anna can know that Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michelle","Anna","Marget"],"index":4499,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860024452,"difficulty":0.0139975548}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Vernon. Diane's card is shown to Jessica. Diane's card is shown to Alexandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessica can now know whether Diane can know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Diane","Vernon","Jessica","Alexandra"],"index":918,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8996073008,"difficulty":0.1003926992}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin knows whether or not everyone's forehead is muddy. It is publicly announced that Danielle does not know whether Danielle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agentc 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) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Benjamin can now know that Linda can know that Danielle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Danielle","Benjamin"],"index":1718,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9685817957,"difficulty":0.0314182043}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Dorothy. Dorothy's card is shown to William. Doris's card is shown to William. Carl's card is shown to William. Dorothy's card is shown to Doris. William's card is shown to Carl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doris can now know that Carl can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","William","Doris","Carl"],"index":9549,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9768710732,"difficulty":0.0231289268}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jack can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daniel","Jack","Tim"],"index":7048,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9782360792,"difficulty":0.0217639208}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Claude. Bobbie's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Claude","James","Bobbie"],"index":2715,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9784508944,"difficulty":0.0215491056}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Angelo. Angelo's card is shown to Michael. Michael's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Angelo does not know whether Angelo picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Angelo can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angelo","Michael","Marie"],"index":7772,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7651920915,"difficulty":0.2348079085}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"John can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Lee"],"index":1033,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9421901107,"difficulty":0.0578098893}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heather's card is shown to Deloris. Everette's card is shown to Deloris. John's card is shown to Deloris. Everette's card is shown to Heather. John's card is shown to Heather. Deloris's card is shown to Everette. Heather's card is shown to John. Everette's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deloris can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deloris","Heather","Everette","John"],"index":4610,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9240355492,"difficulty":0.0759644508}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theodore knows whether someone's forehead is muddy. It is publicly announced that Bobbi knows whether Walter's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Walter can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bobbi","Walter","Theodore","Wallace"],"index":5867,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9812520742,"difficulty":0.0187479258}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Steven. Steven's card is shown to Patricia. Patricia's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Patricia","James"],"index":9470,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9789392948,"difficulty":0.0210607052}
-{"premise":"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":"Leonard can now know whether Tia can know that Tia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tia","Leonard"],"index":6821,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.835375309,"difficulty":1.835375309}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Judith can now know that Dorothy can know that Ronald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Clare","Dorothy","Judith"],"index":6968,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864836335,"difficulty":0.0135163665}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Patricia. Patricia's card is shown to Leonard. Kenneth's card is shown to Leonard. Leonard's card is shown to Kenneth. Edwin's card is shown to Kenneth. Leonard's card is shown to Edwin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know that Leonard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Leonard","Kenneth","Edwin"],"index":929,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9775300622,"difficulty":0.0224699378}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Russell is thirsty. It is publicly announced that Russell does not know whether Shirley is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"George can now know whether Russell can know whether Russell is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Shirley","Russell","David"],"index":4220,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8826510906,"difficulty":0.1173489094}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Dave. Dave's card is shown to Sara. It is publicly announced that someone picked a red card. It is publicly announced that Dave does not know whether or not everyone picked a red card. It is publicly announced that Dave knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Sara can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dave","Sara"],"index":4553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8786487579,"difficulty":0.1213512421}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Manuel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Christopher can now know that Manuel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christopher","Robert","Manuel","Tomasa"],"index":2748,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9797033668,"difficulty":1.9797033668}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jorge knows whether Steve's forehead is muddy. It is publicly announced that Steve knows whether Jorge's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jorge can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jorge","Steve","Masako"],"index":5132,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9843565822,"difficulty":0.0156434178}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Miriam can now know that Billie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Megan","Billie","Miriam","Peter"],"index":3144,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9765265584,"difficulty":0.0234734416}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daisy does not know whether Greg is thirsty. It is publicly announced that Daisy knows whether Daisy is thirsty. It is publicly announced that Jane does not know whether Greg is thirsty. It is publicly announced that Jane knows whether Jane is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Daisy can now know that Greg can know whether Daisy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jane","Daisy","Greg"],"index":1360,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7312173247,"difficulty":1.7312173247}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candice knows whether Mark's forehead is muddy. It is publicly announced that Candice's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(2) ] (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":"Candice can now know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roxanne","Candice","Mark"],"index":1691,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9806314707,"difficulty":0.0193685293}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Letisha can now know that Norma can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Willie","Letisha","Norma"],"index":7915,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856869578,"difficulty":0.0143130422}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jon's card is shown to William. William's card is shown to Jon. It is publicly announced that someone picked a red card. It is publicly announced that Jon does not know whether Jon picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows 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":"William can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Jon"],"index":1104,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9755403399,"difficulty":0.0244596601}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony knows whether Anthony is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know whether Anthony can know whether Anthony is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Anthony"],"index":4929,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9007721543,"difficulty":0.0992278457}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Kirk can now know whether Kirk's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carl","Michael","Kirk"],"index":4189,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9131389856,"difficulty":1.9131389856}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty does not know whether Gerry is thirsty. It is publicly announced that Betty is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] 0","hypothesis":"Betty can now know whether Gerry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gerry","Tamara","Betty"],"index":7282,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.713608861,"difficulty":1.713608861}
-{"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 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":"Michelle can now know whether Jeffrey can know that Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mike","Jeffrey","Michelle","James"],"index":9374,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7088100314,"difficulty":1.7088100314}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melody's card is shown to Renee. Renee's card is shown to Melody. It is publicly announced that someone picked a red card. It is publicly announced that Melody does not know whether Melody picked a red card. It is publicly announced that Renee knows whether Melody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Melody can now know that Renee can know whether Melody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Renee","Melody"],"index":6771,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8210901022,"difficulty":0.1789098978}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheldon's card is shown to Patrick. Patrick's card is shown to Sheldon. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Sheldon knows whether Patrick picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Patrick can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Patrick","Sheldon"],"index":3005,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9779444337,"difficulty":0.0220555663}
-{"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)","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":"Raven can now know that Christopher can know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Mary","Raven"],"index":3132,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9824894667,"difficulty":0.0175105333}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guadalupe knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agenta knows 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":"Guadalupe can now know whether Maud can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maud","Doris","Guadalupe"],"index":2700,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9753463864,"difficulty":0.0246536136}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Walter. Dollie's card is shown to Joseph. Walter's card is shown to Dorothy. Joseph's card is shown to Dollie. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether Dollie picked a red card. It is publicly announced that Walter picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Dollie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Walter","Joseph","Dorothy","Dollie"],"index":9428,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9707435966,"difficulty":0.0292564034}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Cassandra can now know whether David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cassandra","David"],"index":9504,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6657791138,"difficulty":1.6657791138}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Gaston. Leon's card is shown to Gaston. Gaston's card is shown to Leon. Barbara's card is shown to Leon. It is publicly announced that someone picked a red card. It is publicly announced that Gaston picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Barbara can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gaston","Barbara","Leon"],"index":3527,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9780429602,"difficulty":0.0219570398}
-{"premise":"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 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 Eugene does not know whether Eugene's forehead is muddy.","smcdel_problem":"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) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Judy can now know that Judy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eugene","Brian","Judy"],"index":3431,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9574613571,"difficulty":1.9574613571}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alma does not know whether Alma's forehead is muddy. It is publicly announced that Clifford's forehead is not muddy. It is publicly announced that Alma's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] [ ! ~(2) ] Agenta knows whether (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 2) ] [ ! ~(4) ] [ ! ~(2) ] 0","hypothesis":"Johnson can now know whether Clifford can know whether Clifford's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnson","Alma","Sonya","Clifford"],"index":6352,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.946454525,"difficulty":0.053545475}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Corinne. Timothy's card is shown to Micheal. Corinne's card is shown to Timothy. Micheal's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Corinne can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Corinne","Micheal","Timothy"],"index":2776,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9219537377,"difficulty":0.0780462623}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nick's card is shown to Martha. Bettye's card is shown to Nick. It is publicly announced that someone picked a red card. It is publicly announced that Bettye knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (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:3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Bettye can now know that Martha can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Bettye","Nick","John"],"index":3913,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8857197165,"difficulty":0.1142802835}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to David. David's card is shown to Brandon. David's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brandon can now know that Brandon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Brandon","Jason"],"index":2326,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9790645242,"difficulty":0.0209354758}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether Loretta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Rose can now know that Loretta can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Loretta","Rose","Edward","Robert"],"index":9298,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9802661538,"difficulty":0.0197338462}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Cole. Cole's card is shown to Thomas. Cole's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Cole does not know whether Charles picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Charles can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cole","Thomas","Charles"],"index":2886,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9700229168,"difficulty":0.0299770832}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phyllis does not know whether Brad is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Annamae can now know whether Phyllis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brad","Annamae","Phyllis","Daniel"],"index":1404,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5840551853,"difficulty":1.5840551853}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Tim. William's card is shown to Mike. Tim's card is shown to William. Matthew's card is shown to William. Tim's card is shown to Matthew. William's card is shown to Matthew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tim can now know that Mike can know whether Tim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tim","Mike","William","Matthew"],"index":2043,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6867142916,"difficulty":1.6867142916}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Avery does not know whether Avery's forehead is muddy. It is publicly announced that Joseph knows whether Avery's forehead is muddy.","smcdel_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 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 2) ] 0","hypothesis":"George can now know that Avery's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Avery","Joseph"],"index":3715,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.976696372,"difficulty":0.023303628}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Lee can now know whether Lillian can know whether Lee's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lillian","Lee","Helen"],"index":1363,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9460901022,"difficulty":0.0539098978}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerome knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Tina can now know whether Jerome can know whether Jerome is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tina","Jerome"],"index":7200,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8946959972,"difficulty":0.1053040028}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Alice. Alice's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know that Alice can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alice","John"],"index":5837,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6313129663,"difficulty":0.3686870337}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Marquita is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Mary can now know that Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marquita","Mary","Peter"],"index":3508,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9760366082,"difficulty":1.9760366082}
-{"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 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":"Samuel can now know whether Diane can know whether Samuel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Cassandra","Samuel"],"index":5329,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9413995743,"difficulty":0.0586004257}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know that Teresa can know that Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","George","Sandra","Teresa"],"index":6676,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9822930694,"difficulty":0.0177069306}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lou is thirsty. It is publicly announced that Danielle knows whether Lou is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Larry can now know whether Lou is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lou","Danielle","Larry"],"index":9231,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.707228303,"difficulty":0.292771697}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Michael. John's card is shown to Ricardo. Ricardo's card is shown to John. Michael's card is shown to Jamie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Ricardo","John","Jamie"],"index":1765,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9784321785,"difficulty":0.0215678215}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Tamara. Tamara's card is shown to Frank. Roy's card is shown to Frank. Frank's card is shown to Roy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Roy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tamara","Frank","Roy"],"index":9208,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9177441001,"difficulty":0.0822558999}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lona does not know whether Lona's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mauro can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bessie","Mauro","Lona"],"index":7849,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.97808218,"difficulty":0.02191782}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monty does not know whether Liz is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Diana can now know whether Liz can know whether Liz is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monty","Liz","Diana","Phillip"],"index":7017,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8703434467,"difficulty":0.1296565533}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Andrew can now know that James can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","James","Andrew","Carol"],"index":4803,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9530751109,"difficulty":0.0469248891}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Sheldon can now know that Dianne can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dianne","Sheldon","Michael"],"index":9437,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9852519035,"difficulty":0.0147480965}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marjorie can now know that Rita can know that Rita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tina","Rita","Julissa","Marjorie"],"index":6757,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865650535,"difficulty":0.0134349465}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erwin knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Kevin can now know that Erwin can know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gabriel","Frances","Kevin","Erwin"],"index":8558,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6279665232,"difficulty":0.3720334768}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leo knows whether someone is thirsty. It is publicly announced that Eunice knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marsha can now know whether Leo can know that Eunice is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leo","Marsha","Eunice"],"index":4362,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.534689486,"difficulty":1.534689486}
-{"premise":"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 Steven's forehead is muddy. It is publicly announced that Steven does not know whether or not everyone's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentb knows that (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) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lessie can now know that Anita can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anita","Lessie","Steven","Olga"],"index":3646,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9777684808,"difficulty":0.0222315192}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to William. William's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Christine does not know whether Christine picked a red card. It is publicly announced that William knows whether William picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Christine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Christine"],"index":2078,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9729970098,"difficulty":0.0270029902}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yvette's card is shown to Christopher. Christopher's card is shown to Candy. Christopher's card is shown to Yvette. Candy's card is shown to Yvette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Yvette can now know whether Christopher can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Candy","Yvette"],"index":3422,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9758338332,"difficulty":0.0241661668}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Charles","Mary"],"index":7539,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.978277266,"difficulty":0.021722734}
-{"premise":"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 Suzanne's forehead is muddy. It is publicly announced that Lori does not know whether Lori's forehead is muddy. It is publicly announced that Lori does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Suzanne can now know that Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lori","Guy","Suzanne"],"index":8793,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.955344975,"difficulty":0.044655025}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Nancy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Nancy can now know whether Robert can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Nancy","Joanne","Mary"],"index":4850,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9021662474,"difficulty":0.0978337526}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen does not know whether Carmen's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Grace can now know whether Carmen can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Grace","Carmen"],"index":6899,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9563630819,"difficulty":0.0436369181}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerald knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Lewis can now know whether Gerald can know that Lewis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Mary","Lewis","Gerald"],"index":9020,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6380633712,"difficulty":1.6380633712}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"John can now know that Cindy can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harold","John","Cindy","David"],"index":3243,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9791991115,"difficulty":0.0208008885}
-{"premise":"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 does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Linda can now know that Victor can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","William","Victor","Dominga"],"index":3534,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7728558779,"difficulty":1.7728558779}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerry does not know whether Susan is thirsty. It is publicly announced that Rhoda does not know whether Susan is thirsty. It is publicly announced that Rhoda does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agenta knows whether (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"John can now know whether Jerry can know that Susan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Susan","Jerry","Rhoda"],"index":4098,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6941175461,"difficulty":0.3058824539}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Pam. Pam's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Brian picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Pam can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Pam","William"],"index":9308,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9784315228,"difficulty":0.0215684772}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Arthur can now know whether Gertha can know that Gertha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gertha","Kyle","Arthur"],"index":4145,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.591468513,"difficulty":0.408531487}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carroll's card is shown to Asia. Asia's card is shown to Jack. John's card is shown to Jack. Jack's card is shown to Carroll. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Asia can now know whether Carroll can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Asia","Jack","Carroll","John"],"index":3462,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7972032428,"difficulty":0.2027967572}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmie does not know whether Anna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jimmie can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jason","Jimmie","Dora","Anna"],"index":5230,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9633848667,"difficulty":0.0366151333}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phillip's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Phillip can now know that Stacy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Phillip","Stacy"],"index":2712,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6916860938,"difficulty":1.6916860938}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Maria. Maria's card is shown to Joe. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Joe can now know whether Joe picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Joe","James"],"index":2782,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6725078821,"difficulty":1.6725078821}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susan can now know that Karen can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Susan","Betty","John"],"index":2468,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860258698,"difficulty":0.0139741302}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Karlene is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Patricia can now know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karlene","Jason","Patricia","Ethel"],"index":9500,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5830253959,"difficulty":0.4169746041}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Debora can now know that Bruce can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Catherine","Ernest","Bruce","Debora"],"index":8074,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9771018624,"difficulty":0.0228981376}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jarod can now know whether Warren can know whether Jarod's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Warren","Jarod"],"index":7757,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9385361671,"difficulty":0.0614638329}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Isabel's card is shown to Timothy. Timothy's card is shown to Linda. Isabel's card is shown to Linda. Timothy's card is shown to Isabel. Linda's card is shown to Isabel. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Isabel does not know whether Isabel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Timothy can now know that Isabel can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Linda","Isabel"],"index":8519,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9770525694,"difficulty":0.0229474306}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maura's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 (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":"Philip can now know whether Maura can know whether Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maura","Frank","Philip","Sean"],"index":9320,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9427475333,"difficulty":0.0572524667}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carmen can now know that Mae can know that Carmen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mae","Amanda","Richard","Carmen"],"index":9399,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865309596,"difficulty":0.0134690404}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know whether Elizabeth can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tanisha","Kevin","Sandra","Elizabeth"],"index":9186,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9187079072,"difficulty":0.0812920928}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Benjamin can now know whether Miriam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Benjamin","Cathy","Miriam"],"index":4156,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.959924221,"difficulty":0.040075779}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond does not know whether Candace is thirsty. It is publicly announced that Candace does not know whether Steven is thirsty. It is publicly announced that Raymond is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Raymond can now know whether Candace can know whether Vicky is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Raymond","Vicky","Candace"],"index":7679,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.874950707,"difficulty":0.125049293}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joe can now know that Catherine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Catherine","Steven","David","Joe"],"index":8402,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9804390669,"difficulty":0.0195609331}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Charles. Charles's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Charles can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Cynthia"],"index":7944,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.606581986,"difficulty":0.393418014}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chad is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Richard can now know whether Chad can know that Chad is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chad","Richard","Austin"],"index":6837,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5826282501,"difficulty":0.4173717499}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alesia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Alesia can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mathew","Alesia"],"index":6416,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9766134024,"difficulty":0.0233865976}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Herbert does not know whether Julia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Julia can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Herbert","Scott","Julia","Bonnie"],"index":4909,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9701299667,"difficulty":0.0298700333}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Barbara can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Kathy","Clifford","Barbara"],"index":7130,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856457114,"difficulty":0.0143542886}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Sandra. Sandra's card is shown to Ellyn. Jennifer's card is shown to Ellyn. Jennifer's card is shown to Albert. Sandra's card is shown to Jennifer. Albert's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Sandra picked a red card. It is publicly announced that Ellyn knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Sandra can now know that Ellyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Ellyn","Albert","Jennifer"],"index":9036,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9683961868,"difficulty":0.0316038132}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Joseph can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Darryl","Anita","Timothy"],"index":3973,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9795053005,"difficulty":0.0204946995}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Al can now know whether Robin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robin","Al","Daniel"],"index":6748,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9547297359,"difficulty":0.0452702641}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elva's card is shown to Janice. Janice's card is shown to Heidi. Elva's card is shown to Heidi. Janice's card is shown to Elva. Heidi's card is shown to Elva. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Elva does not know whether Elva picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Heidi can now know whether Elva can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janice","Heidi","Elva"],"index":2221,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6643006802,"difficulty":0.3356993198}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lenna knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Gregory can now know that Lenna can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Lenna","Robert","Gregory"],"index":3058,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9854700565,"difficulty":0.0145299435}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jaime can now know that Manuel can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Manuel","Jaime","Jason","Mary"],"index":7063,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9728786349,"difficulty":0.0271213651}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that (1|2|3))","n_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":"Fern can now know that Raymond can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Fern","Michele","Raymond"],"index":4802,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9778059721,"difficulty":0.0221940279}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Orlando's card is shown to Ellen. Orlando's card is shown to Marian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Orlando can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Orlando","Ellen","Marian"],"index":8510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9140527844,"difficulty":0.0859472156}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Rickie can now know whether Margaret can know that Rickie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rickie","Margaret"],"index":8635,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9421287775,"difficulty":0.0578712225}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Roslyn can now know whether Jose can know that Roslyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jose","Roslyn"],"index":561,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8110319376,"difficulty":1.8110319376}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). May's card is shown to Maxine. Maxine's card is shown to May. It is publicly announced that someone picked a red card. It is publicly announced that May does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (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":"May can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maxine","May"],"index":356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9646934867,"difficulty":0.0353065133}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know that Debra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debra","Victoria","Paul","Maria"],"index":7379,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864231944,"difficulty":0.0135768056}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gretchen's card is shown to Ernest. Ernest's card is shown to Gretchen. It is publicly announced that someone picked a red card. It is publicly announced that Gretchen knows whether or not nobody picked a red card. It is publicly announced that Ernest does not know whether Ernest picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(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 (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gretchen can now know whether Ernest can know that Gretchen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ernest","Gretchen"],"index":6844,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7620959282,"difficulty":0.2379040718}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Sherman. Sherman's card is shown to Donald. Keith's card is shown to Donald. Donald's card is shown to Keith. Keith's card is shown to Marie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sherman can now know whether Donald can know that Marie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sherman","Donald","Keith","Marie"],"index":3078,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6602804065,"difficulty":0.3397195935}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Sha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Paul can now know whether Archie can know whether Allen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Archie","Sha","Allen"],"index":9130,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9715572596,"difficulty":0.0284427404}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander does not know whether Alexander's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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)","n_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":"David can now know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alexander","David","Tamekia"],"index":6172,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9079641104,"difficulty":1.9079641104}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (1&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":"Francis can now know whether Ronald can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Teresita","Ronald","Trinidad","Francis"],"index":121,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5227351785,"difficulty":0.4772648215}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Donald. Donald's card is shown to Fred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know that Carl can know whether Carl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Carl","Fred"],"index":2275,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6759136915,"difficulty":1.6759136915}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Antwan can now know that William can know that Diana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Diana","William","Antwan"],"index":2625,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865195751,"difficulty":0.0134804249}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorene knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Dorene can now know that Dorene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dorene","David"],"index":3260,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9732457995,"difficulty":0.0267542005}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether or not everyone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 2) ] Agentc knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lisa can now know that Mark can know whether Sidney's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sidney","Mark","Lisa"],"index":6534,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8926048875,"difficulty":0.1073951125}
-{"premise":"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 Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Mary can now know whether Philip can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Philip"],"index":4846,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.975472033,"difficulty":0.024527967}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Matthew. April's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that April knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"April can now know that Matthew can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","April","Laura"],"index":546,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9774436355,"difficulty":0.0225563645}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Crystal. Crystal's card is shown to Ronald. Virginia's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ronald can now know whether Crystal can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Ronald","Virginia"],"index":6004,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9642993808,"difficulty":0.0357006192}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Juan can know whether Sherry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Candida","Sherry","Barbara","Juan"],"index":5130,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6600893736,"difficulty":0.3399106264}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Eric. Roy's card is shown to Eric. Charles's card is shown to Jody. Jody's card is shown to Charles. Jody's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that Jody does not know whether Eric picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Roy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eric","Jody","Charles","Roy"],"index":3749,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9771652222,"difficulty":0.0228347778}
-{"premise":"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 Mark's forehead is muddy. It is publicly announced that Daniel'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 3) ] [ ! ~(2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Mark can now know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ross","Daniel","Mark"],"index":2929,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9808549285,"difficulty":0.0191450715}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Freeda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Mary can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","Freeda"],"index":9187,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9742423892,"difficulty":0.0257576108}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jim knows whether someone's forehead is muddy. It is publicly announced that Jean knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Eddie can now know that Billy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jean","Billy","Jim","Eddie"],"index":8101,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9808523059,"difficulty":0.0191476941}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lauri knows whether or not nobody is thirsty. It is publicly announced that Lauri is thirsty. It is publicly announced that Ruby does not know whether Danny is thirsty. It is publicly announced that Ruby does not know whether Danny is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Danny can now know whether Lauri is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Danny","Ruby","Lauri"],"index":7719,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7369732261,"difficulty":0.2630267739}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry knows whether someone's forehead is muddy.","smcdel_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":"Alan can now know whether Joselyn can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alan","Sherry","Joselyn"],"index":7951,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9743167162,"difficulty":0.0256832838}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sharri can now know that Jeffrey can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharri","Jeffrey","Mary"],"index":6450,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9784073234,"difficulty":0.0215926766}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adelina does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Adelina can now know whether Mike can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mike","Adelina"],"index":5471,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5411112309,"difficulty":0.4588887691}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alexander's card is shown to Shawn. Shawn's card is shown to Alexander. It is publicly announced that someone picked a red card. It is publicly announced that Shawn does not know whether or not everyone picked a red card. It is publicly announced that Shawn knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Shawn can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shawn","Alexander"],"index":9398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9705345631,"difficulty":0.0294654369}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Claude knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Neil can now know whether Claude can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Neil","Claude"],"index":7587,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5867342949,"difficulty":0.4132657051}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to Jerry. Jerry's card is shown to Erin. It is publicly announced that someone picked a red card. It is publicly announced that Erin does not know whether Erin picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 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":"Erin can now know whether Jerry can know whether Erin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jerry","Erin"],"index":1781,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9117793441,"difficulty":0.0882206559}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Melissa. Melissa's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether or not everyone picked a red card. It is publicly announced that Melissa knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Dorothy can now know whether Melissa can know that Melissa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melissa","Dorothy"],"index":6048,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7453463674,"difficulty":0.2546536326}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Bella is thirsty. It is publicly announced that Bella does not know whether Thomas is thirsty. It is publicly announced that Thomas does not know whether Corina is thirsty. It is publicly announced that Thomas does not know whether Johnnie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Johnnie can now know that Bella can know that Johnnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Bella","Johnnie","Corina"],"index":9271,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.973772049,"difficulty":0.026227951}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","James","Joe","Christopher"],"index":7361,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9849521518,"difficulty":0.0150478482}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Heather. Heather's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Lawrence does not know whether Lawrence picked a red card. It is publicly announced that Heather knows whether Lawrence picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Heather can now know whether Lawrence can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Heather","Lawrence"],"index":3694,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9757288098,"difficulty":0.0242711902}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Bobbie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Steven can now know that Christopher can know that Bobbie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Steven","Bertha","Bobbie"],"index":6454,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857903719,"difficulty":0.0142096281}
-{"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":"Kaitlyn can now know that Derick can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kaitlyn","Frank","Derick","Terry"],"index":2643,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9727534056,"difficulty":0.0272465944}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Morris does not know whether Hayley is thirsty. It is publicly announced that Hayley is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Magdalene does not know whether Morris is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Suzette can now know whether Hayley is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Hayley","Suzette","Magdalene","Morris"],"index":5150,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7326875329,"difficulty":0.2673124671}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Vikki can now know that Vikki's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dennis","Ignacio","Michael","Vikki"],"index":1169,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9849103093,"difficulty":0.0150896907}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Anna can now know that Rosemary can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rosemary","Anna"],"index":8832,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9769405127,"difficulty":0.0230594873}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Rodolfo. Virginia's card is shown to Martina. Martina's card is shown to Virginia. Rodolfo's card is shown to Bessie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bessie can now know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rodolfo","Martina","Virginia","Bessie"],"index":2127,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786215425,"difficulty":0.0213784575}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Melody can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Melody","Richard","Joseph"],"index":3702,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5402728915,"difficulty":1.5402728915}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Solomon knows whether Glen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Solomon can now know that Elizabeth can know whether Jeanette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Jeanette","Solomon","Glen"],"index":6052,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.96496135,"difficulty":0.03503865}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deborah can now know that Warren can know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bonnie","Warren","Deborah","Kimberly"],"index":8439,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864736795,"difficulty":0.0135263205}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Michael can now know whether Douglas can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Douglas","Michael"],"index":4421,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9706035256,"difficulty":0.0293964744}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Roberto can now know that Jennifer can know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","William","Jennifer","Roberto"],"index":8522,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8542232513,"difficulty":1.8542232513}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mitchell's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Mitchell can now know whether John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mitchell","Beverly","John"],"index":5933,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.944850862,"difficulty":0.055149138}
-{"premise":"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 (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Melissa can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jose","Melissa","Monte"],"index":2451,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8169908524,"difficulty":0.1830091476}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Toni knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Warren can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Toni","Warren"],"index":991,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9745278358,"difficulty":0.0254721642}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Allison can now know that Pam can know that Jorge is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pam","Stephan","Allison","Jorge"],"index":6524,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9800316095,"difficulty":0.0199683905}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lola does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_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":"Alice can now know whether Lola can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lola","Alice","Christian"],"index":2314,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9738127589,"difficulty":0.0261872411}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Jean. Jean's card is shown to Michael. Kimberly's card is shown to Michael. Jean's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jean can now know that Jean picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jean","Michael","Kimberly"],"index":7819,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9788626432,"difficulty":0.0211373568}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Douglas can now know whether Matthew can know whether Matthew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","Jonathan","Matthew","Justin"],"index":1152,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8121709824,"difficulty":0.1878290176}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Frances can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Frances"],"index":6643,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5033928752,"difficulty":1.5033928752}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vivian knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know that Vivian can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florence","Vivian","James","Lisa"],"index":8153,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9765833616,"difficulty":0.0234166384}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evangelina's card is shown to Johnny. Johnny's card is shown to Christine. Johnny's card is shown to Genie. Johnny's card is shown to Evangelina. Christine's card is shown to Evangelina. It is publicly announced that someone picked a red card. It is publicly announced that Genie does not know whether Genie picked a red card. It is publicly announced that Christine knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Genie can now know whether Johnny picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Johnny","Christine","Genie","Evangelina"],"index":5875,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.647290647,"difficulty":0.352709353}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Mark can now know that Virgil can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mark","Virgil"],"index":8393,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865208864,"difficulty":0.0134791136}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Roy can now know that Etta can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Roy","Etta"],"index":7912,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9849190712,"difficulty":0.0150809288}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether or not everyone is thirsty. It is publicly announced that Virginia does not know whether or not everyone is thirsty. It is publicly announced that Justin does not know whether Rick is thirsty. It is publicly announced that Barbara does not know whether Rick is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows that (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Rick can now know that Virginia can know that Justin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Justin","Virginia","Rick"],"index":1902,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9608483911,"difficulty":0.0391516089}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elena does not know whether or not everyone's forehead is muddy. It is publicly announced that Troy knows whether someone's forehead is muddy. It is publicly announced that Elena does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Troy can now know that Elena can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elena","Troy"],"index":3956,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8629399538,"difficulty":0.1370600462}
-{"premise":"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 knows whether or not everyone's forehead is muddy. It is publicly announced that Jon knows whether Jon'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) ] 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 2) ] 0","hypothesis":"Jon can now know whether Dwight can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dwight","Jon"],"index":508,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.937004447,"difficulty":0.062995553}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luis does not know whether Ron is thirsty. It is publicly announced that Luis knows whether Luis is thirsty. It is publicly announced that Eugene does not know whether Ron is thirsty. It is publicly announced that Eugene knows whether Eugene is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ron can now know whether Luis can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","Luis","Ron"],"index":1039,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9749762416,"difficulty":0.0250237584}
-{"premise":"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 Johnnie knows whether or not everyone's forehead is muddy. It is publicly announced that Johnnie does not know whether Johnnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Bonnie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bonnie","Johnnie","Elanor"],"index":8116,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9627400041,"difficulty":0.0372599959}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janet does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Janet can now know whether Jasmine can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Jasmine","Dale","Randy"],"index":5819,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.517295301,"difficulty":0.482704699}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Thomas. Thomas's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card. It is publicly announced that Thomas knows whether Thomas picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Thomas can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thomas","Mary"],"index":1483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7825222611,"difficulty":0.2174777389}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to James. Karl's card is shown to Leslie. Charles's card is shown to Karl. James's card is shown to Karl. It is publicly announced that someone picked a red card. It is publicly announced that Leslie does not know whether or not everyone picked a red card. It is publicly announced that Karl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agenta knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Charles can now know that Leslie can know whether Karl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","James","Leslie","Karl"],"index":6953,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6564950943,"difficulty":0.3435049057}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Manuela can now know that Constance can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clifford","Manuela","Cecil","Constance"],"index":3680,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9826785326,"difficulty":0.0173214674}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether Carolyn's forehead is muddy. It is publicly announced that Victoria's forehead is not muddy. It is publicly announced that Carolyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] [ ! ~(2) ] Agentd knows that (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] [ ! ~(2) ] 0","hypothesis":"Victoria can now know that Carolyn can know whether Kimbery's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stewart","Carolyn","Kimbery","Victoria"],"index":9039,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9040893316,"difficulty":0.0959106684}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sandra can now know whether Mary can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cathy","Sandra","Mary"],"index":6244,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5610311031,"difficulty":0.4389688969}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Patricia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (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:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gerard can now know that Wilma can know that Wilma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Patricia","Wilma","Gerard"],"index":6926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.968680799,"difficulty":0.031319201}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Emil can now know that Alice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emil","Alice","Shawn"],"index":5237,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.986045301,"difficulty":1.986045301}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Henry does not know whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Thomas can now know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Henry","Helen","Thomas","Ruth"],"index":8533,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6993991137,"difficulty":0.3006008863}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Sara. Sara's card is shown to Carmelo. Sara's card is shown to Roland. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sara can now know that Carmelo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sara","Carmelo","Roland"],"index":7930,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9791850448,"difficulty":0.0208149552}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 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":"Jimmy can now know whether Julio can know that Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lenard","Susan","Jimmy","Julio"],"index":1167,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7986283302,"difficulty":0.2013716698}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Jeremy. Shawnta's card is shown to Richard. Richard's card is shown to Shawnta. It is publicly announced that someone picked a red card. It is publicly announced that Jeremy picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Richard can now know that Jeremy can know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeremy","Richard","Shawnta"],"index":7881,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.978092134,"difficulty":0.021907866}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizebeth is thirsty. It is publicly announced that Diane knows whether someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"William can now know whether Diane can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","William","Elizebeth"],"index":6604,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6123830676,"difficulty":0.3876169324}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lidia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Lidia can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pamela","Paul","Lidia","Janet"],"index":8354,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859878421,"difficulty":0.0140121579}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Claude can now know whether David can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Claude"],"index":6302,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9784871936,"difficulty":0.0215128064}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty. It is publicly announced that Theresa does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Michael can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Michael","Theresa"],"index":5318,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7099377513,"difficulty":0.2900622487}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Xavier can now know whether Quentin can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irvin","Erin","Quentin","Xavier"],"index":3411,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9747374654,"difficulty":0.0252625346}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edward can now know whether Katherine can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joann","Misty","Katherine","Edward"],"index":710,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9791128635,"difficulty":0.0208871365}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"William can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Nancy"],"index":2516,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864583611,"difficulty":0.0135416389}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Ashley can now know whether Beverly can know that Beverly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Ashley","Janice","Aurora"],"index":8822,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9542834759,"difficulty":0.0457165241}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Larry does not know whether Lynette is thirsty. It is publicly announced that Joe does not know whether Lynette is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Thomas can now know whether Joe can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Lynette","Thomas","Larry"],"index":3661,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9593949914,"difficulty":0.0406050086}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kathleen can now know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cheryl","Kathleen","Dean"],"index":3939,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9762084484,"difficulty":0.0237915516}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Diane. Michelle's card is shown to Stephen. Diane's card is shown to Michelle. Stephen's card is shown to Michelle. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Diane can now know that Stephen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diane","Stephen","Michelle"],"index":8733,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9652127624,"difficulty":0.0347872376}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether Margaret's forehead is muddy. It is publicly announced that Margaret's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Bonnie can now know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bonnie","Velma","Margaret"],"index":4486,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853906631,"difficulty":0.0146093369}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elaine does not know whether Shemeka is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Shemeka can now know whether Ginger can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shemeka","Elaine","Ginger","Patrick"],"index":2171,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9163754582,"difficulty":0.0836245418}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Mildred can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Robert","Mildred","Derek"],"index":8023,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9169386625,"difficulty":0.0830613375}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah does not know whether Sarah's forehead is muddy. It is publicly announced that Diana does not know whether Diana's forehead is muddy. It is publicly announced that Sarah'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 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Lewis can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diana","Sarah","Lewis"],"index":1075,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5471343398,"difficulty":0.4528656602}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Harvey. Harvey's card is shown to Patricia. Harvey's card is shown to Randolph. Patricia's card is shown to Randolph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Randolph can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harvey","Patricia","Randolph"],"index":1880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9158126712,"difficulty":0.0841873288}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis does not know whether Louis's forehead is muddy. It is publicly announced that Derek knows whether Lorene's forehead is muddy. It is publicly announced that Ethel's forehead is not muddy. It is publicly announced that Derek's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] (Agentb knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Derek can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Louis","Derek","Ethel","Lorene"],"index":6467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.978222847,"difficulty":0.021777153}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"William can now know whether Charles can know whether Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Charles"],"index":4945,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8696829081,"difficulty":0.1303170919}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Marcos's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Marcos can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dan","Patricia","Marcos"],"index":4904,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9807510376,"difficulty":0.0192489624}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacey's card is shown to James. Stacey's card is shown to Henry. James's card is shown to Stacey. It is publicly announced that someone picked a red card. It is publicly announced that Stacey does not know whether Henry picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Stacey can now know that James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Henry","Stacey"],"index":910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9618890285,"difficulty":0.0381109715}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Stephen can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bertram","Steve","Stephen","Patricia"],"index":2699,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860834479,"difficulty":0.0139165521}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyong knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Madeleine can now know whether Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Scott","Kyong","Madeleine"],"index":5967,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.962785542,"difficulty":0.037214458}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Madelyn knows whether or not nobody is thirsty. It is publicly announced that Madelyn is thirsty. It is publicly announced that Alisha does not know whether Glen is thirsty. It is publicly announced that Alisha does not know whether Glen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Madelyn can now know whether Alisha is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glen","Alisha","Madelyn"],"index":4751,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6844108701,"difficulty":1.6844108701}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to David. Hilda's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Hilda knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know that Hilda can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Hilda","William"],"index":5830,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9725900888,"difficulty":0.0274099112}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Renee can now know that Meredith can know that Shemeka's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shemeka","Barbara","Renee","Meredith"],"index":7228,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9781090021,"difficulty":0.0218909979}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty does not know whether Rheba is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Betty can now know whether Carolyn can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Carolyn","Rheba"],"index":4415,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9705553651,"difficulty":0.0294446349}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Denise does not know whether Colleen is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Colleen can now know whether Colleen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Denise","Colleen"],"index":289,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6702498198,"difficulty":0.3297501802}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Adam can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Louise","William","Adam","Joshua"],"index":5473,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9772835374,"difficulty":0.0227164626}
-{"premise":"There are three 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. It is publicly announced that Dennis knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Olive can now know whether Dennis can know that Mildred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mildred","Dennis","Olive"],"index":6869,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8877639771,"difficulty":0.1122360229}
-{"premise":"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 Shirley's forehead is muddy. It is publicly announced that Randy does not know whether Randy's forehead is muddy. It is publicly announced that Randy 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Irma can now know whether Irma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Randy","Irma","Shirley"],"index":4555,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8456353545,"difficulty":0.1543646455}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Donna's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Douglas can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Douglas","Donna"],"index":4497,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9658154249,"difficulty":0.0341845751}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Naomi knows whether or not everyone is thirsty. It is publicly announced that Darla is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Darla can now know whether Ann can know that Naomi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ann","Naomi","Darla"],"index":5295,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5161554813,"difficulty":1.5161554813}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lorraine is thirsty. It is publicly announced that Lorraine does not know whether Anna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Stacey can now know that Lorraine can know whether Cameron is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stacey","Anna","Lorraine","Cameron"],"index":4918,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6029940248,"difficulty":1.6029940248}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Lola is not thirsty. It is publicly announced that Ronald does not know whether Jason is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Ronald can now know that Ronald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lola","Jason","Jeannie","Ronald"],"index":6510,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9741199613,"difficulty":0.0258800387}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Samantha can now know whether Mary can know that Omar is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Omar","Margaret","Samantha","Mary"],"index":9141,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5435273647,"difficulty":1.5435273647}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Linda knows whether Pearl is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Linda can now know that Pearl can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pearl","Linda"],"index":1733,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9456212521,"difficulty":0.0543787479}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to William. Gary's card is shown to Patricia. William's card is shown to Gary. Patricia's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gary can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Patricia","Gary"],"index":138,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6583198905,"difficulty":0.3416801095}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lester's card is shown to Shane. Shane's card is shown to Lester. It is publicly announced that someone picked a red card. It is publicly announced that Shane does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Lester can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shane","Lester"],"index":7846,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9685625434,"difficulty":0.0314374566}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ralph can now know whether Hector can know whether Hector's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ralph","Joe","Hector","Paul"],"index":6247,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9705171585,"difficulty":0.0294828415}
-{"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":"Charlotte can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","John","Mary","Charlotte"],"index":7853,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9827572107,"difficulty":0.0172427893}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harriett does not know whether Chester is thirsty. It is publicly announced that Lucienne knows whether someone is thirsty. It is publicly announced that Catherine does not know whether or not everyone is thirsty. It is publicly announced that Catherine does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Harriett can now know whether Catherine can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Catherine","Chester","Harriett","Lucienne"],"index":730,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8919767737,"difficulty":0.1080232263}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ashley can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathleen","Matthew","Nellie","Ashley"],"index":7335,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853573442,"difficulty":0.0146426558}
-{"premise":"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 or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows 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":"Suzanne can now know that Gilbert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gilbert","Derek","Suzanne"],"index":8524,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9746161699,"difficulty":0.0253838301}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sean knows whether Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Crystal can now know that Julius can know whether Julius's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julius","Jeffrey","Sean","Crystal"],"index":7464,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9645472765,"difficulty":0.0354527235}
-{"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 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":"Travis can now know whether Alma can know whether Bradley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bradley","Martin","Travis","Alma"],"index":96,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9483118057,"difficulty":0.0516881943}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Norbert. Marty's card is shown to Gloria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marty can now know that Norbert can know that Marty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norbert","Marty","Gloria"],"index":6699,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9791563749,"difficulty":0.0208436251}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marty knows whether William's forehead is muddy. It is publicly announced that William knows whether Marty's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Marty can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marty","William","Randy"],"index":2090,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9844195247,"difficulty":0.0155804753}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine's forehead is not muddy. It is publicly announced that Peter 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) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Peter can now know that Penelope can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Penelope","Peter","Geraldine"],"index":2131,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9784047008,"difficulty":0.0215952992}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alvin can now know whether Frank can know whether Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alvin","Joseph","Roderick","Frank"],"index":1241,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9707710147,"difficulty":0.0292289853}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Paul knows whether Lyle's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Paul can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Paul","Lyle"],"index":4615,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9784439802,"difficulty":0.0215560198}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy does not know whether Troy's forehead is muddy. It is publicly announced that Troy knows whether or not nobody's forehead is muddy. It is publicly announced that Troy 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) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Troy can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Troy","Sheila","Mary"],"index":9224,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9711599946,"difficulty":0.0288400054}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Rhonda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"David can now know that Roberta can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","David","Rhonda","Roberta"],"index":2064,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857873917,"difficulty":0.0142126083}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Gloria can now know whether Ralph can know whether Ralph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ralph","Gloria"],"index":272,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9693915248,"difficulty":0.0306084752}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elva can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Elva","William"],"index":3042,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.980414629,"difficulty":0.019585371}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tawnya's card is shown to Mary. Mary's card is shown to Julie. Tawnya's card is shown to Julie. Jeffrey's card is shown to Tawnya. Mary's card is shown to Jeffrey. Julie's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Julie can now know whether Julie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Julie","Tawnya","Jeffrey"],"index":7691,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.639950335,"difficulty":1.639950335}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (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":"Virginia can now know that Alba can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Virginia","Candice","Margarita","Alba"],"index":2869,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8323299885,"difficulty":0.1676700115}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antonio does not know whether or not everyone is thirsty. It is publicly announced that Norman does not know whether Lori is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Norman can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lori","Antonio","Norman"],"index":4837,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9598772526,"difficulty":0.0401227474}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Sandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Phillip can now know that Phillip picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Phillip","Joseph","Sandra"],"index":3438,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9799300432,"difficulty":0.0200699568}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Susan can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christine","Susan"],"index":8207,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9780454636,"difficulty":0.0219545364}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Ellis. Ellis's card is shown to James. Ellis's card is shown to Amanda. James's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that Amanda knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Amanda can now know whether Ellis can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellis","James","Amanda"],"index":2848,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9600564837,"difficulty":0.0399435163}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Elizabeth can now know whether Carl can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Elizabeth","Carl"],"index":3207,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9752578139,"difficulty":0.0247421861}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jewel does not know whether Robert is thirsty. It is publicly announced that Jewel is not thirsty. It is publicly announced that Robert knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know that Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jewel","Robert","Nicole"],"index":7011,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9590873718,"difficulty":0.0409126282}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie does not know whether Marie's forehead is muddy. It is publicly announced that Shelley knows whether Marie's forehead is muddy.","smcdel_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 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 2) ] 0","hypothesis":"Herbert can now know that Shelley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Herbert","Marie","Shelley"],"index":2736,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9763574004,"difficulty":0.0236425996}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether Gerald's forehead is muddy. It is publicly announced that Russel knows whether Agustin's forehead is muddy. It is publicly announced that Wesley's forehead is not muddy. It is publicly announced that Russel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] (Agentb knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Russel can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerald","Russel","Wesley","Agustin"],"index":5048,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5836622715,"difficulty":0.4163377285}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether 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 4) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Raymond can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Dorcas","Joanna","Raymond"],"index":7334,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9782205224,"difficulty":0.0217794776}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Kelly. Tina's card is shown to Kelly. Kelly's card is shown to Clifton. Tina's card is shown to Clifton. Kelly's card is shown to David. Kelly's card is shown to Tina. David's card is shown to Tina. It is publicly announced that someone picked a red card. It is publicly announced that Tina does not know whether Tina picked a red card. It is publicly announced that Kelly does not know whether Clifton picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"David can now know whether Tina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kelly","Clifton","David","Tina"],"index":7748,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7509512901,"difficulty":1.7509512901}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gregory can now know whether Doris can know whether Doris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Gregory","Doris"],"index":4566,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9709734917,"difficulty":0.0290265083}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Rhonda can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rhonda","Melanie"],"index":8072,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9776855111,"difficulty":0.0223144889}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to John. John's card is shown to Connie. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"John can now know whether Connie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Connie","Carolyn"],"index":3719,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.672965467,"difficulty":1.672965467}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nelson is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Brandon can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brandon","Nelson"],"index":3012,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9782249928,"difficulty":0.0217750072}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"George can now know that Jack can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["George","Jack"],"index":1885,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9719220996,"difficulty":0.0280779004}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether Joseph's forehead is muddy. It is publicly announced that Shirley knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jerry can now know that Shirley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shirley","Jerry","Joseph"],"index":2462,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9598351717,"difficulty":0.0401648283}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether Carol's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Irwin can now know whether Carol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amanda","Irwin","Patricia","Carol"],"index":9523,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9642320871,"difficulty":0.0357679129}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cruz knows whether Melanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Joshua can now know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cruz","Joshua","Donald","Melanie"],"index":1994,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9812074304,"difficulty":0.0187925696}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Brian. Oscar's card is shown to Brian. Brian's card is shown to Irene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Irene can now know that Oscar picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Irene","Oscar"],"index":6573,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.978728652,"difficulty":0.021271348}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Caridad. Cheryl's card is shown to Caridad. William's card is shown to Irene. William's card is shown to Cheryl. Caridad's card is shown to William. Cheryl's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Irene does not know whether Caridad picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Irene can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Caridad","Irene","Cheryl","William"],"index":7373,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9746850133,"difficulty":0.0253149867}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darin's card is shown to Earl. Scott's card is shown to Jessie. Darin's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Darin picked a black card. It is publicly announced that Earl does not know whether Scott picked a red card. It is publicly announced that Earl does not know whether Jessie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jessie can now know whether Earl can know that Earl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earl","Jessie","Scott","Darin"],"index":5447,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7437451482,"difficulty":0.2562548518}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marina knows whether Jimmy's forehead is muddy. It is publicly announced that Steve's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] [ ! ~(4) ] Agentc 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) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Jimmy can now know whether Marina can know that Marina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ivan","Marina","Jimmy","Steve"],"index":4526,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8577401042,"difficulty":1.8577401042}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lorene can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorene","Samantha","William","Joan"],"index":4418,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9829009175,"difficulty":0.0170990825}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frankie does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Frankie knows whether Terry is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Terry can now know whether Frankie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Terry","Frankie"],"index":8000,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9738878012,"difficulty":0.0261121988}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Naomi knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentc knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Mark can now know whether Aurelia can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Naomi","Aurelia","Mark","David"],"index":5381,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9559365511,"difficulty":0.0440634489}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Seth knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Seth can now know whether Seth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Seth","Henry","Vickie"],"index":5599,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9565505981,"difficulty":0.0434494019}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether or not nobody is thirsty. It is publicly announced that David is thirsty. It is publicly announced that Stanley does not know whether Betty is thirsty. It is publicly announced that Stanley does not know whether Betty is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Stanley can now know whether David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Stanley","David"],"index":8662,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7487165332,"difficulty":0.2512834668}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corey knows whether Stephen's forehead is muddy. It is publicly announced that Stephen knows whether Corey's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Patricia can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Corey","Stephen","Patricia"],"index":6505,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9773614407,"difficulty":0.0226385593}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeremy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dorothy can now know whether Dorothy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeremy","Dorothy","Robert"],"index":5911,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6005764008,"difficulty":1.6005764008}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Josefina. Melissa's card is shown to Josefina. Melissa's card is shown to Ruth. Josefina's card is shown to Melissa. Ruth's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Josefina picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Ruth can now know whether Ruth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Josefina","Ruth","Melissa"],"index":410,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6649491787,"difficulty":1.6649491787}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henrietta's card is shown to Penny. Penny's card is shown to Henrietta. Penny's card is shown to Jerry. It is publicly announced that someone picked a red card. It is publicly announced that Jerry knows whether someone picked a red card. It is publicly announced that Henrietta picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] 0","hypothesis":"Henrietta can now know that Henrietta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Penny","Henrietta","Jerry"],"index":3891,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9714928865,"difficulty":0.0285071135}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila does not know whether or not everyone's forehead is muddy. It is publicly announced that Johnny knows whether Johnny'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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Johnny can now know whether Lillian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Johnny","Lillian","Sheila"],"index":9333,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.895802021,"difficulty":0.104197979}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Richard. Richard's card is shown to Gregory. Charles's card is shown to Wanda. Richard's card is shown to Charles. Gregory's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Wanda picked a red card. It is publicly announced that Richard does not know whether Gregory picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Charles can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Gregory","Wanda","Charles"],"index":4584,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9716652036,"difficulty":0.0283347964}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Kelly. Kelly's card is shown to Leslie. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Leslie can now know that Kelly can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kelly","Leslie"],"index":5059,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9791994691,"difficulty":1.9791994691}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] (Agentb knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"David can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","David"],"index":1630,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9802830219,"difficulty":0.0197169781}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Therese's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Therese","Joseph","Tammy","Raymond"],"index":7479,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.986433506,"difficulty":0.013566494}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christian does not know whether Christian's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Christian'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 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Christian can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Christian","Ana"],"index":3927,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9769072533,"difficulty":0.0230927467}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edmund knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that 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":"Jeanene can now know that Jeanene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jeanene","Edmund"],"index":1462,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9744868875,"difficulty":0.0255131125}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Julie can now know whether Nicole can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicole","Mozelle","Christopher","Julie"],"index":8566,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9785494208,"difficulty":0.0214505792}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that 1)","n_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 whether Reginald can know that Reginald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Reginald","Nancy","James"],"index":4468,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7620301843,"difficulty":1.7620301843}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rebecca can now know whether Jane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jane","Luz","Rebecca","Wilford"],"index":7661,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9614255428,"difficulty":0.0385744572}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alphonse knows whether Alphonse is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Alphonse can now know whether Maria can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maria","Alphonse"],"index":8103,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9216002226,"difficulty":0.0783997774}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Deanna can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Lois","Deanna"],"index":6996,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.947396636,"difficulty":0.052603364}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether or not everyone's forehead is muddy. It is publicly announced that Jason does not know whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Wilfred can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karla","Jason","Wilfred"],"index":5010,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9675303102,"difficulty":0.0324696898}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice does not know whether Yvonne is thirsty. It is publicly announced that Tania knows whether someone is thirsty. It is publicly announced that Pearl does not know whether or not everyone is thirsty. It is publicly announced that Pearl does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Tania can now know that Pearl can know whether Yvonne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pearl","Yvonne","Janice","Tania"],"index":1258,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.719065249,"difficulty":1.719065249}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melisa can now know whether Neil can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jody","Neil","Edward","Melisa"],"index":3221,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9786546826,"difficulty":0.0213453174}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adrian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Adrian can now know that Adrian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Adrian","Catherine","Thomas","John"],"index":3174,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9820890427,"difficulty":1.9820890427}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gordon can now know whether Julie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Erik","Randall","Gordon"],"index":2944,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5474492908,"difficulty":0.4525507092}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Pam can now know that Marcus can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pam","Marcus","Frank","Edward"],"index":34,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.978741765,"difficulty":0.021258235}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen does not know whether Stephen's forehead is muddy. It is publicly announced that James knows whether Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Toni can now know whether Toni's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Toni","Stephen","James"],"index":8374,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9075784683,"difficulty":1.9075784683}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Angela. Angela's card is shown to Jeffrey. Jeffrey's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Jeffrey","Lisa"],"index":3141,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9788264036,"difficulty":0.0211735964}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Margaret. Glenda's card is shown to Margaret. Margaret's card is shown to Andrew. Margaret's card is shown to Glenda. Andrew's card is shown to Glenda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Andrew","Glenda"],"index":1261,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9781121016,"difficulty":0.0218878984}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Mercedes can now know that Olivia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Olivia","Mercedes"],"index":3698,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858264327,"difficulty":0.0141735673}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandy does not know whether or not everyone's forehead is muddy. It is publicly announced that Brandy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Cheryl can now know that Brandy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cheryl","Brandy"],"index":3872,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8316800594,"difficulty":1.8316800594}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorraine's card is shown to Ethan. Charles's card is shown to Lorraine. Ethan's card is shown to Lorraine. It is publicly announced that someone picked a red card. It is publicly announced that Ethan does not know whether Lorraine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Ethan can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Ethan","Lorraine"],"index":6120,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7518850565,"difficulty":0.2481149435}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether Jerry is thirsty. It is publicly announced that Jerry does not know whether Robert is thirsty. It is publicly announced that Frances is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] Agentc knows that (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Seth can now know that Robert can know that Jerry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Frances","Seth","Jerry"],"index":7888,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9742255211,"difficulty":0.0257744789}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiffany's forehead is muddy. It is publicly announced that Laura does not know whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (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":"Tiffany can now know that Laura can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Laura","Tiffany"],"index":5651,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9733948708,"difficulty":0.0266051292}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terri's card is shown to James. Elizabeth's card is shown to James. Elizabeth's card is shown to Terri. James's card is shown to Elizabeth. Terri's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that James picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Elizabeth can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Terri","Elizabeth"],"index":2323,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9776491523,"difficulty":0.0223508477}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyle knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Kyle can now know that Kyle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Trisha","Kyle"],"index":1704,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9784013629,"difficulty":0.0215986371}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Robert. Robert's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether or not everyone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Robert can now know that Richard can know that Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Richard"],"index":4870,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8973840475,"difficulty":0.1026159525}
-{"premise":"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 does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_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":"Gabriella can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gabriella","Harry","Shona"],"index":4028,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9683221579,"difficulty":0.0316778421}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Jimmy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jimmy can now know that John can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Jimmy"],"index":5936,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9765218496,"difficulty":0.0234781504}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frederick does not know whether Brenda is thirsty. It is publicly announced that Frederick knows whether or not everyone is thirsty. It is publicly announced that Catherine knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Frederick can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brenda","Catherine","Frederick"],"index":5151,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5892208219,"difficulty":1.5892208219}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Dana. Gary's card is shown to Dana. Gary's card is shown to Timothy. William's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Dana can know whether Dana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dana","William","Timothy","Gary"],"index":9273,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8997254372,"difficulty":0.1002745628}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Gwendolyn can now know whether Edward can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cary","Edward","Roy","Gwendolyn"],"index":5251,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9195244312,"difficulty":0.0804755688}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Laura. Donald's card is shown to Jessie. Wendy's card is shown to Jessie. Jessie's card is shown to Wendy. It is publicly announced that someone picked a red card. It is publicly announced that Laura does not know whether Wendy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Jessie can now know whether Laura can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laura","Jessie","Donald","Wendy"],"index":652,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7812322378,"difficulty":1.7812322378}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Theresa can now know whether Ronald can know whether Theresa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Theresa","Ronald"],"index":5244,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7567245364,"difficulty":0.2432754636}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Delbert. Delbert's card is shown to Jeffrey. Shannon's card is shown to Jeffrey. Delbert's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Shannon can now know whether Delbert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Delbert","Jeffrey","Shannon"],"index":2820,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9636529684,"difficulty":0.0363470316}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Anthony can now know that Samantha can know that Samantha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charlie","Samantha","Anthony"],"index":6386,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9628232121,"difficulty":0.0371767879}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Manuel is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Sarah can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sarah","Manuel"],"index":3295,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.963373363,"difficulty":0.036626637}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 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":"Joseph can now know that Daniel can know that Michele's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jolynn","Joseph","Daniel","Michele"],"index":4206,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823294282,"difficulty":0.0176705718}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Melinda. Rodney's card is shown to Melinda. Melinda's card is shown to Richard. Rodney's card is shown to Richard. Melinda's card is shown to Rodney. Richard's card is shown to Rodney. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that Rodney picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melinda","Richard","Rodney"],"index":913,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9778416157,"difficulty":0.0221583843}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Nancy's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Nicholas can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Nancy","Nicholas"],"index":7312,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9854446054,"difficulty":0.0145553946}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 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":"Viva can now know that Emilio can know that Viva's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alfredo","Viva","Amanda","Emilio"],"index":667,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9825750589,"difficulty":0.0174249411}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebekah's card is shown to Christine. Christine's card is shown to Rebekah. It is publicly announced that someone picked a red card. It is publicly announced that Rebekah knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (~(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":"Christine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christine","Rebekah"],"index":1012,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.972383678,"difficulty":0.027616322}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"James can now know that Richard can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","James"],"index":1501,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9565390944,"difficulty":0.0434609056}
-{"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 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":"Lawrence can now know that Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lawrence","Kimberly","Joe"],"index":434,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9825714231,"difficulty":0.0174285769}
-{"premise":"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 Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Joshua can now know whether Edward can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Joshua","Cathy","Michael"],"index":3505,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8604574203,"difficulty":0.1395425797}
-{"premise":"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 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":"Jill can now know whether Madalyn can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Madalyn","Jill"],"index":5621,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5893192291,"difficulty":1.5893192291}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 (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":"Linda can now know that Richard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Connie","Linda","Richard","Dyan"],"index":8154,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9740892053,"difficulty":0.0259107947}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alton's card is shown to Nancy. Alton's card is shown to Dominic. Nancy's card is shown to Alton. Julian's card is shown to Alton. Nancy's card is shown to Julian. Alton's card is shown to Julian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dominic can now know whether Alton can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Dominic","Alton","Julian"],"index":8130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9733691216,"difficulty":0.0266308784}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 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":"Diane can now know that Gregory can know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Diane","Donald","Gregory"],"index":1366,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9822824001,"difficulty":0.0177175999}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nina does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Antonio can now know that Nina can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Antonio","Nina","Mary"],"index":5095,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9623911977,"difficulty":0.0376088023}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlton knows whether Doris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Carlton can now know that Doris can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Clyde","Carlton","Kimberly"],"index":3642,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.985506773,"difficulty":0.014493227}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Rachel can now know that James can know whether Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachel","Julie","James","Margaret"],"index":9554,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5897791982,"difficulty":1.5897791982}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Eric can now know whether Anthony can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Eric","Anthony"],"index":6212,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9577883482,"difficulty":0.0422116518}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to James. Robert's card is shown to Wayne. James's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Wayne picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"James can now know whether Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Wayne","Robert"],"index":8438,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9593288898,"difficulty":0.0406711102}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (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":"Rhonda can now know whether Joshua can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rhonda","Robert","Alfonso","Joshua"],"index":6468,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9761719704,"difficulty":0.0238280296}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phillip's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows 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":"Lara can now know whether Daniel can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phillip","Daniel","Lara"],"index":6620,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9387038946,"difficulty":0.0612961054}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Clara. Clara's card is shown to Jacqulyn. Clara's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Marie does not know whether Marie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Marie can now know that Marie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clara","Jacqulyn","Marie"],"index":8239,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9765630364,"difficulty":0.0234369636}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emma can now know that Evelyn can know that Jessica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Judy","Emma","Evelyn","Jessica"],"index":4641,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9865294695,"difficulty":0.0134705305}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know that Lester can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lester","Sarah","Elizabeth"],"index":9285,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8257978559,"difficulty":0.1742021441}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mike's card is shown to Rita. Mike's card is shown to Patricia. Rita's card is shown to Mike. Steven's card is shown to Mike. Rita's card is shown to Steven. Mike's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know whether Patricia can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rita","Patricia","Mike","Steven"],"index":1938,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8065052032,"difficulty":1.8065052032}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phyllis's forehead is 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":"Roland can now know whether Phyllis can know that Roland's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Phyllis","Victoria","Roland"],"index":3836,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8253415227,"difficulty":1.8253415227}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Kim. Kim's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Kim does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Helen can now know whether Kim can know whether Kim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kim","Helen"],"index":4234,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.873508513,"difficulty":0.126491487}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Larry can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Larry","Bobby"],"index":8559,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.985996902,"difficulty":0.014003098}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darryl's card is shown to Geraldine. Jerry's card is shown to Geraldine. Geraldine's card is shown to Coral. Jerry's card is shown to Coral. Geraldine's card is shown to Darryl. Geraldine's card is shown to Jerry. Darryl's card is shown to Jerry. It is publicly announced that someone picked a red card. It is publicly announced that Jerry does not know whether Jerry picked a red card. It is publicly announced that Geraldine does not know whether Coral picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Geraldine can now know that Darryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Geraldine","Coral","Darryl","Jerry"],"index":6940,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9742874503,"difficulty":0.0257125497}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(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":"Josie can now know that Gary can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Belinda","Gary","Kurtis","Josie"],"index":470,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9715588093,"difficulty":0.0284411907}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Danny can now know that James can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pamela","James","Danny"],"index":12,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9587554932,"difficulty":0.0412445068}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Faith's card is shown to Robert. Robert's card is shown to Jacqueline. Faith's card is shown to Candace. Candace's card is shown to Faith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Jacqueline can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Jacqueline","Candace","Faith"],"index":2077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8922277093,"difficulty":0.1077722907}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ursula's card is shown to James. James's card is shown to Ursula. It is publicly announced that someone picked a red card. It is publicly announced that Ursula does not know whether Ursula picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ursula can now know that James can know that Ursula picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Ursula"],"index":9171,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9762998819,"difficulty":0.0237001181}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sommer's card is shown to Derek. Derek's card is shown to Sommer. Stephen's card is shown to Sommer. Derek's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Sommer knows whether or not nobody picked a red card. It is publicly announced that Derek knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Derek can now know that Sommer can know whether Sommer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Derek","Sommer","Stephen"],"index":6141,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7612990737,"difficulty":0.2387009263}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether Meagan can know whether Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Meagan","Dorothy"],"index":4143,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9720785022,"difficulty":0.0279214978}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amina does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Logan can now know that Amina can know that Logan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesus","Logan","Amina","Marie"],"index":1695,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.962434411,"difficulty":1.962434411}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guy's card is shown to Jamie. Jamie's card is shown to Guy. It is publicly announced that someone picked a red card. It is publicly announced that Guy knows whether Guy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Guy can now know that Guy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jamie","Guy"],"index":3969,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9787436128,"difficulty":1.9787436128}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pearl knows whether Luis's forehead is muddy. It is publicly announced that Pearl's forehead is muddy.","smcdel_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 (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Luis can now know that Jennifer can know that Luis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Pearl","Luis"],"index":1007,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9809561372,"difficulty":0.0190438628}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Doreen. Jonathan's card is shown to Doreen. Kelly's card is shown to Jonathan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doreen can now know whether Kelly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doreen","Kelly","Mark","Jonathan"],"index":9100,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.653742373,"difficulty":1.653742373}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jennifer can now know whether Christopher can know that Devin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Jennifer","Philip","Devin"],"index":7007,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7728923559,"difficulty":0.2271076441}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leona can now know that Valene can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leona","Valene","Lisa"],"index":7043,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9728523493,"difficulty":0.0271476507}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Melvin. Melvin's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Melvin can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Melvin","Elizabeth"],"index":5617,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9789102674,"difficulty":0.0210897326}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Michelle. Douglas's card is shown to Michelle. Michelle's card is shown to Ashley. Douglas's card is shown to Cassandra. Michelle's card is shown to Douglas. Cassandra's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Michelle knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] Agentc knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Cassandra can now know whether Michelle can know that Cassandra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Ashley","Cassandra","Douglas"],"index":3705,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7352535129,"difficulty":0.2647464871}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mohammad's card is shown to Lisa. Lisa's card is shown to Modesta. Mohammad's card is shown to Modesta. Lisa's card is shown to Mohammad. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mohammad can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lisa","Modesta","Mohammad"],"index":7005,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9117357731,"difficulty":0.0882642269}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Irene. Claudia's card is shown to Irene. Julie's card is shown to Claudia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Julie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Irene","Julie","Michelle","Claudia"],"index":454,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9778019786,"difficulty":0.0221980214}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl does not know whether Tony is thirsty. It is publicly announced that Carl is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] 0","hypothesis":"Tony can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tony","Steven","Carl"],"index":5083,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9767638445,"difficulty":0.0232361555}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Summer does not know whether Chris is thirsty. It is publicly announced that Charles does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Summer can now know whether Chris can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Summer","Chris","David"],"index":7023,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9742703438,"difficulty":0.0257296562}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Silvia can now know that Randall can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bill","Daniel","Silvia","Randall"],"index":2958,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9803041816,"difficulty":0.0196958184}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlene knows whether or not nobody's forehead is muddy. It is publicly announced that Pricilla knows whether Pricilla's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 2) ] (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))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Carlene can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carlene","Pricilla","Rhonda"],"index":7009,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9781780243,"difficulty":0.0218219757}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Calvin. Jose's card is shown to Patsy. Calvin's card is shown to Jose. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Patsy picked a red card. It is publicly announced that Calvin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Patsy can now know that Calvin can know whether Patsy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Calvin","Patsy","Jose"],"index":2058,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6826965213,"difficulty":1.6826965213}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"John can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Grady","William","John"],"index":9445,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9782895446,"difficulty":0.0217104554}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kathy can now know that Donald can know that Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ramiro","Devin","Donald","Kathy"],"index":5108,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9798654914,"difficulty":0.0201345086}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Michael is thirsty. It is publicly announced that John knows whether John is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know that Michael can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","John"],"index":1737,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7311061025,"difficulty":0.2688938975}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know whether Christopher can know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Mark","Christopher"],"index":7831,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9402734041,"difficulty":0.0597265959}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Colleen's card is shown to Ray. Colleen's card is shown to Anna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anna can now know whether Ray can know that Colleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ray","Anna","Colleen"],"index":8452,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6780728102,"difficulty":0.3219271898}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Rhonda can now know that Ruth can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rhonda","David","Ruth","Alvin"],"index":1070,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.75465101,"difficulty":0.24534899}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Pearl. Pearl's card is shown to Harold. Harold's card is shown to Steven. Steven's card is shown to Samantha. It is publicly announced that someone picked a red card. It is publicly announced that Samantha does not know whether Pearl picked a red card. It is publicly announced that Harold picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] 0","hypothesis":"Samantha can now know that Pearl can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pearl","Harold","Steven","Samantha"],"index":4699,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9728250504,"difficulty":0.0271749496}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allan knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Allan can now know whether George can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["George","Allan"],"index":2153,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9746313095,"difficulty":0.0253686905}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mina's card is shown to Jean. Mina's card is shown to Michele. Jean's card is shown to Mina. Michael's card is shown to Mina. Jean's card is shown to Michael. Mina's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jean can now know whether Michele can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jean","Michele","Mina","Michael"],"index":542,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9756827354,"difficulty":0.0243172646}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Janine is thirsty. It is publicly announced that Janine knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Ronald can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Janine","Ronald"],"index":7563,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9288430214,"difficulty":0.0711569786}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacey does not know whether Marguerite is thirsty. It is publicly announced that Wilbur does not know whether Harold is thirsty. It is publicly announced that Harold knows whether Harold is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentd knows whether 4) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Wilbur can now know whether Wilbur is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wilbur","Stacey","Marguerite","Harold"],"index":3669,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6948254704,"difficulty":0.3051745296}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Fred knows whether Bridgette's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Bridgette can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Fred","Bridgette"],"index":6933,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9784960151,"difficulty":0.0215039849}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Rosa. Joann's card is shown to Brenda. Brenda's card is shown to Joann. It is publicly announced that someone picked a red card. It is publicly announced that Rosa picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Brenda can now know whether Rosa can know whether Joann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosa","Brenda","Joann"],"index":7338,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8909764886,"difficulty":1.8909764886}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eli does not know whether Eli's forehead is muddy. It is publicly announced that Luther's forehead is not muddy. It is publicly announced that Eli's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] [ ! ~(2) ] Agentc knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] [ ! ~(2) ] 0","hypothesis":"Johanna can now know whether Ryan can know that Ryan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ryan","Eli","Johanna","Luther"],"index":2959,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8452972174,"difficulty":1.8452972174}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Charles. James's card is shown to Brian. Brian's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Brian","James"],"index":7168,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9726041555,"difficulty":0.0273958445}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leona's card is shown to Ronnie. Leona's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leona can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leona","Ronnie","Joseph"],"index":1564,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.979665935,"difficulty":0.020334065}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Shannon knows whether Andrew's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Andrew can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Shannon","Andrew"],"index":4748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9849736691,"difficulty":0.0150263309}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chelsea knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jackie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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)) ] [ ! ~(1) ] Agentb knows whether (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&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Charles can now know whether Chelsea can know whether Chelsea's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jackie","Charles","Clarence","Chelsea"],"index":6133,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.943123579,"difficulty":1.943123579}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Joseph. Joseph's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta 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) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Randy can now know that Randy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Randy"],"index":2994,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9533535838,"difficulty":1.9533535838}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Walter does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Charles can now know whether Bryce can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bryce","Charles","Walter"],"index":8506,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8991817832,"difficulty":0.1008182168}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Betty can now know whether Erin can know that Ann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erin","Ann","Betty"],"index":8886,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9551520944,"difficulty":0.0448479056}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Bennie. Bennie's card is shown to Gerald. Gerald's card is shown to David. David's card is shown to Jarrod. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Bennie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bennie","Gerald","David","Jarrod"],"index":6568,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9353274703,"difficulty":0.0646725297}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty. It is publicly announced that Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] 0","hypothesis":"Mary can now know whether Jocelyn can know whether Jocelyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Michael","Jocelyn"],"index":846,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8221434951,"difficulty":0.1778565049}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Jane can know that Jane is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Grace","Katherine","Jennifer","Jane"],"index":3205,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9802053571,"difficulty":0.0197946429}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether someone's forehead is muddy. It is publicly announced that Reina's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agentb knows that 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":"Reina can now know that Ricky's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ricky","Reina","Julie","Mario"],"index":2356,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9778099656,"difficulty":0.0221900344}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leslie does not know whether Jonathan is thirsty. It is publicly announced that Leslie does not know whether Jonathan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Jonathan can now know that Debra can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jonathan","Gloria","Debra","Leslie"],"index":8520,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.974144876,"difficulty":0.025855124}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tara's card is shown to Beryl. Kelly's card is shown to Beryl. Kelly's card is shown to Tara. Beryl's card is shown to Kelly. Tara's card is shown to Kelly. Beryl's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Stephen knows whether someone picked a red card. It is publicly announced that Kelly does not know whether Kelly picked a red card. It is publicly announced that Kelly knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kelly can now know whether Tara can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beryl","Tara","Kelly","Stephen"],"index":8617,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9724083543,"difficulty":0.0275916457}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pat does not know whether Pat's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Pat can now know that Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pat","Catherine","Alan","Nancy"],"index":1181,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9794580936,"difficulty":0.0205419064}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Claudia. Claudia's card is shown to John. Claudia's card is shown to Anthony. John's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"John can now know that Anthony can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Claudia","John","Anthony"],"index":8124,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9717283249,"difficulty":0.0282716751}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Anne can now know whether Dorothy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Dorothy","Anne","Thomas"],"index":2250,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5033675432,"difficulty":0.4966324568}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dixie's card is shown to Raymond. Juan's card is shown to Raymond. Gilberto's card is shown to Raymond. Dixie's card is shown to Gilberto. Juan's card is shown to Gilberto. It is publicly announced that someone picked a red card. It is publicly announced that Raymond knows whether Raymond picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dixie can now know whether Raymond picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Raymond","Dixie","Juan","Gilberto"],"index":9606,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7918571234,"difficulty":0.2081428766}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamela's card is shown to Christine. Pamela's card is shown to Lois. Christine's card is shown to Pamela. Lois's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Lois does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lois can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christine","Lois","Pamela"],"index":5603,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.966355443,"difficulty":0.033644557}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Susan can now know that Ronald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Susan","William"],"index":4046,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856092334,"difficulty":0.0143907666}
-{"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 (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":"Sharon can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sharon","Taina","Leon","Mindy"],"index":7630,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7681522369,"difficulty":0.2318477631}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Audrey can now know that Stephen can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Teodora","Audrey","Stephen","Amy"],"index":4360,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9774479866,"difficulty":0.0225520134}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tyrone knows whether Tyrone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Denise can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Chase","Tyrone","Denise"],"index":4416,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9817974567,"difficulty":0.0182025433}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joy's card is shown to Micheal. Joy's card is shown to Mary. Mary's card is shown to Joy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Micheal can now know whether Micheal picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Micheal","Mary","Joy"],"index":7386,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6349377036,"difficulty":1.6349377036}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Dale can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marlon","Dale","Nathan"],"index":9348,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.854560554,"difficulty":0.145439446}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Rosalie. Katherine's card is shown to Carol. Rosalie's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Rosalie does not know whether Carol picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rosalie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Katherine","Rosalie","Carol"],"index":2786,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.977504015,"difficulty":0.022495985}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 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":"Marguerite can now know that Teresa can know that Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marguerite","Kathleen","Sharon","Teresa"],"index":8913,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9822047353,"difficulty":0.0177952647}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Margaret can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","John","Ruth","Helen"],"index":1310,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9803285599,"difficulty":0.0196714401}
-{"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 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":"George can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alfred","George","Jean","Sue"],"index":4746,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9826263189,"difficulty":0.0173736811}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Herbert. Virgie's card is shown to Herbert. Herbert's card is shown to Virgie. David's card is shown to Virgie. It is publicly announced that someone picked a red card. It is publicly announced that Herbert picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"David can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Herbert","David","Virgie"],"index":3684,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.977696538,"difficulty":0.022303462}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandy can now know whether Florence can know that Sandy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandy","Florence","Joan","Ingrid"],"index":2470,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6665572524,"difficulty":1.6665572524}
-{"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 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":"Kenneth can now know that Robert can know whether Louis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Robert","Kenneth","Benjamin"],"index":2808,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8828966618,"difficulty":0.1171033382}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carolyn can now know whether Bruce's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emmett","Bruce","Richard","Carolyn"],"index":525,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9608032703,"difficulty":0.0391967297}
-{"premise":"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 knows whether Elizabeth's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 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 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Elizabeth can now know that David can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","David","Kayla"],"index":9339,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9714211226,"difficulty":1.9714211226}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Goldie knows whether Goldie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Goldie can now know that Tammy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nicole","Tammy","Goldie","Jay"],"index":8250,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856721163,"difficulty":0.0143278837}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Otis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Ron can now know that Ron's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Yvonne","Cristobal","Ron","Otis"],"index":2727,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9861600995,"difficulty":0.0138399005}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Marvin can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Grace","Marvin","Lois"],"index":425,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.985943079,"difficulty":0.014056921}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Henry can now know that Amy can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Luis","Henry","Michael","Amy"],"index":8052,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9801504612,"difficulty":0.0198495388}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pilar can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rhonda","Selma","Pilar","Christin"],"index":7865,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9797897339,"difficulty":0.0202102661}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sheri can now know that Maria can know whether Diann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diann","Sheri","Maria"],"index":1662,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9608420134,"difficulty":0.0391579866}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy. It is publicly announced that Sean does not know whether Sean's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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) ] Agenta knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know whether Michael can know that Sean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Sean","Timothy","Michael"],"index":616,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8426235914,"difficulty":0.1573764086}
-{"premise":"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 Victor does not know whether Victor's forehead is muddy. It is publicly announced that Carolyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Carolyn can now know that Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Victor","Carolyn","Sarah"],"index":3547,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9775576591,"difficulty":1.9775576591}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Stacie can now know that Julie can know whether Julie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julie","Stacie","Robert","Rosemarie"],"index":3367,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9636110663,"difficulty":0.0363889337}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Marshall does not know whether Shannon is thirsty. It is publicly announced that Barbara does not know whether Shannon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Linda can now know that Shannon can know whether Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Shannon","Linda","Marshall"],"index":7516,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5910078883,"difficulty":1.5910078883}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth is thirsty. It is publicly announced that Ruth does not know whether Toby is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ruth can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Toby","Ruth"],"index":9468,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.908084929,"difficulty":0.091915071}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Linda can now know whether Raymond is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Michael","Linda"],"index":6333,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6096147299,"difficulty":1.6096147299}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cynthia does not know whether Lucretia is thirsty. It is publicly announced that Cynthia is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Cynthia can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffrey","Lucretia","Cynthia"],"index":4726,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9636229873,"difficulty":0.0363770127}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to Russell. Russell's card is shown to Carole. Monica's card is shown to Carole. Larry's card is shown to Carole. Russell's card is shown to Monica. Carole's card is shown to Larry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carole can now know that Monica can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Russell","Carole","Monica","Larry"],"index":7807,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9774892926,"difficulty":0.0225107074}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allen knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Betty can now know that Wanda can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wanda","Betty","Allen"],"index":2702,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9716491103,"difficulty":0.0283508897}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eliza can now know that Tina can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Eliza","Tina","Michael"],"index":7945,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.644549787,"difficulty":0.355450213}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jerry can now know that George can know whether George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Jerry","George"],"index":8985,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9555609822,"difficulty":0.0444390178}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Emma. Jessica's card is shown to Emma. Jessica's card is shown to Jason. Jason's card is shown to Jessica. It is publicly announced that someone picked a red card. It is publicly announced that Jason picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Emma can now know that Jason can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emma","Jason","Jessica"],"index":6409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9737033248,"difficulty":0.0262966752}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Larry can now know that Marc can know whether Larry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Pamela","Marc"],"index":5055,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5301980376,"difficulty":0.4698019624}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know that Debra can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruth","Debra","Ashley","Charlotte"],"index":5940,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.982693851,"difficulty":0.017306149}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leo's card is shown to Kari. Kari's card is shown to Ione. Leo's card is shown to Ione. Mike's card is shown to Ione. Leo's card is shown to Mike. It is publicly announced that someone picked a red card. It is publicly announced that Kari knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Leo can now know that Ione can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kari","Leo","Ione","Mike"],"index":6994,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9704148173,"difficulty":0.0295851827}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Thomas. Norman's card is shown to Thomas. Philip's card is shown to Thomas. Thomas's card is shown to Jennifer. Norman's card is shown to Jennifer. Philip's card is shown to Jennifer. Thomas's card is shown to Norman. Philip's card is shown to Norman. Norman's card is shown to Philip. It is publicly announced that someone picked a red card. It is publicly announced that Thomas picked a red card. It is publicly announced that Jennifer does not know whether Jennifer picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agentd knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Philip can now know that Jennifer can know whether Norman picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Jennifer","Norman","Philip"],"index":6209,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7410218716,"difficulty":0.2589781284}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lourdes's card is shown to Matthew. Clara's card is shown to Lourdes. Jennifer's card is shown to Lourdes. Matthew's card is shown to Clara. Clara's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Matthew can now know that Clara can know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Lourdes","Clara","Jennifer"],"index":624,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6013119221,"difficulty":0.3986880779}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Randall can now know that Floyd can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Randall","Phebe","Floyd","Susan"],"index":2773,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9747276902,"difficulty":0.0252723098}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Robert can now know whether Scott can know whether George is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Robert","George"],"index":1580,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8411123157,"difficulty":0.1588876843}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Audra knows whether Bobby's forehead is muddy. It is publicly announced that Bobby knows whether Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bobby can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Audra","Bobby"],"index":4157,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9840901494,"difficulty":0.0159098506}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Luis can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Luis","Jean","Philip","Robert"],"index":2840,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9849224091,"difficulty":0.0150775909}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jesse can now know that Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Philip","Lori","Jesse","Ruth"],"index":4404,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864532351,"difficulty":0.0135467649}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Elmer. Elmer's card is shown to Gregory. Elmer's card is shown to Joseph. Gregory's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elmer can now know whether Joseph can know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elmer","Gregory","Joseph"],"index":4509,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6571776867,"difficulty":1.6571776867}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Pamela can now know whether Nancy can know that Pamela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Pamela"],"index":7796,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9486181736,"difficulty":0.0513818264}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gilbert is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Gilbert can now know whether Sadie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gilbert","Sadie","Jose"],"index":7575,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9042954445,"difficulty":0.0957045555}
-{"premise":"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 does not know whether Bernice's forehead is muddy. It is publicly announced that Francis knows whether Bernice's forehead is muddy.","smcdel_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) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Francis can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sherry","Bernice","Francis"],"index":6860,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9682120085,"difficulty":0.0317879915}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Jessie. Imogene's card is shown to Jessie. Joseph's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Jessie does not know whether Imogene picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jessie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Jessie","John","Imogene"],"index":5729,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9687690735,"difficulty":0.0312309265}
-{"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 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":"Calvin can now know whether Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Calvin","Eric","Benjamin"],"index":3015,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8564270735,"difficulty":0.1435729265}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Guillermo knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Gabriel can now know whether Guillermo can know whether Guillermo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gabriel","Guillermo"],"index":4144,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7878941298,"difficulty":0.2121058702}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Nora can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nora","Matthew","Vickie","David"],"index":1901,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9759741426,"difficulty":0.0240258574}
-{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harry","Samuel","Michael","Mildred"],"index":8557,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9676808119,"difficulty":0.0323191881}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernice does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Bernice can now know whether Alejandro can know whether Bernice is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alejandro","Bernice"],"index":6116,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7768045068,"difficulty":0.2231954932}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that June is thirsty. It is publicly announced that June does not know whether Maude is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Maude can now know that Maude is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maude","June"],"index":1251,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9744730592,"difficulty":0.0255269408}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dana does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Danielle can now know that Sandra can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dana","Danielle","Sandra","Shelly"],"index":3832,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9604004622,"difficulty":0.0395995378}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patty's card is shown to Maria. Stacy's card is shown to Patty. Patty's card is shown to Stacy. It is publicly announced that someone picked a red card. It is publicly announced that Patty knows whether someone picked a red card. It is publicly announced that Stacy does not know whether or not everyone picked a red card. It is publicly announced that Stacy knows whether or not nobody picked a red card. It is publicly announced that Stacy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Patty can now know that Stacy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Patty","Stacy"],"index":5350,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9379043579,"difficulty":0.0620956421}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Kenneth can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brian","Peggy","Kenneth"],"index":4797,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9783331752,"difficulty":0.0216668248}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Lisa. Lisa's card is shown to Irene. Lisa's card is shown to John. Irene's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Irene picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Irene can now know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lisa","Irene","John"],"index":1391,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9778876901,"difficulty":0.0221123099}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vincent is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Vincent can now know whether Alfred can know that Alfred is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bill","Vincent","Francis","Alfred"],"index":4290,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5352275372,"difficulty":1.5352275372}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Vicki's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vicki","Constance","Delbert","John"],"index":9440,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9849046469,"difficulty":0.0150953531}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evan's card is shown to Cynthia. Millie's card is shown to Evan. Lenna's card is shown to Evan. Cynthia's card is shown to Millie. Millie's card is shown to Lenna. It is publicly announced that someone picked a red card. It is publicly announced that Lenna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Cynthia can now know that Evan can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Evan","Millie","Lenna"],"index":2029,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9659152627,"difficulty":0.0340847373}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","George","Daniel","Sean"],"index":267,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864402413,"difficulty":0.0135597587}
-{"premise":"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 Carmen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Ronnie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronnie","Kevin","Ming","Carmen"],"index":8244,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9818142056,"difficulty":0.0181857944}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Harry can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Harry","Mary"],"index":2812,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9768331051,"difficulty":0.0231668949}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know that Kristopher can know whether Jessica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Jessica","Kristopher"],"index":1881,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9574203491,"difficulty":0.0425796509}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Faye can now know that Marlin can know that Brittany is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marlin","Brittany","Faye"],"index":1413,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9793788195,"difficulty":0.0206211805}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to Kent. Kent's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Kent knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kent can now know that Martha can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kent","Martha","Kevin"],"index":5828,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9725482464,"difficulty":0.0274517536}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mark can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Michael","James"],"index":4357,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9806210399,"difficulty":0.0193789601}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Abbie can now know that Denise's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Abbie","Denise","Donald"],"index":824,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9860576987,"difficulty":0.0139423013}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugenia's card is shown to Mary. Mary's card is shown to Eugenia. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Eugenia"],"index":5852,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9717098475,"difficulty":0.0282901525}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that John can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Paul","John","Clark"],"index":4762,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9819312096,"difficulty":0.0180687904}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (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":"Cheryl can now know whether Richard can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wilma","Cheryl","Richard"],"index":6537,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9762204885,"difficulty":0.0237795115}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard is thirsty. It is publicly announced that Richard does not know whether Troy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Velva can now know that Troy can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Velva","Troy","Richard","Chester"],"index":9276,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9762915969,"difficulty":0.0237084031}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna does not know whether or not everyone is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty. It is publicly announced that Alma does not know whether Joseph is thirsty. It is publicly announced that Donna does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"William can now know that Alma can know whether Alma is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Alma","William","Joseph"],"index":2921,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5380387902,"difficulty":0.4619612098}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald knows whether or not nobody is thirsty. It is publicly announced that Ronald is thirsty. It is publicly announced that Joy does not know whether Adam is thirsty. It is publicly announced that Joy does not know whether Adam is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ronald can now know that Adam is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adam","Joy","Ronald"],"index":2650,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9553442001,"difficulty":0.0446557999}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Owen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Owen can now know whether Aleen can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aleen","Jennifer","Lynn","Owen"],"index":5769,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9597514868,"difficulty":0.0402485132}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stewart knows whether Stewart's forehead is muddy. It is publicly announced that Stewart's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Lynda can now know that Lynda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adele","Lynda","Stewart"],"index":1426,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9852795601,"difficulty":0.0147204399}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 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":"Virginia can now know that Mary can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Virginia","Mary","Shirley","John"],"index":7131,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9822830558,"difficulty":0.0177169442}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlie's card is shown to William. William's card is shown to Charlie. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether Marta picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Marta can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marta","William","Charlie"],"index":6019,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9689025283,"difficulty":0.0310974717}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leon can now know that Leon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marjorie","Charlene","William","Leon"],"index":1144,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864231944,"difficulty":0.0135768056}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marilyn's card is shown to Jerry. Jerry's card is shown to Marilyn. It is publicly announced that someone picked a red card. It is publicly announced that Jerry does not know whether or not everyone picked a red card. It is publicly announced that Jerry knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Jerry can now know that Marilyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jerry","Marilyn"],"index":1263,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8946508765,"difficulty":1.8946508765}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Betsy can now know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betsy","Scott","George","Suzanne"],"index":9427,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.986448586,"difficulty":0.013551414}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Calvin's card is shown to Michael. Ralph's card is shown to Calvin. Donna's card is shown to Calvin. Michael's card is shown to Ralph. Ralph's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Donna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd 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 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Ralph can now know whether Donna can know that Calvin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Calvin","Ralph","Donna"],"index":7279,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5521048903,"difficulty":0.4478951097}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Ellen. Gladys's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ellen can now know whether Gladys can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ellen","Gladys","Timothy"],"index":4813,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8120833039,"difficulty":0.1879166961}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anita's card is shown to Daniel. Michael's card is shown to Daniel. Daniel's card is shown to Michael. Anita's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Daniel picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb: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:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Daniel can now know whether Anita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daniel","Anita","Michael"],"index":3079,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6708350182,"difficulty":0.3291649818}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold does not know whether Michelle is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Harold can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jana","Michelle","Harold"],"index":2459,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.970252037,"difficulty":0.029747963}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana knows whether Tony's forehead is muddy. It is publicly announced that Tony knows whether Diana's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Tony can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diana","Tony","Gary"],"index":2024,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9841878414,"difficulty":0.0158121586}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Lawrence can now know that Virginia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lawrence","Virginia"],"index":3788,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7273436785,"difficulty":0.2726563215}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcia 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 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":"Marcia can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lynda","Robert","Marcia"],"index":2089,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8536192179,"difficulty":1.8536192179}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Alfredo","Thomas","William"],"index":2647,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9859651327,"difficulty":0.0140348673}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgia does not know whether Georgia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Georgia can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Georgia","Cheryl"],"index":850,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9781252742,"difficulty":0.0218747258}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Kenneth can know that Larissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","George","Kenneth","Larissa"],"index":8881,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864322543,"difficulty":0.0135677457}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Manuel. Randall's card is shown to Kyle. Manuel's card is shown to Randall. Kyle's card is shown to Randall. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kyle can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Manuel","Kyle","Randall"],"index":2282,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9196817875,"difficulty":0.0803182125}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Ralph. Ralph's card is shown to Richard. Ralph's card is shown to Candice. Richard's card is shown to Candice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ralph can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Richard","Candice"],"index":5601,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9785897136,"difficulty":0.0214102864}
-{"premise":"There are three 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 muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Geoffrey can now know that Jesse can know that Jesse's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesse","Steven","Geoffrey"],"index":6807,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9818556905,"difficulty":1.9818556905}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steve's card is shown to Sharon. Renato's card is shown to Steve. Sharon's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether Steve picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Sharon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Renato","Sharon","Steve"],"index":2870,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9688091874,"difficulty":0.0311908126}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Margaret can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peggy","Margaret","Carolann"],"index":1223,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9754983783,"difficulty":0.0245016217}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Jermaine. Kathleen's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Scott does not know whether Jermaine picked a red card. It is publicly announced that Jermaine picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Scott can now know whether Scott picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Scott","Jermaine","Andrea","Kathleen"],"index":755,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7509513497,"difficulty":1.7509513497}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Nancy's forehead is muddy. It is publicly announced that Jesus 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 2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Nancy can now know whether Jesus can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jesus","Nancy"],"index":6649,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9324932694,"difficulty":0.0675067306}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Donald can now know that Harriet can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Terry","Donald","Margaret","Harriet"],"index":9564,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9787893295,"difficulty":0.0212106705}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Carl can now know whether Daniel can know that Daniel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carl","Daniel"],"index":7998,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6488042474,"difficulty":1.6488042474}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Mary can now know that Michael can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Mary"],"index":4655,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9721758366,"difficulty":0.0278241634}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joann does not know whether or not everyone is thirsty. It is publicly announced that Nellie does not know whether or not everyone is thirsty. It is publicly announced that Melissa does not know whether John is thirsty. It is publicly announced that Joann does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Melissa can now know that Nellie can know whether Joann is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joann","Melissa","Nellie","John"],"index":1015,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5750556588,"difficulty":0.4249443412}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emil's card is shown to Eduardo. Eduardo's card is shown to Emil. It is publicly announced that someone picked a red card. It is publicly announced that Eduardo does not know whether Elsie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Emil can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eduardo","Emil","Elsie"],"index":8856,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9694445133,"difficulty":0.0305554867}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Claude's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 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":"Randy can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Claude","Daniel","Robert","Randy"],"index":5312,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9816083312,"difficulty":0.0183916688}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Inez can now know that Tanya can know whether Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tanya","Inez","Dorothy","Jason"],"index":9481,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8467389345,"difficulty":0.1532610655}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Claire knows whether Claire's forehead is muddy. It is publicly announced that Claire's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Claire can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francisco","Marjorie","Claire"],"index":7142,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9852765203,"difficulty":0.0147234797}
-{"premise":"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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Veronica can now know that Carole can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carole","Veronica"],"index":4617,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9785467982,"difficulty":0.0214532018}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Rachel. Elizabeth's card is shown to Rachel. Rachel's card is shown to Michael. Elizabeth's card is shown to Michael. Michael's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Rachel picked a red card. It is publicly announced that Rachel knows whether Elizabeth picked a red card. It is publicly announced that Elizabeth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Elizabeth can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rachel","Michael","Elizabeth"],"index":6472,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9679797292,"difficulty":0.0320202708}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lindsey can now know that Sharlene can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rhonda","Sharlene","Michael","Lindsey"],"index":2019,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9756186008,"difficulty":0.0243813992}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know that Sheila's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Sheila","Sidney"],"index":1368,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864479303,"difficulty":0.0135520697}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether Annie'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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Julie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Annie","Julie"],"index":4869,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9730780125,"difficulty":0.0269219875}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryon's card is shown to Hollis. Brian's card is shown to Hollis. Hollis's card is shown to Bryon. Hollis's card is shown to Brian. Bryon's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hollis","Bryon","Brian"],"index":9565,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.972305119,"difficulty":0.027694881}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ernest can now know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Eric","Ernest"],"index":1819,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9863960743,"difficulty":0.0136039257}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Teresa can now know that Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Sharon","Teresa","Raymond"],"index":9494,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9784251451,"difficulty":0.0215748549}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosetta's card is shown to Lawrence. Robert's card is shown to Lawrence. Lawrence's card is shown to Rosetta. Robert's card is shown to Rosetta. Lawrence's card is shown to Myrtle. Lawrence's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Myrtle does not know whether Myrtle picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Rosetta picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(2) ] (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"Lawrence can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Rosetta","Myrtle","Robert"],"index":9563,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9626831412,"difficulty":0.0373168588}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Glenda can now know that Glenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margaret","Mildred","George","Glenda"],"index":8251,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9748395085,"difficulty":1.9748395085}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Janet. Juliette's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janet can now know whether Janet picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janet","Linda","Juliette"],"index":538,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6645362973,"difficulty":1.6645362973}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marjorie does not know whether or not everyone is thirsty. It is publicly announced that John knows whether John is thirsty. It is publicly announced that Monica does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"John can now know that Marjorie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monica","Marjorie","John","Stanley"],"index":7593,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9699847102,"difficulty":0.0300152898}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond knows whether someone is thirsty. It is publicly announced that Raymond does not know whether Leon is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Raymond can now know that Leon can know whether Leon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Leon"],"index":8518,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.740473628,"difficulty":0.259526372}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lindsey does not know whether Lindsey's forehead 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 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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Timothy can now know that Lindsey can know whether Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Lindsey","John","Timothy"],"index":3735,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9054929614,"difficulty":0.0945070386}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne does not know whether or not everyone's forehead is muddy. It is publicly announced that Rob knows whether someone's forehead is muddy. It is publicly announced that Wayne does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Wayne can now know that Rob can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Wayne","Rob"],"index":8706,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9769780636,"difficulty":0.0230219364}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether Bruno is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Dorothy can now know that Bruno can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bruno","Dorothy","James"],"index":911,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9763823152,"difficulty":0.0236176848}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Timothy knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Joan can now know whether Timothy can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Timothy","Joan"],"index":2673,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9728276134,"difficulty":0.0271723866}
-{"premise":"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 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 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Philip can now know whether Frances's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Andrew","Frances","Philip"],"index":5164,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9123077989,"difficulty":0.0876922011}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan does not know whether Juan's forehead is muddy. 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)) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Juan can now know whether Julia can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julia","Juan","Regina","Dawn"],"index":2184,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9315120578,"difficulty":0.0684879422}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Adriana can now know that Francisco can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Adriana","Francisco"],"index":3348,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9793660641,"difficulty":0.0206339359}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Virginia can now know whether Courtney can know that Timothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Courtney","Virginia"],"index":3231,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6518793106,"difficulty":0.3481206894}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kurtis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Kurtis can now know whether Gary can know that Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kurtis","Gary","Mary"],"index":5804,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9386133552,"difficulty":0.0613866448}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Corey. Willie's card is shown to Michael. Corey's card is shown to Willie. Michael's card is shown to Willie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Corey can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Corey","Michael","Willie"],"index":69,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9822922945,"difficulty":0.0177077055}
-{"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":"Felix can now know that Bobby can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Felix","Steve","Bobby","Greg"],"index":301,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9857080579,"difficulty":0.0142919421}
-{"premise":"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 Miguel's forehead is muddy. It is publicly announced that Gina's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] Agentb 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) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"John can now know that Miguel can know that Miguel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","John","Miguel","Gina"],"index":2051,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9651986361,"difficulty":0.0348013639}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know whether Dennis can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Deborah","Dennis","Richard"],"index":1942,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9874360561,"difficulty":0.0125639439}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether or not nobody's forehead is muddy. 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) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Martha can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jimmy","Cynthia","Martha","Tracy"],"index":1492,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9557337761,"difficulty":0.0442662239}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Orlando does not know whether or not everyone's forehead is muddy. It is publicly announced that Lori knows whether someone's forehead is muddy. It is publicly announced that Orlando does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Lori can now know whether Orlando can know whether Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Orlando","Lori"],"index":9311,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9753469229,"difficulty":0.0246530771}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentc 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) ] 0","hypothesis":"Christene can now know whether Shaun can know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Shaun","Christene","Linda"],"index":6897,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.964679718,"difficulty":0.035320282}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chester knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Chester can now know whether Gerald can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Chester","Gerald","Alison"],"index":9113,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9889673591,"difficulty":0.0110326409}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold knows whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ricky can now know that Kenneth can know that Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Harold","Ricky","Charlie"],"index":6046,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9677063823,"difficulty":0.0322936177}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antoinette knows whether someone's forehead is muddy. It is publicly announced that Donald knows whether Blanche's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Donald can now know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Blanche","Antoinette","Joan"],"index":7268,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9295819402,"difficulty":0.0704180598}
-{"premise":"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 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 (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Lloyd can now know whether William can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lloyd","William"],"index":5186,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9886224866,"difficulty":0.0113775134}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (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":"Reinaldo can now know whether Mary can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Reinaldo","Mary","Juan","Daniel"],"index":7508,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9874815345,"difficulty":0.0125184655}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jean can now know that Lula can know that Jean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jean","Darla","Lula"],"index":3653,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9733321667,"difficulty":0.0266678333}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Malcolm can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amanda","Malcolm","John"],"index":8974,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8101721406,"difficulty":0.1898278594}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josephine knows whether Louise's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Josephine can now know whether Savannah can know whether Savannah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josephine","Robert","Savannah","Louise"],"index":6457,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9849519134,"difficulty":0.0150480866}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori knows whether Ruben's forehead is muddy. It is publicly announced that Lori knows whether someone's forehead is muddy. It is publicly announced that Lori's forehead is muddy.","smcdel_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 (1|2|3)) ] [ ! 2 ] Agentb knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Lori can now know that Sterling can know that Ruben's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruben","Lori","Sterling"],"index":526,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9558631182,"difficulty":0.0441368818}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rodney's card is shown to Jeremiah. Casandra's card is shown to Jeremiah. Casandra's card is shown to Rodney. Larry's card is shown to Casandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rodney can now know whether Jeremiah can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeremiah","Larry","Rodney","Casandra"],"index":4503,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9311789274,"difficulty":0.0688210726}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earl knows whether Norman's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Earl can now know whether Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patrick","Earl","Norman","Robert"],"index":5491,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9533250332,"difficulty":0.0466749668}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lillie's card is shown to Mildred. John's card is shown to Lillie. Lillie's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know that Lillie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mildred","Lillie","John","William"],"index":5578,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9575734735,"difficulty":0.0424265265}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Leslie can now know whether Mary can know that Leslie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Leslie","Sean","Thomas"],"index":480,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8755429983,"difficulty":0.1244570017}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edna does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Natalie can now know that Cynthia can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Natalie","Carla","Edna","Cynthia"],"index":5349,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9882772565,"difficulty":0.0117227435}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Thomas. Linda's card is shown to Billy. Billy's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Billy knows whether someone picked a red card. It is publicly announced that Linda does not know whether or not everyone picked a red card. It is publicly announced that Linda knows whether or not nobody picked a red card. It is publicly announced that Linda does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Linda can now know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Billy","Linda"],"index":5735,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8969300389,"difficulty":0.1030699611}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julie","Amber","David"],"index":6242,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.980935216,"difficulty":0.019064784}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lana's card is shown to Lyle. Lyle's card is shown to Lana. James's card is shown to Lana. Lyle's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Lana picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Lyle can now know that Lana can know whether Lana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lyle","Lana","James"],"index":1231,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6489847302,"difficulty":0.3510152698}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether Joyce's forehead is muddy. It is publicly announced that Dana does not know whether Dana's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Joyce can now know that Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dana","Joyce","Raymond"],"index":4818,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9395601153,"difficulty":0.0604398847}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kasey knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Joshua can now know that Patricia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Leah","Kasey","Joshua"],"index":7197,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9890398979,"difficulty":0.0109601021}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to James. James's card is shown to Heather. Heather's card is shown to Curtis. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Heather","William","Curtis"],"index":8215,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9578745961,"difficulty":0.0421254039}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gilberto does not know whether Helen is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gilberto can now know that Helen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gilberto","Helen"],"index":3645,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9599755406,"difficulty":0.0400244594}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashlee's card is shown to Ida. Ida's card is shown to Diana. Ida's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ashlee can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ida","Ashlee","Diana","Linda"],"index":4104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9887341261,"difficulty":0.0112658739}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jamie is not thirsty. It is publicly announced that Glenn is not thirsty. It is publicly announced that Jamie does not know whether Mike is thirsty. It is publicly announced that Mike knows whether Mike is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] Agentb knows whether (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Jamie can now know whether Brandi can know that Jamie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandi","Jamie","Glenn","Mike"],"index":6178,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9193847179,"difficulty":0.0806152821}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fred does not know whether Vanessa is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Kevin can now know that Fred can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Fred","Vanessa","Kevin"],"index":5413,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9875589013,"difficulty":0.0124410987}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Richard. Richard's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Edward can now know whether Richard can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Edward","Pamela"],"index":4089,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9719150066,"difficulty":0.0280849934}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether someone is thirsty. It is publicly announced that Sonya knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"John can now know that Sonya can know that Sonya is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Laura","Sonya"],"index":5923,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9691330194,"difficulty":0.0308669806}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ricardo knows whether someone's forehead is muddy. It is publicly announced that Noelia knows whether Craig's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jerome can now know whether Noelia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Noelia","Craig","Ricardo","Jerome"],"index":8262,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9829152822,"difficulty":0.0170847178}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows that (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":"Daryl can now know that Ann can know whether Daryl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ann","Daryl","Pamela","Julie"],"index":9469,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8852465749,"difficulty":0.1147534251}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether David is thirsty. It is publicly announced that Ruth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] 0","hypothesis":"Joseph can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Ruth","Joseph"],"index":3976,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9539986849,"difficulty":0.0460013151}
-{"premise":"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 does not know whether Eugene's forehead is muddy. It is publicly announced that Denise 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) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Denise can now know that Estella's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eugene","Denise","Estella"],"index":7213,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9293844104,"difficulty":0.0706155896}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Dawn can now know that Caitlin can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Erin","John","Dawn","Caitlin"],"index":8947,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9718423486,"difficulty":0.0281576514}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Mary can now know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Fred"],"index":5335,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9857535362,"difficulty":0.0142464638}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Stephen can now know that James can know whether Joycelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cecil","James","Stephen","Joycelyn"],"index":1490,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7624223232,"difficulty":0.2375776768}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether Emery's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Emery can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emery","Anthony","Brian","Nathan"],"index":5441,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9898961782,"difficulty":0.0101038218}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Edward. Silvia's card is shown to Edward. Edward's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Edward can now know whether Walter picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edward","Walter","Silvia"],"index":3065,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5386470556,"difficulty":1.5386470556}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michelle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Willie","Brandon","Michelle"],"index":238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9790403843,"difficulty":0.0209596157}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Susan. Linda's card is shown to Richard. Richard's card is shown to Linda. Susan's card is shown to Gregory. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Richard","Linda","Gregory"],"index":8499,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8532710075,"difficulty":0.1467289925}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathlene does not know whether Perry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Barbara can now know whether Kathlene can know whether Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeanett","Kathlene","Barbara","Perry"],"index":4583,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9228131771,"difficulty":0.0771868229}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Esther can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","Esther","Joseph"],"index":5500,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9790696502,"difficulty":0.0209303498}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rick's card is shown to Norma. Rick's card is shown to Margaret. Margaret's card is shown to Rick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rick can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Norma","Margaret","Rick"],"index":4363,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9881718755,"difficulty":0.0118281245}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Candy can now know that Kimberly is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lucia","Kimberly","Candy","Seth"],"index":6629,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9574875832,"difficulty":1.9574875832}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Michael's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&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) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Michael can now know that Stanley can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Stanley"],"index":5840,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.983843863,"difficulty":0.016156137}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Grover. Cynthia's card is shown to Julio. Julio's card is shown to Cynthia. Julio's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Julio does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Cynthia can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Grover","Julio","Cynthia","Robert"],"index":8704,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6614816189,"difficulty":0.3385183811}
-{"premise":"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 Jeanie knows whether Raul's forehead is muddy. It is publicly announced that Jeanie knows whether Erica's forehead is muddy.","smcdel_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) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jeanie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erica","Jeanie","Raul"],"index":792,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9663527012,"difficulty":0.0336472988}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Abigail does not know whether Rosie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ricky can now know that Abigail can know that Rosie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rosie","Abigail","Ricky","Cheryl"],"index":1656,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9708031416,"difficulty":0.0291968584}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda's forehead is muddy. It is publicly announced that Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Domingo can now know that Glenna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glenna","Domingo","Wanda"],"index":3255,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9543503523,"difficulty":0.0456496477}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shawn's card is shown to Nancy. Nancy's card is shown to Shawn. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Shawn can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nancy","Shawn"],"index":9393,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9867562056,"difficulty":0.0132437944}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Danny can now know that Charles can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Danny","Charles"],"index":404,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9738529921,"difficulty":0.0261470079}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Damian does not know whether Carrie is thirsty. It is publicly announced that Damian knows whether Damian is thirsty. It is publicly announced that Kimberly does not know whether Carrie is thirsty. It is publicly announced that Kimberly knows whether Kimberly is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Damian can now know whether Kimberly can know whether Carrie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","Damian","Carrie"],"index":2303,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.965456605,"difficulty":0.034543395}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 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) ] [ ! ~(1) ] 0","hypothesis":"Guadalupe can now know that Barbara can know whether Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diane","Guadalupe","Barbara","Matthew"],"index":5918,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8755248785,"difficulty":1.8755248785}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robin does not know whether Elizabeth is thirsty. It is publicly announced that Richard knows whether or not nobody is thirsty. It is publicly announced that Robin does not know whether Richard is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know that Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frances","Robin","Elizabeth","Richard"],"index":2967,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9313619733,"difficulty":0.0686380267}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Dorothy. Dorothy's card is shown to Richard. Alejandro's card is shown to Annie. Dorothy's card is shown to Annie. Richard's card is shown to Annie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alejandro","Dorothy","Richard","Annie"],"index":3414,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9737756848,"difficulty":0.0262243152}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Marilee can now know that Laura can know that Marilee is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marilee","Laura"],"index":7809,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9714891911,"difficulty":0.0285108089}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Sharon. Sharon's card is shown to Nicholas. It is publicly announced that someone picked a red card. It is publicly announced that Sharon knows whether someone picked a red card. It is publicly announced that Sharon picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(1) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Nicholas can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sharon","Nicholas"],"index":606,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9863923192,"difficulty":0.0136076808}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Pamela is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Pamela can now know whether Stephen can know whether Beth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Beth","Pamela","Stephen"],"index":2310,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9264891744,"difficulty":0.0735108256}
-{"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 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Holly can now know whether Matthew can know whether Holly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Setsuko","Holly","Matthew","Ken"],"index":1632,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.936368525,"difficulty":0.063631475}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shanna knows whether Yong's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"John can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shanna","Cynthia","Yong","John"],"index":7292,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9880631566,"difficulty":0.0119368434}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Willie can now know that Benjamin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willie","Shawn","Benjamin","Christine"],"index":6065,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9556036592,"difficulty":0.0443963408}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shane does not know whether William is thirsty. It is publicly announced that Shane does not know whether William is thirsty. It is publicly announced that William does not know whether Ginger is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Shane can now know whether Ginger can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Ginger","Shane"],"index":8970,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9119745493,"difficulty":0.0880254507}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy. It is publicly announced that Tania knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Alan can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alan","Robert","Tania"],"index":7481,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9722078443,"difficulty":0.0277921557}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether Christine can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Christine","Felicia"],"index":7467,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9850162268,"difficulty":0.0149837732}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Penelope 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 (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":"Shanna can now know whether Penelope can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shanna","Carl","Penelope"],"index":6803,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7455449104,"difficulty":1.7455449104}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Marlin can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edward","Marlin","Jesse","Duane"],"index":7642,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8528952599,"difficulty":0.1471047401}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Cecelia. Cecelia's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether or not everyone picked a red card. It is publicly announced that Cecelia knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Deborah can now know that Cecelia can know that Cecelia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cecelia","Deborah"],"index":8489,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9324162602,"difficulty":1.9324162602}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Virginia can now know that Bennie can know that Louise is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bennie","Virginia","Louise","Ann"],"index":4082,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9738425612,"difficulty":0.0261574388}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas is thirsty. It is publicly announced that Thomas does not know whether Gerald is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Gerald can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gerald","Thomas"],"index":8975,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9736949801,"difficulty":0.0263050199}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 1)","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":"Kenneth can now know whether Donald can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Hannah","Kenneth","Donald"],"index":8498,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6469154358,"difficulty":0.3530845642}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony does not know whether Anthony's forehead is muddy. It is publicly announced that Stephanie knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] (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 2) ] 0","hypothesis":"Anthony can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Matilda","Anthony","Stephanie"],"index":9255,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9880378246,"difficulty":0.0119621754}
-{"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":"Lee can now know whether Gaye can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gaye","Beverly","Lee"],"index":9340,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9842776656,"difficulty":0.0157223344}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know that Nicolas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Nicolas","Joseph","Elizabeth"],"index":5922,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9589560628,"difficulty":0.0410439372}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Thomas can know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Thomas","Joseph","Jesse"],"index":274,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8187359571,"difficulty":1.8187359571}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cecelia's card is shown to Helen. Helen's card is shown to David. Andrea's card is shown to David. David's card is shown to Andrea. Andrea's card is shown to Cecelia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know that David can know that Helen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","David","Andrea","Cecelia"],"index":8270,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.972602129,"difficulty":0.027397871}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Jean can now know that George can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["George","Jean"],"index":2853,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9868676662,"difficulty":0.0131323338}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathy's card is shown to James. Kathy's card is shown to Yahaira. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Charles can now know whether James can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Charles","Yahaira","Kathy"],"index":3915,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.987922132,"difficulty":0.012077868}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louis knows whether someone is thirsty. It is publicly announced that Louis knows whether Kaitlyn is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Louis can now know whether Kaitlyn can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kaitlyn","Louis"],"index":6270,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9630247355,"difficulty":0.0369752645}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Raymond can now know that Kathleen can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Antonio","Kathleen","Raymond"],"index":8843,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9868938923,"difficulty":0.0131061077}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita does not know whether Rita's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that Rita'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 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"David can now know that Rita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Rita","Emery"],"index":312,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9415683746,"difficulty":0.0584316254}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Teresa can now know that Harold can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Teresa","Mabel","Michele"],"index":704,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9856697917,"difficulty":0.0143302083}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Nellie can now know whether Nellie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nellie","Douglas","Rosa","Carol"],"index":8789,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9721763134,"difficulty":0.0278236866}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Randy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Linda can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Randy","Kevin","Lindsay","Linda"],"index":44,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9872931242,"difficulty":0.0127068758}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn's forehead is muddy. It is publicly announced that Andy does not know whether Andy'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&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":"Andy can now know that Carolyn can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andy","Carolyn"],"index":4847,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6435370445,"difficulty":1.6435370445}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kitty knows whether Kitty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kitty can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessie","Kitty","Oscar","Larry"],"index":3682,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9778222442,"difficulty":0.0221777558}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Pauline","Robert","Marilyn","Bridgette"],"index":4375,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9883624911,"difficulty":0.0116375089}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Earnest can now know that Christopher can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earnest","Clorinda","John","Christopher"],"index":4541,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.987955749,"difficulty":0.012044251}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terry can now know whether Charles can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Terry","Charles","Bertha"],"index":1569,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8887289166,"difficulty":0.1112710834}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 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":"Richard can now know that Michael can know whether Ruby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Beverly","Richard","Ruby"],"index":9471,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8680929542,"difficulty":0.1319070458}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Ronald. George's card is shown to Ronald. Ronald's card is shown to Gloria. Jennifer's card is shown to Gloria. Ronald's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronald","Jennifer","Gloria","George"],"index":6389,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9894768,"difficulty":0.0105232}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason does not know whether Jason's forehead is muddy. It is publicly announced that Jason knows whether or not nobody's forehead is muddy. It is publicly announced that Jason 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) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jason can now know whether Jane's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jason","Jane","Melissa"],"index":3473,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9726033807,"difficulty":0.0273966193}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Sylvia can now know whether Sylvia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sylvia","Darrell","Mary"],"index":8598,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9722731113,"difficulty":0.0277268887}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathy knows whether someone is thirsty. It is publicly announced that Kathy does not know whether Derek is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Derek can now know that Kathy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kathy","Derek"],"index":7249,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9756284952,"difficulty":0.0243715048}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Meryl can now know whether Karen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Earnestine","Meryl","Karen","Carla"],"index":6173,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9777655005,"difficulty":0.0222344995}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Graciela can now know that David can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","David","Charles","Graciela"],"index":3159,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9732776284,"difficulty":0.0267223716}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Shannon can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roy","Brandon","Shannon","Orville"],"index":9177,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.979552567,"difficulty":0.020447433}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Wesley is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Vera can now know that Kathleen can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Wesley","Vera","Kathleen"],"index":42,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9873769283,"difficulty":0.0126230717}
-{"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 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know that John can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Stephanie","David"],"index":5121,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9715009928,"difficulty":0.0284990072}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josephine's card is shown to Charles. Charles's card is shown to Josephine. It is publicly announced that someone picked a red card. It is publicly announced that Josephine does not know whether Josephine picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Josephine can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Josephine"],"index":9122,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9880957603,"difficulty":0.0119042397}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernestine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Gregg can now know whether Betty can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregg","Ernestine","Rachel","Betty"],"index":4304,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9814024568,"difficulty":0.0185975432}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nettie does not know whether Jeanne is thirsty. It is publicly announced that Christine knows whether or not nobody is thirsty. It is publicly announced that Nettie does not know whether Christine is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Nettie","Jeanne","Christine"],"index":1357,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9646047354,"difficulty":0.0353952646}
-{"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":"Margaret can now know whether Shirley can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Margaret","Emily","Shirley"],"index":6731,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5325960517,"difficulty":0.4674039483}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jesus can now know that Larry can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","Larry","Margaret","Jesus"],"index":8618,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.979257524,"difficulty":0.020742476}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know whether Sarah can know whether Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Barbara","Michele","Sarah"],"index":6262,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8193091154,"difficulty":0.1806908846}
-{"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 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":"Dina can now know that Mitzi can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Mitzi","Dina","James"],"index":1342,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8373770714,"difficulty":0.1626229286}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Buck knows whether Eddie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] (Agentd knows that 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":"Eddie can now know that Cheryl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Buck","Cheryl","Kathy","Eddie"],"index":8657,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9483395815,"difficulty":0.0516604185}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 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":"Maria can now know whether Brenda can know whether Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Isaac","Brenda","Dwayne","Maria"],"index":202,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9286655188,"difficulty":1.9286655188}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felicia's card is shown to Lorenzo. Lorenzo's card is shown to Felicia. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Felicia can now know whether Felicia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lorenzo","Felicia"],"index":4029,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6270473599,"difficulty":0.3729526401}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows 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":"Robert can now know that Nikki can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edith","Sarah","Nikki","Robert"],"index":6970,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.985475719,"difficulty":0.014524281}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Crystal does not know whether Lori is thirsty. It is publicly announced that Mel knows whether someone is thirsty. It is publicly announced that Julie does not know whether or not everyone is thirsty. It is publicly announced that Julie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Julie can now know whether Crystal can know that Crystal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Lori","Crystal","Mel"],"index":5317,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9401550889,"difficulty":1.9401550889}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Mikel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mikel can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mikel","James","Maria"],"index":2744,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8903365135,"difficulty":0.1096634865}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cecil's card is shown to David. Cecil's card is shown to Gabriela. Gabriela's card is shown to Cecil. It is publicly announced that someone picked a red card. It is publicly announced that Cecil does not know whether Cecil picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"David can now know whether Cecil can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Gabriela","Cecil"],"index":2508,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9528903365,"difficulty":0.0471096635}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Bobbi can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Sylvia","Thomas","Bobbi"],"index":1800,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9879641533,"difficulty":0.0120358467}
-{"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 (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":"Shelly can now know that Leroy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leroy","Jason","Terri","Shelly"],"index":6991,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9872309566,"difficulty":0.0127690434}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura does not know whether Laura's forehead is muddy. It is publicly announced that Christopher knows whether someone's forehead is muddy. It is publicly announced that Andrew does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Laura can now know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Courtney","Christopher","Andrew"],"index":3667,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9268081188,"difficulty":0.0731918812}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jared does not know whether Robert is thirsty. It is publicly announced that Robert is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Kristy does not know whether Jared is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Eva can now know that Kristy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Eva","Kristy","Jared"],"index":8434,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9586777687,"difficulty":0.0413222313}
-{"premise":"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 Elizabeth's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Robert can now know that Don can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Don","Robert","Elizabeth"],"index":4211,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9837355614,"difficulty":0.0162644386}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd knows whether Carlos's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Carlos can now know whether Lloyd can know whether Marjorie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carlos","Marjorie","Lloyd","Cynthia"],"index":7922,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9852312803,"difficulty":0.0147687197}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Raymond is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gary can now know that Raymond can know that Raymond is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gary","Raymond","Betty"],"index":5503,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9722904563,"difficulty":0.0277095437}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Orville's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Orville can now know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Paul","Ronald","Orville"],"index":3075,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9737338424,"difficulty":0.0262661576}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Patrick can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Patrick","Angela"],"index":1296,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9747087955,"difficulty":0.0252912045}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gavin knows whether Louis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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) ] 0","hypothesis":"Louis can now know whether John can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Louis","Gavin","John","Paul"],"index":7244,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8869577646,"difficulty":1.8869577646}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nancy can now know whether Maggie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Gwenn","John","Maggie"],"index":9153,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9252640009,"difficulty":0.0747359991}
-{"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":"Rhonda can now know that Kara can know whether Kara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Rhonda","Kara","Jimmy"],"index":2649,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7810392976,"difficulty":1.7810392976}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Michael can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Catherine","Michael"],"index":4979,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9811142087,"difficulty":0.0188857913}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lavina can now know that Gail can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gail","Blaine","Lavina","Melvin"],"index":7227,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9809096456,"difficulty":0.0190903544}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sean's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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":"Geneva can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sean","Geneva","Kenneth","Howard"],"index":3594,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9861288667,"difficulty":0.0138711333}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne knows whether Joanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Johnny can now know whether Joanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Johnny","John","Kristina","Joanne"],"index":4181,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9849687815,"difficulty":0.0150312185}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theodora does not know whether Mildred is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Richard can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Aileen","Richard","Mildred","Theodora"],"index":6429,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9874952435,"difficulty":0.0125047565}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia does not know whether Virginia's forehead is muddy. It is publicly announced that Ashley 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) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Ashley can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Virginia","Ashley","Malcom"],"index":1028,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9888970256,"difficulty":0.0111029744}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leticia's card is shown to Shane. Deborah's card is shown to Shane. Shane's card is shown to Leticia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shane can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shane","Leticia","Deborah"],"index":309,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8838319182,"difficulty":0.1161680818}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeannie's card is shown to Rufina. Charles's card is shown to Robert. Jeannie's card is shown to Robert. Rufina's card is shown to Charles. Robert's card is shown to Charles. Rufina's card is shown to Jeannie. Charles's card is shown to Jeannie. It is publicly announced that someone picked a red card. It is publicly announced that Rufina picked a red card. It is publicly announced that Jeannie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jeannie can now know that Rufina can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rufina","Robert","Charles","Jeannie"],"index":2648,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5562630892,"difficulty":1.5562630892}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 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":"Joshua can now know that Ann can know that Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joshua","Tony","Ann","Theodore"],"index":2391,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9720692635,"difficulty":0.0279307365}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittany's card is shown to Michael. Michael's card is shown to Brittany. It is publicly announced that someone picked a red card. It is publicly announced that Brittany knows whether or not nobody picked a red card. It is publicly announced that Michael does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Brittany can now know whether Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Brittany"],"index":7771,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9728994966,"difficulty":0.0271005034}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Roberto's forehead is muddy. It is publicly announced that Todd's forehead is muddy.","smcdel_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 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 3) ] [ ! 2 ] 0","hypothesis":"Roberto can now know whether Thomas can know whether Todd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Todd","Roberto"],"index":3809,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9663317204,"difficulty":0.0336682796}
-{"premise":"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 or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Juanita can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Juanita","Edward","Ben"],"index":8021,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9894346595,"difficulty":0.0105653405}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter does not know whether Joel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Peter can now know whether Mike can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rodney","Mike","Joel","Peter"],"index":2442,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9380776882,"difficulty":0.0619223118}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lauren knows whether Benjamin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Benjamin can now know that Juliana can know that Benjamin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lauren","Juliana","Benjamin","Brian"],"index":4120,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9657434821,"difficulty":0.0342565179}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that William knows whether Lela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"William can now know whether Lela can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Caryn","Lela"],"index":4650,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9859045148,"difficulty":0.0140954852}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tina's card is shown to Johnny. Johnny's card is shown to Tina. Johnny's card is shown to Alfonso. It is publicly announced that someone picked a red card. It is publicly announced that Alfonso knows whether someone picked a red card. It is publicly announced that Tina picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] 0","hypothesis":"Alfonso can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Johnny","Tina","Alfonso"],"index":1418,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9863688946,"difficulty":0.0136311054}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephane does not know whether Willie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentd knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Timothy can now know whether Willie can know that Yolanda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephane","Willie","Yolanda","Timothy"],"index":134,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8554342389,"difficulty":0.1445657611}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yvonne knows whether Yvonne is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Orville can now know whether Yvonne can know that Orville is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Yvonne","Orville"],"index":7211,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8993428946,"difficulty":1.8993428946}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|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":"Jose can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ilona","Jose","Mark","Jason"],"index":1636,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9802442789,"difficulty":0.0197557211}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emerson does not know whether Melissa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Melissa can now know whether Christina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Scott","Emerson","Christina","Melissa"],"index":3659,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8698358536,"difficulty":0.1301641464}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Chris. Chris's card is shown to Cindy. Chris's card is shown to Jean. Chris's card is shown to Angela. Cindy's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Jean does not know whether Jean picked a red card. It is publicly announced that Cindy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Angela can now know whether Chris picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Chris","Cindy","Jean","Angela"],"index":6077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5781547427,"difficulty":0.4218452573}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony's forehead is not muddy. It is publicly announced that Douglas knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] (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) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Tony can now know whether Dallas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julie","Douglas","Tony","Dallas"],"index":3298,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9594524503,"difficulty":0.0405475497}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know whether Nelson can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Robert","Nelson"],"index":9397,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9677676558,"difficulty":0.0322323442}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monique's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that Carrol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Monique","Gregory","Robert","Carrol"],"index":4782,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9532254338,"difficulty":0.0467745662}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Deborah can now know whether Betty can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Ronald","Deborah"],"index":5080,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9859619737,"difficulty":0.0140380263}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Trisha does not know whether Elouise is thirsty. It is publicly announced that Trisha knows whether Trisha is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Trisha can now know that Elouise can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elouise","Trisha"],"index":6134,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8513511419,"difficulty":1.8513511419}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Susan can now know that Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Peter","Susan","Jaime"],"index":6317,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9541073442,"difficulty":0.0458926558}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Glenn. Glenn's card is shown to Elaine. It is publicly announced that someone picked a red card. It is publicly announced that Glenn does not know whether Glenn picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Elaine can now know whether Glenn can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Glenn","Elaine"],"index":6950,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9661829472,"difficulty":0.0338170528}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Brian. James's card is shown to Helen. Brian's card is shown to James. Denise's card is shown to James. Brian's card is shown to Denise. James's card is shown to Denise. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Denise can now know whether Helen can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Helen","James","Denise"],"index":2446,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9414528012,"difficulty":0.0585471988}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bonita can now know that Sylvester can know whether Sylvester's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bonita","Sylvester","Stephanie","Travis"],"index":3434,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9682844877,"difficulty":0.0317155123}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Elizabeth can now know whether Minerva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","Minerva"],"index":3774,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9872264266,"difficulty":0.0127735734}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angelica does not know whether Joann is thirsty. It is publicly announced that Joann knows whether someone is thirsty. It is publicly announced that Angelica does not know whether Joann is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Joann can now know that Angelica can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeanna","Angelica","Joann"],"index":6640,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6885045767,"difficulty":0.3114954233}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Beatrice. Robert's card is shown to Beatrice. Robert's card is shown to Elizabeth. Elizabeth's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth knows whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Beatrice can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Beatrice","Elizabeth","Robert"],"index":2,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7433175445,"difficulty":0.2566824555}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Meaghan can now know that Dorothy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Meaghan","Dorothy"],"index":3670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9812219739,"difficulty":0.0187780261}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Sarah. Gene's card is shown to Sarah. Gene's card is shown to Wanda. Wanda's card is shown to Gene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know that Sarah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Sarah","Wanda","Gene"],"index":4269,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9562837481,"difficulty":0.0437162519}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to John. John's card is shown to Andrea. John's card is shown to Denise. Andrea's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Denise knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Denise can now know that Andrea can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Andrea","Denise"],"index":7409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6531053185,"difficulty":0.3468946815}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eloisa's card is shown to Peggy. Gina's card is shown to Peggy. Denise's card is shown to Gina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Peggy can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Peggy","Denise","Eloisa","Gina"],"index":2829,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9881928563,"difficulty":0.0118071437}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jo's card is shown to Virginia. Rudy's card is shown to Jo. Jo's card is shown to Rudy. It is publicly announced that someone picked a red card. It is publicly announced that Jo knows whether someone picked a red card. It is publicly announced that Rudy does not know whether or not everyone picked a red card. It is publicly announced that Rudy knows whether or not nobody picked a red card. It is publicly announced that Rudy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jo can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Virginia","Jo","Rudy"],"index":3300,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9483448267,"difficulty":0.0516551733}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Shirley can now know that Sharon can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Sharon","Shirley","Ciara"],"index":1879,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5197777748,"difficulty":0.4802222252}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Edward can now know that Frank can know that Angelica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angelica","Edward","Frank"],"index":5526,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.97488904,"difficulty":0.02511096}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kevin can now know whether Ronald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kevin","Ronald","Emily"],"index":472,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8720411062,"difficulty":0.1279588938}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Larraine can now know whether Richard can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Larraine","Richard"],"index":2001,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9882311225,"difficulty":0.0117688775}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether James is thirsty. It is publicly announced that Joseph does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Danielle can now know that Rodrigo can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Rodrigo","Danielle","Joseph"],"index":9517,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8756950498,"difficulty":0.1243049502}
-{"premise":"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 Amber's forehead is muddy. It is publicly announced that Timothy knows whether someone's forehead is muddy. It is publicly announced that Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] Agentc knows whether (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Anthony can now know whether Amber can know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amber","Timothy","Anthony"],"index":8285,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9707891941,"difficulty":0.0292108059}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Lida is thirsty. It is publicly announced that Brian knows whether or not everyone is thirsty. It is publicly announced that Billy knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Lida can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lida","Billy","Brian"],"index":145,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9468767047,"difficulty":0.0531232953}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kelly can now know that Kelly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kelly","Michael","John"],"index":7514,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9644404054,"difficulty":0.0355595946}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tina can now know whether Helen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bradford","Helen","Lloyd","Tina"],"index":1120,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8833147883,"difficulty":0.1166852117}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sallie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Richard can now know whether Kenny's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cindie","Richard","Sallie","Kenny"],"index":5666,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9736117721,"difficulty":0.0263882279}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (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":"Emily can now know that Leah can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leah","Emily","Rose"],"index":2389,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9861394167,"difficulty":0.0138605833}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monika knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Nichole can now know that Monika can know that Vera's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vera","Nichole","Monika","John"],"index":6840,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9670101404,"difficulty":0.0329898596}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Sean's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Sean can now know that Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sean","Jose","Sandra","Gerardo"],"index":6144,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9505758882,"difficulty":0.0494241118}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alicia can now know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Mary","Alicia","Joseph"],"index":6765,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9821332097,"difficulty":0.0178667903}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Christopher. Michael's card is shown to Christopher. Christopher's card is shown to Paul. Michael's card is shown to Paul. Paul's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Paul","Michael"],"index":654,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8723335266,"difficulty":0.1276664734}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edwin knows whether Anna's forehead is muddy. It is publicly announced that Anna does not know whether or not everyone's forehead is muddy. It is publicly announced that Anna does not know whether Anna's forehead 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 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Garry can now know that Anna can know whether Edwin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Garry","Amy","Anna","Edwin"],"index":2601,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.850638628,"difficulty":0.149361372}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Denise can now know that Carrie can know that Melinda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carrie","Marcia","Denise","Melinda"],"index":7476,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9729130268,"difficulty":0.0270869732}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan does not know whether Bryan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Bryan can now know whether Nick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nick","Paula","Bryan"],"index":706,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9365326166,"difficulty":0.0634673834}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Cynthia. Cynthia's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia picked a black card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(1&2)) ] 0","hypothesis":"Eric can now know that Cynthia can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cynthia","Eric"],"index":3384,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9746590853,"difficulty":0.0253409147}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy. It is publicly announced that Edward's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Edward can now know whether Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Renee","Aaron","Edward"],"index":3829,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9771263003,"difficulty":0.0228736997}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know whether Katherine can know that Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Katherine","Barbara"],"index":2244,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8147111535,"difficulty":1.8147111535}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Mary","Richard"],"index":656,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9628653526,"difficulty":0.0371346474}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 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":"John can now know whether James can know that Nathan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Nathan","Patrick","James"],"index":6308,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6891634464,"difficulty":0.3108365536}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_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":"Kevin can now know that Helen can know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","Kevin","Nicholas"],"index":5612,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.967486918,"difficulty":0.032513082}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Kathleen. Kathleen's card is shown to Archie. Kathleen's card is shown to Edward. Archie's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Archie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Edward can now know whether Kathleen can know that Archie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Archie","Edward"],"index":3871,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9673008323,"difficulty":0.0326991677}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herbert's card is shown to Heather. Heather's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Herbert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Tracy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Heather","Tracy","Herbert"],"index":9015,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9867729545,"difficulty":0.0132270455}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christine does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Christine can now know that Wanda can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edwin","Deneen","Christine","Wanda"],"index":8997,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9777418971,"difficulty":0.0222581029}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marie can now know that Thomas can know whether Marie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Michael","Thomas","Reva"],"index":9460,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9754071832,"difficulty":0.0245928168}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Charles can now know that Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Richard","James","Charles"],"index":5708,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9504083395,"difficulty":0.0495916605}
-{"premise":"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 Angela's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Steven can now know that Angela can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Angela","Steven"],"index":2576,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9776192904,"difficulty":0.0223807096}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Anthony. Anthony's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Anthony can now know that Elizabeth can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anthony","Elizabeth"],"index":8693,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9772596359,"difficulty":0.0227403641}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know that Walter can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jamie","Walter","Michelle","Bruce"],"index":2403,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.979793191,"difficulty":0.020206809}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Connie can now know that Charles can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Matthew","Donna","Connie"],"index":8591,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9675228596,"difficulty":0.0324771404}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rebecca can now know whether Pamela can know whether Pamela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Otis","Pamela","Rebecca"],"index":8887,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9819513559,"difficulty":0.0180486441}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cassondra does not know whether Carl is thirsty. It is publicly announced that Mozella is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] 0","hypothesis":"Cassondra can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carl","Mozella","Cassondra"],"index":3852,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7677209973,"difficulty":0.2322790027}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ilona does not know whether Ilona's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kum can now know that Deidra can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kum","Ilona","Robert","Deidra"],"index":8035,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8235545158,"difficulty":0.1764454842}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gertrude knows whether Roger's forehead is muddy. It is publicly announced that Gertrude 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) ] [ ! ~(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) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Gertrude can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roger","Gertrude"],"index":3833,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9886553288,"difficulty":0.0113446712}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carina is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Robert can now know whether Bonnie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Bonnie","Carina"],"index":8474,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9298411012,"difficulty":0.0701588988}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Chauncey can now know that Opal's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Opal","Chauncey","John"],"index":4487,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9615944624,"difficulty":0.0384055376}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Latasha's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Marie can now know that Theresa can know that Latasha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Latasha","Marie","Theresa"],"index":6140,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9710738659,"difficulty":0.0289261341}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marjorie's card is shown to Rena. Rena's card is shown to Greta. Rena's card is shown to Marjorie. Greta's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Greta does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 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:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Rena can now know whether Marjorie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rena","Greta","Marjorie"],"index":700,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8635850549,"difficulty":1.8635850549}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darlene's card is shown to Robert. Robert's card is shown to Jack. Darlene's card is shown to Jack. Jack's card is shown to Darlene. It is publicly announced that someone picked a red card. It is publicly announced that Jack does not know whether Jack picked a red card. It is publicly announced that Jack knows whether someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(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:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Jack","Darlene"],"index":1761,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6039259434,"difficulty":1.6039259434}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether 1)","n_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":"Gregory can now know whether Rachel can know whether Rachel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rachel","Melissa","Gregory"],"index":1159,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9626240134,"difficulty":1.9626240134}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sue knows whether Alfred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Laura can now know that Deborah can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alfred","Sue","Laura","Deborah"],"index":3484,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9727635384,"difficulty":0.0272364616}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patty's card is shown to Ethel. Patty's card is shown to David. Patty's card is shown to Brigid. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that Ethel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ethel","Patty","David","Brigid"],"index":2855,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9556273818,"difficulty":0.0443726182}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Robert can now know that Karen can know whether Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Karen","Robert"],"index":1051,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9710891843,"difficulty":0.0289108157}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jesus can now know whether Woodrow can know that Woodrow's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antonio","Woodrow","Katherine","Jesus"],"index":214,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.610134244,"difficulty":1.610134244}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Jerry. Ramon's card is shown to Laura. Jerry's card is shown to Ramon. Laura's card is shown to Ramon. It is publicly announced that someone picked a red card. It is publicly announced that Laura knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Laura can now know that Laura picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jerry","Laura","Ramon"],"index":1584,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9499867558,"difficulty":0.0500132442}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether (1&2&3))","n_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 Marie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Marie","Jonathan"],"index":8544,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8951097727,"difficulty":1.8951097727}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clyde can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","James","Rebecca","Clyde"],"index":14,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9806287289,"difficulty":0.0193712711}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Camilla can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Shawn","Camilla","Michael"],"index":1111,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9789760709,"difficulty":0.0210239291}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gretchen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Gretchen can now know that Melody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gretchen","Melody"],"index":4334,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9025509357,"difficulty":0.0974490643}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelo's card is shown to Curtis. Lauren's card is shown to Curtis. Mark's card is shown to Curtis. Angelo's card is shown to Mark. Lauren's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Curtis knows whether Curtis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Curtis can now know that Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Curtis","Angelo","Lauren","Mark"],"index":3783,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9534454942,"difficulty":0.0465545058}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jamie's card is shown to Nancy. Nancy's card is shown to Jamie. It is publicly announced that someone picked a red card. It is publicly announced that Nancy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jamie can now know whether Nancy can know that Jamie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Jamie"],"index":1798,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9626948237,"difficulty":0.0373051763}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne knows whether Suzanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Adeline can now know that Mae can know that Suzanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mae","Adeline","Suzanne","Hershel"],"index":9110,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9678763151,"difficulty":0.0321236849}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Michael. Steven's card is shown to Linda. John's card is shown to Linda. Linda's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Linda can now know that Michael can know whether Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Linda","Steven","John"],"index":4329,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5198705196,"difficulty":0.4801294804}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eugene can now know that Eugene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eugene","Young","Joshua","Daniel"],"index":5419,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9626626968,"difficulty":0.0373373032}
-{"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 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":"Lois can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roy","John","Janice","Lois"],"index":4274,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9457694292,"difficulty":0.0542305708}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Dennis can now know whether John can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Dennis"],"index":5845,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9848026633,"difficulty":0.0151973367}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know that Eileen can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Michael","Eileen","Veronica"],"index":6126,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8902766109,"difficulty":0.1097233891}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Robert. George's card is shown to Calvin. Ted's card is shown to Calvin. Ted's card is shown to George. Robert's card is shown to Ted. George's card is shown to Ted. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Ted does not know whether Calvin picked a red card. It is publicly announced that Robert does not know whether Calvin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Ted can now know that George can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Calvin","George","Ted"],"index":2943,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9726993442,"difficulty":0.0273006558}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"George can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","George"],"index":6602,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8952996135,"difficulty":0.1047003865}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie is thirsty. It is publicly announced that Julie does not know whether Mitchell is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Julie can now know whether Julie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mitchell","Julie"],"index":4824,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.805655241,"difficulty":1.805655241}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Dale is thirsty. It is publicly announced that Thomas knows whether Thomas is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dale can now know whether Thomas can know that Dale is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dale","Thomas"],"index":3550,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9312562346,"difficulty":0.0687437654}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Imelda knows whether or not everyone's forehead is muddy. It is publicly announced that Evelyn knows whether Evelyn'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) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Evelyn can now know that Imelda can know that Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Imelda","Evelyn"],"index":7581,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.954701066,"difficulty":0.045298934}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Linda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Linda can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clint","Jose","Linda"],"index":1744,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9777665138,"difficulty":0.0222334862}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Donna. Christopher's card is shown to Helen. Christopher's card is shown to Christine. Christine's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Helen knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd: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:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Christopher can now know that Christine can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Helen","Christine","Christopher"],"index":7126,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9890996814,"difficulty":0.0109003186}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Virginia. Donald's card is shown to Alberta. Alberta's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virginia","Alberta","Donald"],"index":1517,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9760962129,"difficulty":0.0239037871}
-{"premise":"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 Neva's forehead is muddy. It is publicly announced that Suzanne knows whether someone's forehead is muddy. It is publicly announced that Suzanne's forehead is muddy.","smcdel_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 (1|2|3)) ] [ ! 2 ] 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) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Neva can now know whether Suzanne can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Neva","Suzanne","Annamarie"],"index":3239,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9767075181,"difficulty":0.0232924819}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha does not know whether Barry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Richard can now know that Chad can know that Martha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Chad","Richard","Barry"],"index":7776,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9695916176,"difficulty":0.0304083824}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Dalia. Connie's card is shown to Keith. Dalia's card is shown to Phillip. Connie's card is shown to Phillip. Keith's card is shown to Connie. Phillip's card is shown to Connie. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Phillip can now know whether Dalia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dalia","Keith","Phillip","Connie"],"index":3095,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5876687169,"difficulty":0.4123312831}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cornelia's card is shown to Deirdre. Cornelia's card is shown to Benjamin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cornelia can now know that Deirdre can know that Deirdre picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cornelia","Deirdre","Benjamin"],"index":158,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9736808538,"difficulty":0.0263191462}
-{"premise":"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 Mildred knows whether or not everyone's forehead is muddy. It is publicly announced that Mildred does not know whether Mildred's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Delbert can now know that Delbert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Delbert","Mildred","Victoria"],"index":1309,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9372009039,"difficulty":0.0627990961}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Matthew. Justin's card is shown to John. Matthew's card is shown to Justin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Justin can now know that Justin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","John","Justin"],"index":2561,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9569160342,"difficulty":0.0430839658}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricky's card is shown to Maria. Whitney's card is shown to Maria. Maria's card is shown to Louis. Ricky's card is shown to Louis. Maria's card is shown to Whitney. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maria","Ricky","Louis","Whitney"],"index":2724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9815763235,"difficulty":0.0184236765}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Bernice is thirsty. It is publicly announced that Charles does not know whether Bernice is thirsty. It is publicly announced that Bernice does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Bernice can now know that Charles can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bernice","John","Charles"],"index":959,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8557168245,"difficulty":0.1442831755}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that John does not know whether Thomas is thirsty. It is publicly announced that Lorena does not know whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Thomas can now know whether John can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lorena","Thomas","Viola","John"],"index":1831,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9855002761,"difficulty":0.0144997239}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Randy can now know whether Paul can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randy","Paul"],"index":801,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.988450408,"difficulty":0.011549592}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Matthew can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Matthew","Margaret","Tony"],"index":1,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9753417373,"difficulty":0.0246582627}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Robert can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Mark","David","Joseph"],"index":140,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8660005927,"difficulty":0.1339994073}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Bethany can now know that Russel can know that Russel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Russel","Bethany"],"index":982,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9655784965,"difficulty":0.0344215035}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kimberly can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Kimberly","Gary","Darren"],"index":741,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9902336597,"difficulty":0.0097663403}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Cheryl. James's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cheryl can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Cheryl","Paul"],"index":2731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9547561407,"difficulty":0.0452438593}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiffany 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 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":"Don can now know whether Tiffany's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Don","Tiffany"],"index":7490,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.981459856,"difficulty":0.018540144}
-{"premise":"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 does not know whether Todd's forehead 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)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Todd can now know that Jean can know whether Todd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jean","Todd","Pamela","Yadira"],"index":6618,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8494390249,"difficulty":0.1505609751}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan knows whether Eric's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jana can now know whether Carole can know whether Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Carole","Jonathan","Jana"],"index":5878,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9852716923,"difficulty":0.0147283077}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Leroy is not thirsty. It is publicly announced that Alice does not know whether Jeffery is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Jeffery can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leroy","Jeffery","Angela","Alice"],"index":2291,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7549724579,"difficulty":1.7549724579}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Donna. Donna's card is shown to John. Betty's card is shown to John. John's card is shown to Betty. John's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Donna can now know that John can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","John","Betty","Patricia"],"index":5187,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9879239202,"difficulty":0.0120760798}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mary can now know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Faith","Mary","Dorothy"],"index":973,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9551715851,"difficulty":0.0448284149}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Alexander is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Angela can now know whether Angela is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alexander","Angela","Jennifer","Leland"],"index":3489,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8928523064,"difficulty":1.8928523064}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Sylvester. Dreama's card is shown to Willie. Sylvester's card is shown to Douglas. Dreama's card is shown to Douglas. Willie's card is shown to Dreama. Douglas's card is shown to Dreama. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Willie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sylvester","Willie","Douglas","Dreama"],"index":3118,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9753138423,"difficulty":0.0246861577}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Earl is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Earl can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Earl","Robert"],"index":9249,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7380603552,"difficulty":0.2619396448}
-{"premise":"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 Ray's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"David can now know that Vera's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Scotty","Ray","David","Vera"],"index":970,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9343764782,"difficulty":0.0656235218}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adela's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Danika can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Adela","Danika"],"index":945,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9756130576,"difficulty":0.0243869424}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Virginia can now know whether John can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elena","Rosalie","Virginia","John"],"index":6664,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.988902986,"difficulty":0.011097014}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether 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) ] [ ! (Agentb knows whether 4) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Theresa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nanette","Donald","Theresa","Hattie"],"index":4943,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9697754383,"difficulty":0.0302245617}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry does not know whether Keely is thirsty. It is publicly announced that Bryan knows whether or not nobody is thirsty. It is publicly announced that Larry does not know whether Bryan is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Bryan can now know that Keely is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Larry","Keely","Bryan"],"index":8385,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9320207238,"difficulty":0.0679792762}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steve does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Steve can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Steve","Nicole"],"index":598,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9876686931,"difficulty":0.0123313069}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virgilio does not know whether Virgilio's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"David can now know that Robert can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","David","Virgilio","Richard"],"index":5319,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9654167891,"difficulty":0.0345832109}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Greg knows whether Greg's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mary can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Greg","Patricia","David"],"index":8258,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.987906456,"difficulty":0.012093544}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Grace. Christine's card is shown to Grace. Evelyn's card is shown to Grace. Christine's card is shown to David. Evelyn's card is shown to David. Grace's card is shown to Christine. David's card is shown to Evelyn. Christine's card is shown to Evelyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Grace can now know that Evelyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Grace","David","Christine","Evelyn"],"index":1690,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9558973312,"difficulty":0.0441026688}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Erika. Erika's card is shown to Billy. Erika's card is shown to Joan. Billy's card is shown to Joan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 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:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joan can now know whether Erika can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erika","Billy","Joan"],"index":9322,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.987321794,"difficulty":0.012678206}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kellie does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"David can now know that Kellie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","David","Kellie"],"index":9144,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9869446158,"difficulty":0.0130553842}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Frank can now know whether Felicia can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathy","Frank","John","Felicia"],"index":2361,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6230816245,"difficulty":0.3769183755}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Lori. Paula's card is shown to Sylvester. Sylvester's card is shown to Paula. It is publicly announced that someone picked a red card. It is publicly announced that Paula does not know whether Paula picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Paula can now know that Lori can know that Lori picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lori","Sylvester","Paula"],"index":7269,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9680321217,"difficulty":0.0319678783}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Patricia can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacqueline","Michelle","James","Patricia"],"index":6299,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9754875898,"difficulty":0.0245124102}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Lawrence can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Lawrence","David","Janice"],"index":7154,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9560157657,"difficulty":0.0439842343}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruben knows whether Ana's forehead is muddy. It is publicly announced that Ana does not know whether or not everyone's forehead is muddy. It is publicly announced that Ana does not know whether Ana's forehead 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 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Malinda can now know that Ana can know that Malinda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Malinda","Rebecca","Ana","Ruben"],"index":1024,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9608591795,"difficulty":1.9608591795}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1|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":"Charlene can now know whether Leonard can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leonard","Charlene","Jennifer","Henry"],"index":7275,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9874238372,"difficulty":0.0125761628}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cedric does not know whether Cedric's forehead is muddy. It is publicly announced that Kenny 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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Casey can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cedric","Casey","Kenny","William"],"index":528,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9660751224,"difficulty":0.0339248776}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher does not know whether Susan is thirsty. It is publicly announced that Hannah does not know whether Susan is thirsty. It is publicly announced that Hannah does not know whether Cindy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentb knows whether (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Susan can now know whether Hannah can know that Christopher is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cindy","Susan","Christopher","Hannah"],"index":223,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9037876129,"difficulty":0.0962123871}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn does not know whether Johnie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Johnie can now know whether Johnie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Johnie","Evelyn","Beth"],"index":1485,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8126618862,"difficulty":1.8126618862}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Travis. Travis's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Travis knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Robin can now know that Travis can know whether Robin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Travis","Robin","John"],"index":9612,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5710040331,"difficulty":0.4289959669}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tony can now know that Michelle can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Tony","Melody","Steven"],"index":3071,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9861575365,"difficulty":0.0138424635}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cora's card is shown to Cathleen. Cora's card is shown to Maria. Cathleen's card is shown to Cora. Cathleen's card is shown to Robert. Maria's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Cora picked a red card. It is publicly announced that Cora does not know whether Cora picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Robert can now know whether Cora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cathleen","Maria","Cora","Robert"],"index":141,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5171721578,"difficulty":0.4828278422}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cathy knows whether Chad's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Cathy can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Cathy","Chad","Janice"],"index":6392,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9896553755,"difficulty":0.0103446245}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (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":"Hester can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hester","Mary","Jerry"],"index":3168,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.972823441,"difficulty":0.027176559}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Mark can know that Mark is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Mark","Carl"],"index":1014,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9751926064,"difficulty":0.0248073936}
-{"premise":"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 knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Kevin can now know that Glen can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Glen","Steven"],"index":75,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9890216589,"difficulty":0.0109783411}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vicki's card is shown to Randy. Cara's card is shown to Randy. Melissa's card is shown to Vicki. It is publicly announced that someone picked a red card. It is publicly announced that Randy does not know whether Cara picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Melissa can now know that Vicki picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Randy","Vicki","Cara"],"index":2495,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9548372626,"difficulty":0.0451627374}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jimmie can now know that Katherine can know that Jimmie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmie","Katherine","Debra"],"index":7902,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9721473455,"difficulty":1.9721473455}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francine does not know whether Francine's forehead is muddy. It is publicly announced that Larry does not know whether Larry's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Francine can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Michel","Francine"],"index":760,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9729952216,"difficulty":0.0270047784}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelica's card is shown to George. George's card is shown to Angelica. It is publicly announced that someone picked a red card. It is publicly announced that Angelica does not know whether Angelica picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"George can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["George","Angelica"],"index":2801,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9887427092,"difficulty":0.0112572908}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Jose. Jose's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Jose knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 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":"Jose can now know whether Douglas can know that Jose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jose","Douglas"],"index":2264,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9790338874,"difficulty":1.9790338874}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bradley's card is shown to Jesse. Stephen's card is shown to Jesse. Jesse's card is shown to Bradley. Jesse's card is shown to Stephen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know whether Bradley picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesse","Bradley","Roger","Stephen"],"index":4522,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8467511535,"difficulty":0.1532488465}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kandice does not know whether or not everyone's forehead is muddy. It is publicly announced that Kandice does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows 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":"Kandice can now know that Audra can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Audra","Kandice"],"index":483,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9784182906,"difficulty":0.0215817094}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Violet's card is shown to Kenny. Kenny's card is shown to Rebecca. Violet's card is shown to Rebecca. Kenny's card is shown to Violet. Rebecca's card is shown to Violet. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Violet does not know whether Violet picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kenny can now know whether Violet can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenny","Rebecca","Violet"],"index":7033,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9821395278,"difficulty":0.0178604722}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Nicole. John's card is shown to Nicole. Nicole's card is shown to Nicholas. Nicole's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know whether Nicole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nicole","Nicholas","Michelle","John"],"index":6358,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8245886564,"difficulty":1.8245886564}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Marie knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Marie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marie","Amber","Joshua"],"index":8299,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9770820737,"difficulty":0.0229179263}
-{"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 (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":"Billy can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","William","Charles","Gwen"],"index":3762,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9868509173,"difficulty":0.0131490827}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Truman. Truman's card is shown to Lara. Lara's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Lara picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Lara can now know whether Truman picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Truman","Lara","John"],"index":7069,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5544674397,"difficulty":0.4455325603}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jesse can now know whether Loretta can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jesse","Loretta"],"index":7399,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9547963738,"difficulty":1.9547963738}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Brittney. Brittney's card is shown to Daniel. Daniel's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Brittney does not know whether Brittney picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Brittney can now know whether Daniel can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brittney","Daniel","Jennifer"],"index":556,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9882951975,"difficulty":0.0117048025}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Sally can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Carol","Sally","Cindy"],"index":4436,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9818601012,"difficulty":0.0181398988}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Joseph can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joseph","Carolyn"],"index":5235,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7762268186,"difficulty":0.2237731814}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Jane can now know that Jane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Allen","Jane"],"index":5077,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9660934806,"difficulty":0.0339065194}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Willard can now know that Mark can know whether Willard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mark","Willard"],"index":4860,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9823887944,"difficulty":0.0176112056}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Steven can now know that David can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["David","Steven"],"index":1188,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9769639373,"difficulty":0.0230360627}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Veronica can now know whether Natalie can know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Veronica","Natalie","John","Elizabeth"],"index":1776,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7482344508,"difficulty":0.2517655492}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Ryan. Ryan's card is shown to Travis. Gregory's card is shown to Travis. Gregory's card is shown to Susan. Ryan's card is shown to Gregory. Susan's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Ryan picked a red card. It is publicly announced that Travis knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Gregory can now know that Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","Travis","Susan","Gregory"],"index":2863,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9402785897,"difficulty":0.0597214103}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Latoya does not know whether Steven is thirsty. It is publicly announced that James knows whether or not nobody is thirsty. It is publicly announced that Latoya does not know whether James is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know that Latoya is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Garland","Latoya","Steven","James"],"index":129,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9313274622,"difficulty":0.0686725378}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Clarence. Clarence's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether Clarence picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Clarence can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Clarence","Paul"],"index":7692,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.537227571,"difficulty":0.462772429}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alfredo's card is shown to Gregory. Gregory's card is shown to Alfredo. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Gregory can now know whether Alfredo can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gregory","Alfredo"],"index":7610,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.987521708,"difficulty":0.012478292}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Daniel can now know whether Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kristy","Daniel"],"index":3337,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9876357913,"difficulty":0.0123642087}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann does not know whether Bryan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentd knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Derrick can now know that Bryan can know whether Bryan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ann","Maritza","Bryan","Derrick"],"index":6231,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8601005673,"difficulty":1.8601005673}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (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) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Jennifer can now know that Leroy can know that Madeline's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Madeline","Ricardo","Jennifer","Leroy"],"index":337,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9653207064,"difficulty":0.0346792936}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ricky's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 1)","n_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":"Juan can now know that Juan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Juan","Ricky","Gary"],"index":1338,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9548638463,"difficulty":0.0451361537}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Miriam does not know whether Diana is thirsty. It is publicly announced that Miriam is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Miriam can now know that Miriam is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roberta","Diana","Miriam"],"index":638,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9549683332,"difficulty":0.0450316668}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Howard. Howard's card is shown to Samira. Thomas's card is shown to Olga. Olga's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Olga can now know whether Thomas can know that Olga picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Howard","Samira","Olga","Thomas"],"index":6445,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8990088105,"difficulty":1.8990088105}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lee's card is shown to Kendra. Kendra's card is shown to Lee. It is publicly announced that someone picked a red card. It is publicly announced that Kendra knows whether someone picked a red card. It is publicly announced that Kendra knows whether someone picked a red card. It is publicly announced that Kendra does not know whether Kendra picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lee can now know whether Kendra can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kendra","Lee"],"index":4154,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9735996127,"difficulty":0.0264003873}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that Ricardo can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Ricardo","Joseph"],"index":1927,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9774416089,"difficulty":0.0225583911}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marguerite knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Patricia can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marguerite","Patricia"],"index":5311,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9906869531,"difficulty":0.0093130469}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandon's card is shown to Flora. Flora's card is shown to Walter. Flora's card is shown to Brandon. It is publicly announced that someone picked a red card. It is publicly announced that Brandon does not know whether Brandon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Brandon can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Flora","Walter","Brandon"],"index":6902,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9883143902,"difficulty":0.0116856098}
-{"premise":"There are three 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 or not everyone's forehead is muddy. It is publicly announced that Gloria knows whether Gloria'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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Gloria can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gloria","Shannon","Tommy"],"index":1458,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9712552428,"difficulty":0.0287447572}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lionel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"April can now know whether Lindsy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["April","Maureen","Lionel","Lindsy"],"index":1379,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9896016717,"difficulty":0.0103983283}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kimberly can now know that Arthur can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nanette","Kimberly","Arthur"],"index":5633,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.979473412,"difficulty":0.020526588}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandi can now know that Helen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brandi","Dorothy","Paul","Helen"],"index":3517,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9792111516,"difficulty":0.0207888484}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Gerald can now know that Gerald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gerald","Michael"],"index":2178,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9572768211,"difficulty":0.0427231789}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Mara can now know that Mara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mara","Cleotilde","Russell"],"index":9160,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9583496451,"difficulty":0.0416503549}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Carlos can now know whether Rebecca can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carlos","Rebecca"],"index":8010,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9863331914,"difficulty":0.0136668086}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dortha 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) ] [ ! (Agenta knows whether 3) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Linda can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dortha","Norbert","Linda","Dorothy"],"index":8272,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9893101454,"difficulty":0.0106898546}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peggy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Tracy can now know that Tracy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tracy","Peggy","Rolland","Ann"],"index":3848,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.959870398,"difficulty":0.040129602}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth knows whether Rueben is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Rueben can now know whether Kenneth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kenneth","Rueben"],"index":9238,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7507779002,"difficulty":1.7507779002}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce knows whether Ernest's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Ernest can now know whether Katherine can know whether Katherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katherine","Barton","Joyce","Ernest"],"index":8304,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9837707281,"difficulty":0.0162292719}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bruce can now know whether Robert can know that Monica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Monica","Bruce","Robert"],"index":9116,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9469088912,"difficulty":0.0530911088}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juan can now know whether David can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juan","Elizabeth","David","Robert"],"index":4013,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9871975183,"difficulty":0.0128024817}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Mary can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Grace","Willie","John","Mary"],"index":7601,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9874948859,"difficulty":0.0125051141}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Andrew can now know that Angela can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alton","Angela","Andrew"],"index":8927,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.989117682,"difficulty":0.010882318}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larae's card is shown to Jimmy. Jimmy's card is shown to Larae. It is publicly announced that someone picked a red card. It is publicly announced that Jimmy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Jimmy can now know that Larae can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jimmy","Larae"],"index":9152,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9769251347,"difficulty":0.0230748653}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Laurie can now know that James can know that Laurie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Dean","Laurie"],"index":2419,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9710421562,"difficulty":0.0289578438}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chris is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Regina can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Antonio","Chris","Regina","Melissa"],"index":9601,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.973525703,"difficulty":0.026474297}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 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":"Beth can now know whether Dorothy can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Charles","Roger","Beth"],"index":9201,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7767672539,"difficulty":0.2232327461}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Magdalene. Virginia's card is shown to Margaret. Margaret's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Magdalene picked a black card. It is publicly announced that Magdalene knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Margaret can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Magdalene","Margaret","Virginia"],"index":5250,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9635155201,"difficulty":0.0364844799}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Mario. Mario's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Mario can now know whether Donald can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mario","Donald"],"index":7650,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9808757305,"difficulty":0.0191242695}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Frankie can now know that Chad can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Avery","Christopher","Chad","Frankie"],"index":6981,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9802671671,"difficulty":0.0197328329}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Charles. Larry's card is shown to Neil. Ruby's card is shown to Neil. Larry's card is shown to Ruby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Neil can now know that Charles can know that Larry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Larry","Neil","Ruby"],"index":5752,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9707532525,"difficulty":0.0292467475}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fran knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows 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":"John can now know that Fran can know that Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patrick","Mark","John","Fran"],"index":2839,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9640045166,"difficulty":0.0359954834}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Javier can now know that Hector can know whether George's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hector","George","Javier","Jesse"],"index":7934,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.849273324,"difficulty":0.150726676}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian knows whether Josephine is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Brian can now know that Brian is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brian","Josephine"],"index":1059,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9587588906,"difficulty":0.0412411094}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Peter. Peter's card is shown to Geraldine. Richard's card is shown to Geraldine. Geraldine's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Peter can now know that Geraldine can know whether Peter picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Peter","Geraldine","Richard"],"index":682,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.655688107,"difficulty":1.655688107}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phil does not know whether Ken is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ken can now know that Michael can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Phil","Michael","Ken"],"index":662,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9708886743,"difficulty":0.0291113257}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott does not know whether Marisa is thirsty. It is publicly announced that Erica knows whether someone is thirsty. It is publicly announced that Ann does not know whether or not everyone is thirsty. It is publicly announced that Ann does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Erica can now know that Marisa can know whether Erica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ann","Marisa","Scott","Erica"],"index":2423,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6087630391,"difficulty":0.3912369609}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Callie's card is shown to Maria. Callie's card is shown to Nicole. Nicole's card is shown to Callie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nicole can now know that Callie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Nicole","Callie"],"index":2287,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.95475173,"difficulty":0.04524827}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heather's card is shown to Leonard. Tina's card is shown to Leonard. Tina's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Heather does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(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:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Leonard can now know whether Heather picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leonard","Heather","Tina"],"index":8206,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5668975711,"difficulty":0.4331024289}
-{"premise":"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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Barbara can now know whether Linda can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Barbara"],"index":2926,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9837867618,"difficulty":0.0162132382}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Craig. Craig's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Craig can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Craig","Gary"],"index":7114,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9725573659,"difficulty":0.0274426341}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amelia's card is shown to Patrick. Michael's card is shown to Amelia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Patrick","Amelia"],"index":4552,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8918278813,"difficulty":0.1081721187}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Teresa's forehead is muddy. It is publicly announced that Teresa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Dustin can now know that Dustin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dustin","Ricky","Teresa"],"index":8305,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9483210444,"difficulty":0.0516789556}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eugene can now know that David can know whether Thelma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thelma","David","Eugene"],"index":1757,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9778541923,"difficulty":0.0221458077}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alan does not know whether Marcela is thirsty. It is publicly announced that Alan does not know whether Marcela is thirsty. It is publicly announced that Marcela does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Alan can now know that James can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marcela","James","Alan"],"index":2852,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9775509238,"difficulty":0.0224490762}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maryann knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Maryann can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Maryann","Andrea","Terri"],"index":985,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9775216579,"difficulty":0.0224783421}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Seth is thirsty. It is publicly announced that Carl knows whether Seth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Carl can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Seth","Carl","Leah"],"index":2056,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7396905422,"difficulty":0.2603094578}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Valerie can now know that Betty can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Betty","Valerie"],"index":1354,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9715650082,"difficulty":0.0284349918}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Russell. Russell's card is shown to Mary. Russell's card is shown to Rose. Mary's card is shown to Rose. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Rose can now know whether Russell can know that Rose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Russell","Mary","Rose"],"index":2980,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9665760398,"difficulty":1.9665760398}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeff knows whether Marcia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Pamela can now know that Madelyn can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Madelyn","Jeff","Marcia"],"index":7075,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.974283576,"difficulty":0.025716424}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Judith can now know whether Maryann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Maryann","Judith"],"index":8390,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9853002429,"difficulty":0.0146997571}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Summer is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Summer can now know whether Daniel can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daniel","Summer"],"index":3542,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5745536089,"difficulty":1.5745536089}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rob does not know whether Scott is thirsty. It is publicly announced that Rob is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Scott can now know that Rob is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Scott","Rob"],"index":8126,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9544153214,"difficulty":0.0455846786}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Beverly. Beverly's card is shown to Arlene. Christopher's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know whether Beverly can know whether Arlene picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Christopher","Arlene","Paul"],"index":4119,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9247157574,"difficulty":0.0752842426}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hanna does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ruth can now know that Hanna can know that Jerry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Hanna","Ruth"],"index":172,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9715789557,"difficulty":0.0284210443}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Isaac can now know whether Gale's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Isaac","Linda","Gale"],"index":9605,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9724737406,"difficulty":0.0275262594}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Maria can know that Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Thomas","Patricia"],"index":7904,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9747781157,"difficulty":0.0252218843}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Carly. Mark's card is shown to Helen. Carly's card is shown to Mark. Laura's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Laura does not know whether or not everyone picked a red card. It is publicly announced that Laura does not know whether Laura picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Helen can now know that Laura can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carly","Laura","Helen","Mark"],"index":3631,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5465862155,"difficulty":0.4534137845}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myrtle does not know whether Adam is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Allen can now know that Adam can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Myrtle","Glenn","Allen","Adam"],"index":5706,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9789614677,"difficulty":0.0210385323}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anna is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Alfonzo can now know that Anna can know that Ivan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anna","Ivan","Alfonzo"],"index":5615,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9700503945,"difficulty":0.0299496055}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brent's card is shown to Scott. Brent's card is shown to Adam. Adam's card is shown to Brent. It is publicly announced that someone picked a red card. It is publicly announced that Brent does not know whether Brent picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Scott can now know whether Adam can know that Adam picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Adam","Brent"],"index":657,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9498772025,"difficulty":0.0501227975}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billie's card is shown to Hubert. Beau's card is shown to Hubert. Hubert's card is shown to Billie. Hubert's card is shown to Beau. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Hubert can now know whether Billie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hubert","Billie","Beau"],"index":3038,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9870969057,"difficulty":0.0129030943}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether James's forehead is muddy. It is publicly announced that Donna'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 3) ] [ ! ~(2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Donna can now know that Marcy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marcy","Donna","James"],"index":4192,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9463471174,"difficulty":0.0536528826}
-{"premise":"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 Jennifer knows whether Charles's forehead is muddy. It is publicly announced that Jennifer knows whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Charles can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Jennifer","Charles"],"index":522,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7867657542,"difficulty":0.2132342458}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Mark can now know whether Taina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mark","Taina"],"index":1343,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.967877388,"difficulty":0.032122612}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lester can now know that Sara can know that Sara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lester","Sara","Luther","Linda"],"index":678,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9738200903,"difficulty":0.0261799097}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doreen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Doreen can now know that Victoria can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victoria","Doreen","Danny","Timothy"],"index":5700,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9788616896,"difficulty":0.0211383104}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Tommy. Tommy's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Robert can now know that Tommy can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tommy","Robert"],"index":8868,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9687772989,"difficulty":0.0312227011}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Burt knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Herman can now know that Steve can know that Herman is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Burt","Herman","Steve"],"index":7452,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.97119385,"difficulty":0.02880615}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alton does not know whether Alton's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alton 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) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Joann can now know that Alton can know whether Alton's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joann","Alton"],"index":3267,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7856208682,"difficulty":1.7856208682}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Carmen. Carmen's card is shown to Diane. It is publicly announced that someone picked a red card. It is publicly announced that Diane knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that 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":"Diane can now know that Carmen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carmen","Diane"],"index":265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.947904706,"difficulty":0.052095294}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alisha knows whether Brandon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Martha can now know that Ronald can know whether Martha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Martha","Ronald","Alisha","Brandon"],"index":5606,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9742616415,"difficulty":0.0257383585}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ronda can now know whether Leona can know whether Leona is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leona","Mark","Ronda"],"index":1914,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7772699594,"difficulty":0.2227300406}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Ellen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ellen","Walter","Michael","Robert"],"index":7166,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9753019214,"difficulty":0.0246980786}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Jessica can now know that Faith can know that Jessica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Faith","James","Connie","Jessica"],"index":9531,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9676597118,"difficulty":0.0323402882}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristie's card is shown to Alan. Marjorie's card is shown to Alan. Alan's card is shown to Kristie. Marjorie's card is shown to Monica. Alan's card is shown to Marjorie. Monica's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Alan knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (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:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Marjorie can now know whether Monica can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alan","Kristie","Monica","Marjorie"],"index":7723,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9853889346,"difficulty":0.0146110654}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gerald can now know whether John can know whether Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerald","Irene","John","Denise"],"index":8941,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.961002171,"difficulty":0.038997829}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lina can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diane","Alexander","Lina"],"index":4178,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9866198301,"difficulty":0.0133801699}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos knows whether someone's forehead is muddy. It is publicly announced that Eric knows whether Cecilia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Cecilia can now know whether Cecilia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eric","Cecilia","Carlos","Karen"],"index":4407,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9848271608,"difficulty":0.0151728392}
-{"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 (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":"Alan can now know that Duane can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Duane","Maria","David","Alan"],"index":6790,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9778476954,"difficulty":0.0221523046}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Armandina knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Armandina can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dallas","Armandina","Brain","Sue"],"index":7990,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9619182348,"difficulty":0.0380817652}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Keith is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Katrina can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","James","Keith","Katrina"],"index":5880,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9745864868,"difficulty":0.0254135132}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Harold can now know that Shane can know that Julia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harold","Shane","Julia"],"index":2977,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9727749228,"difficulty":0.0272250772}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Shawn. Julie's card is shown to Diane. Shawn's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Julie does not know whether Diane picked a red card. It is publicly announced that Shawn does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Julie can now know that Diane can know that Julie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shawn","Diane","Julie"],"index":1108,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9686002731,"difficulty":1.9686002731}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Renee. Renee's card is shown to Bruce. Renee's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether someone picked a red card. It is publicly announced that Bruce picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] 0","hypothesis":"Robert can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Renee","Bruce","Robert"],"index":6835,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9791122675,"difficulty":0.0208877325}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Don knows whether Joshua's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Don can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joshua","Don","Sarah","Robert"],"index":3717,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9897150397,"difficulty":0.0102849603}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angela is thirsty. It is publicly announced that Agnes knows whether Angela is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Angela can now know whether Agnes is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Agnes","Sarah"],"index":2627,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6003010273,"difficulty":0.3996989727}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Duncan knows whether someone's forehead is muddy. It is publicly announced that Patricia knows whether Duncan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentb knows whether 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)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Duncan can now know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Duncan","Patricia","Regina"],"index":2087,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9293367267,"difficulty":0.0706632733}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"John can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","John"],"index":4126,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9897917509,"difficulty":0.0102082491}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodney's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Rodney can now know that Reyna can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rodney","Reyna"],"index":6729,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9849163294,"difficulty":0.0150836706}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robin can now know that Joshua can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Robin","Joshua"],"index":1652,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9861078262,"difficulty":0.0138921738}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Alan. Alan's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that Alan picked a black card. It is publicly announced that Alan knows whether Joan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Joan can now know that Alan can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alan","Joan"],"index":8406,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9845736623,"difficulty":0.0154263377}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Christopher. Charles's card is shown to Russell. Charles's card is shown to Anna. Anna's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Anna can know that Russell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Russell","Anna","Charles"],"index":784,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9692357183,"difficulty":0.0307642817}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Kirby","Winifred"],"index":788,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9756327271,"difficulty":0.0243672729}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Veronica can now know that Amanda can know whether Veronica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Amanda","Veronica"],"index":4352,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9662305713,"difficulty":0.0337694287}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allen's card is shown to Judy. Barry's card is shown to Allen. Judy's card is shown to Barry. Allen's card is shown to Barry. It is publicly announced that someone picked a red card. It is publicly announced that Allen knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Allen can now know whether Judy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judy","Allen","Barry"],"index":9360,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6187815666,"difficulty":1.6187815666}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack knows whether someone's forehead is muddy. It is publicly announced that Estelle's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Jack can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Estelle","Jack","Leisha"],"index":7105,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7089829445,"difficulty":0.2910170555}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cheryl can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cheryl","Michelle","James","Milo"],"index":9138,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9895876646,"difficulty":0.0104123354}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina knows whether Loren's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mark can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Tina","Loren"],"index":5044,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9766047597,"difficulty":0.0233952403}
-{"premise":"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 Maria knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Maria can now know whether David can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Maria","David"],"index":8962,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9645601511,"difficulty":1.9645601511}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 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":"Wesley can now know that Timothy can know that Gertrude's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wesley","Gertrude","Elizabeth","Timothy"],"index":8372,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9726196527,"difficulty":0.0273803473}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Kristy. Kristy's card is shown to Scott. Kristy's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kristy can now know whether Kristy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristy","Scott","Joseph"],"index":3392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5306033492,"difficulty":0.4693966508}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bradley knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know that Joyce can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bradley","David","Joyce"],"index":8899,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.97638762,"difficulty":0.02361238}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Eleanor is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Brandy can now know whether Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Brandy","Eleanor"],"index":9380,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8817551136,"difficulty":0.1182448864}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristen does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Kristen knows whether Chung is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Chung can now know whether Kristen can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Chung","Kristen"],"index":5976,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8225706816,"difficulty":0.1774293184}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether Betty's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Betty can now know whether Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Betty","Michelle"],"index":6825,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9801643491,"difficulty":0.0198356509}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristine knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Sara can now know that Karen can know that Carla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sara","Carla","Karen","Kristine"],"index":4194,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9358816147,"difficulty":0.0641183853}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Daniel. Mary's card is shown to Daniel. Linda's card is shown to Melvin. Melvin's card is shown to Linda. Linda's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Melvin does not know whether or not everyone picked a red card. It is publicly announced that Daniel does not know whether Melvin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Daniel can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daniel","Melvin","Linda","Mary"],"index":8148,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5093054771,"difficulty":1.5093054771}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether Angela's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Angela can now know that Charles can know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Angela"],"index":5550,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8724886179,"difficulty":0.1275113821}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald does not know whether Kenneth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Arthur can now know whether Kenneth can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Arthur","Kenneth","Donald"],"index":8701,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9854524732,"difficulty":0.0145475268}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"John can now know that Dean can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dean","John"],"index":558,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9769499302,"difficulty":0.0230500698}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Genevieve's card is shown to Delaine. Delaine's card is shown to Genevieve. Thelma's card is shown to Genevieve. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Delaine can now know that Thelma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Delaine","Genevieve","Kathy","Thelma"],"index":8445,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9520078897,"difficulty":0.0479921103}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dan can now know that Ruby can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Ruby","Dan"],"index":6103,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8384683132,"difficulty":0.1615316868}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Rose. Michael's card is shown to Louis. Rose's card is shown to Louis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rose can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Rose","Louis"],"index":2098,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9541077614,"difficulty":0.0458922386}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Richard can now know that George can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Richard","William","George"],"index":3664,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9695749283,"difficulty":0.0304250717}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether or not everyone is thirsty. It is publicly announced that William knows whether William is thirsty. It is publicly announced that Mary does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mary can now know that William can know whether Carlos is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Ronald","William","Carlos"],"index":4742,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.752892077,"difficulty":0.247107923}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 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":"Jeffrey can now know that Tracy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Phillip","Tracy","Jeffrey"],"index":724,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9602781534,"difficulty":0.0397218466}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jordan's card is shown to Jacob. Andres's card is shown to Jacob. Andres's card is shown to Jordan. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jordan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jacob can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jacob","Jordan","Andres"],"index":9562,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9887972474,"difficulty":0.0112027526}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Virginia can now know that Manuel can know whether Cristobal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cristobal","Virginia","Manuel","Mary"],"index":8775,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8684375286,"difficulty":0.1315624714}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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":"Saundra can now know that Elsie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alissa","Elsie","Saundra","Buck"],"index":707,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9557309151,"difficulty":0.0442690849}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Joseph. Joseph's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Joseph picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Christine can now know whether Joseph can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Christine"],"index":8100,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9725344777,"difficulty":0.0274655223}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Maritza can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Maritza","Mary","Michelle"],"index":2166,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.968246758,"difficulty":0.031753242}
-{"premise":"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 or not nobody's forehead is muddy. It is publicly announced that not everyone'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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Helen can now know whether Patricia can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Patricia","Dorthy","Helen"],"index":5796,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.982486248,"difficulty":0.017513752}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josephine does not know whether Stacy is thirsty. It is publicly announced that Gene knows whether or not nobody is thirsty. It is publicly announced that Josephine does not know whether Gene is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Perry can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Perry","Josephine","Stacy","Gene"],"index":4924,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9733100533,"difficulty":0.0266899467}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorena's card is shown to Gregory. Dustin's card is shown to Gregory. Lorena's card is shown to Donna. Donna's card is shown to Lorena. Lorena's card is shown to Dustin. It is publicly announced that someone picked a red card. It is publicly announced that Donna does not know whether or not everyone picked a red card. It is publicly announced that Gregory does not know whether Donna picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lorena can now know that Donna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Donna","Lorena","Dustin"],"index":8653,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9549289942,"difficulty":0.0450710058}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delores knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows 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":"Rose can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Delores","Ismael","Rose"],"index":298,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5452589989,"difficulty":0.4547410011}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dona's card is shown to Linda. Linda's card is shown to Dona. It is publicly announced that someone picked a red card. It is publicly announced that Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! 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 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Dona can now know that Linda can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Dona","Manuel","Mary"],"index":2301,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5834091306,"difficulty":0.4165908694}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Michael's forehead is muddy. It is publicly announced that Joseph knows whether or not nobody's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Joseph can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Joseph"],"index":3325,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9877061248,"difficulty":0.0122938752}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know whether Grace can know that Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Grace","Mark","Paul"],"index":7350,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6387768984,"difficulty":1.6387768984}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lindsey's card is shown to James. Terrance's card is shown to James. James's card is shown to Lindsey. James's card is shown to Terrance. Lindsey's card is shown to Terrance. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lindsey can now know whether James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Lindsey","Terrance"],"index":6097,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8853843808,"difficulty":1.8853843808}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bruce does not know whether Keri is thirsty. It is publicly announced that Bruce knows whether Bruce is thirsty. It is publicly announced that Earl does not know whether Keri is thirsty. It is publicly announced that Earl knows whether Earl is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Earl can now know whether Bruce can know that Earl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Earl","Bruce","Keri"],"index":7484,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9399155378,"difficulty":0.0600844622}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darrell does not know whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Darrell can now know whether Barbara can know that Darrell is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Mary","Barbara","Darrell"],"index":4162,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8687705994,"difficulty":0.1312294006}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brenda can now know that Roberta can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brenda","Leslie","Roberta"],"index":2729,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9889967442,"difficulty":0.0110032558}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Grace can now know that Matthew can know whether Grace's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raina","Matthew","Jody","Grace"],"index":4764,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7940468788,"difficulty":0.2059531212}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jeff can now know whether Charles can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Rita","Jeff"],"index":1204,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9848570824,"difficulty":0.0151429176}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tai does not know whether Lillie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Tai can now know that Lillie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lillie","Tai","Eric","Millie"],"index":7852,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9708756208,"difficulty":0.0291243792}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Beverly. Hazel's card is shown to Beverly. Beverly's card is shown to Betty. Hazel's card is shown to Kristina. Beverly's card is shown to Hazel. Kristina's card is shown to Hazel. It is publicly announced that someone picked a red card. It is publicly announced that Beverly knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kristina can now know whether Betty can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Betty","Kristina","Hazel"],"index":3603,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9770454168,"difficulty":0.0229545832}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (~(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":"Eric can now know that Cindy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Wayne","Cindy"],"index":7360,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9856932163,"difficulty":0.0143067837}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aaron does not know whether or not everyone is thirsty. It is publicly announced that Dinah does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"David can now know whether Dinah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Aaron","Dinah","David"],"index":4563,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8051647544,"difficulty":0.1948352456}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Joseph. Joseph's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 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":"Joseph can now know whether Debra can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joseph","Debra"],"index":6471,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9603587389,"difficulty":1.9603587389}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Donna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that Phil can know whether Phil's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Donna","Phil","Jane"],"index":1932,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9611932039,"difficulty":0.0388067961}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen does not know whether 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) ] [ ! ~(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":"Raymond can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephen","Gary","Carl","Raymond"],"index":2750,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.986210525,"difficulty":0.013789475}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Louise. Mary's card is shown to Jeffrey. Vernon's card is shown to Mary. Louise's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey does not know whether or not everyone picked a red card. It is publicly announced that Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Vernon can now know whether Louise can know whether Vernon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vernon","Louise","Jeffrey","Mary"],"index":6973,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9507610798,"difficulty":0.0492389202}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emily can now know whether Jacob can know whether Jacob is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emily","Rhonda","Jacob","Hector"],"index":109,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8024915457,"difficulty":0.1975084543}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delisa 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 Marvin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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)) ] [ ! ~(1) ] Agentd knows whether (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Delisa can now know whether Cecilia can know that Marvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marvin","Reginald","Cecilia","Delisa"],"index":6957,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9485008717,"difficulty":0.0514991283}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernadette does not know whether or not everyone's forehead is muddy. It is publicly announced that Cynthia knows whether someone's forehead is muddy. It is publicly announced that Bernadette does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Cynthia can now know that Bernadette can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bernadette","Cynthia"],"index":4598,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9751306176,"difficulty":0.0248693824}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether 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 (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Alisa can now know whether Brian can know whether Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Alisa","Patricia"],"index":3924,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9820324779,"difficulty":1.9820324779}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith knows whether someone's forehead is muddy.","smcdel_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":"Sonya can now know that Judith can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sergio","Judith","Sonya"],"index":5763,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9868744016,"difficulty":0.0131255984}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether or not everyone's forehead is muddy. It is publicly announced that Tara knows whether Tara's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Tara can now know that Jessica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jessica","Tara"],"index":2198,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.940758884,"difficulty":0.059241116}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernie knows whether Ernie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"James can now know whether Chris can know that Chris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Ernie","James","Chris"],"index":9486,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9638216496,"difficulty":0.0361783504}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Melissa. Melissa's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that Melissa does not know whether Melissa picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Melissa can now know that Kyle can know whether Kyle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melissa","Kyle"],"index":7989,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5108345151,"difficulty":0.4891654849}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Lucio. Lucio's card is shown to Jose. It is publicly announced that someone picked a red card. It is publicly announced that Jose picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 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":"Jose can now know whether Lucio can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lucio","Jose"],"index":8180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9815525413,"difficulty":0.0184474587}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Denita can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Denita","Michael"],"index":6452,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9806278944,"difficulty":0.0193721056}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Billy can now know that Catherine can know that Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Billy","Ken","Catherine"],"index":1625,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9698343873,"difficulty":0.0301656127}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Carolyn can now know that Mark can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Jessie","Carolyn","John"],"index":9329,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9789476395,"difficulty":0.0210523605}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edward can now know whether Andrew can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Edward","Andrew","George"],"index":7098,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9675503373,"difficulty":0.0324496627}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 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":"Leslie can now know that Larry can know whether Larry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Larry","Lori","Leslie"],"index":1622,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7789945006,"difficulty":0.2210054994}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gay's forehead is not muddy. It is publicly announced that Juan knows whether Juan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Juan can now know whether Gay can know whether Juan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Juan","Gay"],"index":2413,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9703254104,"difficulty":0.0296745896}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Erinn. Paul's card is shown to Richard. Erinn's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Erinn can now know whether Richard can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erinn","Richard","Paul"],"index":7251,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9161399603,"difficulty":0.0838600397}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline does not know whether or not everyone's forehead is muddy. It is publicly announced that Lauren knows whether Lauren'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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Jacqueline can now know that Jacqueline's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lauren","Dustin","Jacqueline"],"index":2973,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9371268749,"difficulty":1.9371268749}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Ruth can now know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Donald","Ruth","Judson"],"index":9120,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9520379305,"difficulty":1.9520379305}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Nikki. Dan's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Sarah knows whether Dan picked a red card. It is publicly announced that Sarah does not know whether Nikki picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Nikki can now know whether Sarah can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nikki","Sarah","Dan"],"index":9202,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7101643682,"difficulty":1.7101643682}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"David can now know whether Shawn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathy","David","Shawn","Michael"],"index":3586,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8426269293,"difficulty":0.1573730707}
-{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows whether (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":"Charles can now know that Bertha can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charles","Bertha"],"index":2000,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6857191324,"difficulty":0.3142808676}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nathan does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Priscilla can now know whether Raymond can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Priscilla","Raymond","Nathan","John"],"index":4110,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.933285594,"difficulty":0.066714406}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Russel does not know whether Bobby is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Bobby can now know that Allan can know that Russel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bobby","Russel","Allan","Eugene"],"index":4501,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9703971744,"difficulty":0.0296028256}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Jennifer. Margaret's card is shown to Jennifer. Beverly's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beverly can now know that Jennifer can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Beverly","Jennifer","Brian","Margaret"],"index":7468,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9780644178,"difficulty":0.0219355822}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachel's card is shown to Philip. Philip's card is shown to Rachel. It is publicly announced that someone picked a red card. It is publicly announced that Philip does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Rachel can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Philip","Rachel"],"index":8920,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9827521443,"difficulty":0.0172478557}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Catherine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Catherine","Rene","Robert"],"index":466,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9817205667,"difficulty":0.0182794333}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether Shirley is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Antonio can now know whether Shirley can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Antonio","Steven","Shirley"],"index":2175,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5972356796,"difficulty":0.4027643204}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Andrea can now know whether Andrea is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margaret","Andrea","Susan","Donna"],"index":6440,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8804369569,"difficulty":1.8804369569}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Walter can now know that Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aaron","Clinton","Tonita","Walter"],"index":2575,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9583066106,"difficulty":0.0416933894}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Lori does not know whether Angelina is thirsty. It is publicly announced that Jacquie does not know whether Angelina is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Maria can now know that Jacquie can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacquie","Angelina","Maria","Lori"],"index":5770,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9780736566,"difficulty":0.0219263434}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Sandra. Theresa's card is shown to Tracey. Theresa's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Sandra does not know whether Theresa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Sandra can now know whether Theresa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Tracey","Charles","Theresa"],"index":3583,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5990899801,"difficulty":1.5990899801}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know that Trevor can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hattie","Trevor","Patricia","Dorothy"],"index":7039,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9865074158,"difficulty":0.0134925842}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Becky's card is shown to Paulette. Paulette's card is shown to Jon. Becky's card is shown to Jon. Jon's card is shown to Becky. It is publicly announced that someone picked a red card. It is publicly announced that Jon does not know whether Jon picked a red card. It is publicly announced that Jon knows whether someone picked a red card. It is publicly announced that Paulette does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Paulette can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paulette","Jon","Becky"],"index":6679,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9714462161,"difficulty":0.0285537839}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Brian. Samantha's card is shown to Brian. Samantha's card is shown to Patricia. Patricia's card is shown to Samantha. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether Samantha picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Samantha can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Patricia","Samantha"],"index":6098,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9732951522,"difficulty":0.0267048478}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Cheryl can now know that Eric can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cheryl","Eric"],"index":9349,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.986926198,"difficulty":0.013073802}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Javier can now know whether Alicia can know whether Alicia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alicia","Javier","Malcolm"],"index":2701,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9808880091,"difficulty":0.0191119909}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Janice"],"index":3562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9468181133,"difficulty":0.0531818867}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Caron knows whether Anita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Jennifer can now know that George can know that Caron's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Caron","George","Jennifer","Anita"],"index":5115,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9645552635,"difficulty":0.0354447365}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows 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":"James can now know whether Thomas can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Jessica","James","Carla"],"index":2833,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9658349752,"difficulty":0.0341650248}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesus's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Samantha can now know whether Samantha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jesus","Samantha"],"index":8803,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9714007378,"difficulty":0.0285992622}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Corinne knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Corinne can now know whether Nakita can know that Nakita is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Corinne","Nakita","Christopher"],"index":6749,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.840728581,"difficulty":1.840728581}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edith's card is shown to Joseph. Joseph's card is shown to Edith. Edith's card is shown to Salvador. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Salvador can now know whether Edith can know that Salvador picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Edith","Salvador"],"index":3677,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9610669017,"difficulty":0.0389330983}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathaniel's card is shown to Minnie. William's card is shown to Nathaniel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Minnie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Minnie","Nathaniel"],"index":1923,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9832382202,"difficulty":0.0167617798}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Salvador does not know whether Salvador's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Salvador can now know whether Freeda can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leslie","Freeda","Salvador","Jessie"],"index":7758,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9368870258,"difficulty":0.0631129742}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ross can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jean","Maggie","Ross","Florence"],"index":4115,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9893792272,"difficulty":0.0106207728}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeremy can now know that Jeremy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carrie","Melissa","Jeremy","Scott"],"index":3896,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9659612179,"difficulty":0.0340387821}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virgil does not know whether Virgil's forehead is muddy. It is publicly announced that Stephen's forehead is not muddy. It is publicly announced that Virgil's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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) ] [ ! ~(2) ] 0","hypothesis":"Jennifer can now know whether Virgil can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Virgil","Jane","Stephen"],"index":7189,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9650917053,"difficulty":0.0349082947}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Vida knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Barbara can now know whether Vida can know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vida","Christine","Barbara"],"index":6345,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9694563746,"difficulty":0.0305436254}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doris can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Yvonne","Susan","Kristina","Doris"],"index":414,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9886220098,"difficulty":0.0113779902}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Elbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Elbert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elbert","Robert","Thomas","Linda"],"index":8936,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9777215123,"difficulty":0.0222784877}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jill knows whether Jared's forehead is muddy. It is publicly announced that Jill knows whether someone's forehead is muddy. It is publicly announced that Jill's forehead is muddy.","smcdel_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 (1|2|3)) ] [ ! 2 ] Agenta knows that (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) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Jared can now know that Louis can know that Jill's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jared","Jill","Louis"],"index":2479,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9565802217,"difficulty":1.9565802217}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Houston's card is shown to Kenneth. Kenneth's card is shown to Houston. Houston's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Kenneth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know whether Houston can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Houston","Dorothy"],"index":320,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6725428104,"difficulty":1.6725428104}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jesse can now know whether Anna can know whether Anna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Anna","Jesse","Irvin"],"index":981,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9810343385,"difficulty":0.0189656615}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Richard. Kenya's card is shown to Richard. Richard's card is shown to Michael. Richard's card is shown to Kenya. Michael's card is shown to Kenya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that Kenya can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Michael","Kenya"],"index":7349,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9809632301,"difficulty":0.0190367699}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alejandro does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Roland can now know that Alejandro can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alejandro","Roland"],"index":3566,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8214853406,"difficulty":0.1785146594}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Susie can now know whether Diane can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Diane","Susie"],"index":5370,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9870087504,"difficulty":0.0129912496}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Dan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"John can now know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dan","Robert","John","Marshall"],"index":5213,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9829870462,"difficulty":0.0170129538}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco knows whether Blanche's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Francisco can now know that Blanche can know that Lillian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Blanche","Oscar","Francisco","Lillian"],"index":5292,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9673227072,"difficulty":0.0326772928}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valerie knows whether Justin's forehead is muddy. It is publicly announced that Valerie knows whether someone's forehead is muddy. It is publicly announced that Valerie's forehead is muddy.","smcdel_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 (1|2|3)) ] [ ! 2 ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Valerie can now know whether Justin can know that Justin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Justin","Valerie","Cameron"],"index":4970,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9451117516,"difficulty":0.0548882484}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW 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":"Shani can now know that Dennis can know that Dennis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dennis","Robert","Shani","Kenneth"],"index":5126,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9690343738,"difficulty":0.0309656262}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Elizabeth. Cecile's card is shown to Elizabeth. Elizabeth's card is shown to Cecile. Elizabeth's card is shown to Tanya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cecile can now know whether Stephen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Stephen","Cecile","Tanya"],"index":3838,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8279553652,"difficulty":0.1720446348}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Fannie can now know whether Tami can know that Tami's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Fannie","Tami"],"index":3756,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9478523731,"difficulty":0.0521476269}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darrell does not know whether Rosemarie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Donald can now know that Charissa can know that Charissa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rosemarie","Darrell","Donald","Charissa"],"index":3606,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9695413113,"difficulty":0.0304586887}
-{"premise":"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 Donnie's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Julio can now know that Donnie can know whether Donnie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donnie","Julio"],"index":4005,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8085417151,"difficulty":0.1914582849}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Petra's card is shown to Barbara. Barbara's card is shown to Petra. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Barbara can now know that Petra can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barbara","Petra"],"index":6815,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9779763818,"difficulty":0.0220236182}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Robert can now know that Debbie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Debbie","Robert"],"index":8551,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9551362395,"difficulty":0.0448637605}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Kanisha can now know that Penny can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Penny","Kanisha"],"index":2559,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9818627238,"difficulty":0.0181372762}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Charles can now know whether Amy can know whether Amy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Amy"],"index":9310,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9869469404,"difficulty":0.0130530596}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory does not know whether Joyce is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Gregory can now know whether Allan can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allan","Derek","Joyce","Gregory"],"index":7322,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9877004623,"difficulty":0.0122995377}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Leslie. Lauren's card is shown to Leslie. Leslie's card is shown to Lauren. It is publicly announced that someone picked a red card. It is publicly announced that Lauren picked a black card. It is publicly announced that Leslie does not know whether Leslie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Evelyn can now know that Leslie can know that Evelyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leslie","Evelyn","Lauren"],"index":7646,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9683007002,"difficulty":1.9683007002}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Suzann can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Suzann","Darrell","Charles"],"index":3828,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9863909483,"difficulty":0.0136090517}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jenna knows whether Timothy's forehead is muddy. It is publicly announced that Timothy knows whether Jenna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Timothy can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jenna","Timothy","Harold"],"index":6554,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9881084561,"difficulty":0.0118915439}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Belinda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Bryce can now know whether Belinda can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Belinda","Bryce"],"index":4539,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7331299782,"difficulty":0.2668700218}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlie knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Bernard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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)) ] [ ! ~(1) ] Agentd 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))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Charlie can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bernard","Amanda","Mary","Charlie"],"index":3712,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9473286271,"difficulty":0.0526713729}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Gary. Gary's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Gary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Gary can now know whether Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gary","Edward"],"index":1260,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5455799103,"difficulty":1.5455799103}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Philip's card is shown to Stephen. Stephen's card is shown to Cecil. Philip's card is shown to Cecil. Stephen's card is shown to Philip. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephen can now know whether Philip can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephen","Cecil","Philip"],"index":2350,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.98814255,"difficulty":0.01185745}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cynthia","Frederick","June","Michael"],"index":5939,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9796662927,"difficulty":0.0203337073}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 1)","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":"Michael can now know that Myron can know whether Carmelo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carmelo","Michael","Norma","Myron"],"index":3368,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8525798917,"difficulty":0.1474201083}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ana's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Ana can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ana","Ross"],"index":3394,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9873184562,"difficulty":0.0126815438}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Julie. Larry's card is shown to Carol. Julie's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Julie does not know whether Carol picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Larry can now know that Julie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Julie","Carol"],"index":2946,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9561677575,"difficulty":0.0438322425}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Tabitha. Carol's card is shown to Vicky. Carol's card is shown to Jodi. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tabitha can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tabitha","Carol","Vicky","Jodi"],"index":4493,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9741050601,"difficulty":0.0258949399}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Scott can now know that Steven can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","James","Scott","Martin"],"index":248,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.897182405,"difficulty":0.102817595}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Daniel","Christopher","Karen"],"index":4434,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9579597116,"difficulty":0.0420402884}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether someone's forehead is muddy. It is publicly announced that Irma knows whether Neil's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Neil can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Irma","Neil","Timothy","Norbert"],"index":8012,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9885923862,"difficulty":0.0114076138}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Ernestina can now know whether Ernestina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ernestina","Erma"],"index":370,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9767836332,"difficulty":0.0232163668}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Robert. Robert's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ronald can now know whether Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Ronald"],"index":1401,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9894920588,"difficulty":0.0105079412}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon's forehead is muddy. It is publicly announced that Antonia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Antonia can now know that Brandon can know that Jeff's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeff","Brandon","Antonia"],"index":8159,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9628199339,"difficulty":0.0371800661}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stanley does not know whether Bella is thirsty. It is publicly announced that Bella knows whether someone is thirsty. It is publicly announced that Stanley does not know whether Bella is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Ruth can now know that Bella can know whether Stanley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruth","Stanley","Bella"],"index":7053,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5659066439,"difficulty":0.4340933561}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Christopher. Esther's card is shown to Charles. Christopher's card is shown to Esther. Charles's card is shown to Esther. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Christopher can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Charles","Esther"],"index":9029,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9510870576,"difficulty":0.0489129424}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Violet does not know whether Lenny is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lenny can now know that Violet is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Violet","Lenny"],"index":515,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9591706395,"difficulty":1.9591706395}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joann knows whether Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Suzanne can now know that Gregory can know that Joann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gregory","Joann","Suzanne","Robin"],"index":8199,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9667666554,"difficulty":0.0332333446}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charity does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Norma can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charity","Norma","Veola","Melda"],"index":2154,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9815373421,"difficulty":0.0184626579}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maryann's card is shown to Misty. Theresa's card is shown to Horace. Maryann's card is shown to Horace. Horace's card is shown to Theresa. Maryann's card is shown to Theresa. Misty's card is shown to Maryann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Theresa can now know whether Misty picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Misty","Horace","Theresa","Maryann"],"index":6905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.802439034,"difficulty":0.197560966}
-{"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 (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":"Nona can now know whether Leonard can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Muriel","Leonard","Nona","Carolyn"],"index":5480,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9842214584,"difficulty":0.0157785416}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Preston. Thomas's card is shown to Erin. It is publicly announced that someone picked a red card. It is publicly announced that Preston does not know whether Preston picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Preston can now know whether Thomas can know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Preston","Thomas","Erin"],"index":297,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9528566599,"difficulty":0.0471433401}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Juan. Joseph's card is shown to Beth. Juan's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether Juan can know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Juan","Beth","Joseph"],"index":7243,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9149249196,"difficulty":0.0850750804}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mui can now know that Martha can know that Mui's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerry","Mui","Martha","Robert"],"index":5561,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9712500572,"difficulty":0.0287499428}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Robert can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Julia","James","Stefani"],"index":6343,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8869227767,"difficulty":0.1130772233}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antonio knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Antonio can now know that Esther's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Esther","Antonio"],"index":9132,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9054569602,"difficulty":0.0945430398}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josefina's card is shown to Robert. Jessica's card is shown to Robert. Grover's card is shown to Robert. Robert's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Josefina can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josefina","Robert","Jessica","Grover"],"index":3886,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9885250926,"difficulty":0.0114749074}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether John is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Inez can now know that John can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Inez"],"index":6533,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9720706344,"difficulty":0.0279293656}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marlene can now know that Phillip can know that Marlene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Velma","Marlene","Phillip"],"index":9581,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9740876555,"difficulty":0.0259123445}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Linda. Linda's card is shown to Janis. Sharon's card is shown to Janis. Linda's card is shown to Sharon. Janis's card is shown to Sharon. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Sharon does not know whether Sharon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Sharon can now know whether Linda can know whether Janis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Janis","Sharon"],"index":8384,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9564967155,"difficulty":0.0435032845}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Sherry can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sherry","Janeen","Kirby"],"index":5949,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8904855251,"difficulty":0.1095144749}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to David. David's card is shown to Janet. Irene's card is shown to Janet. Janet's card is shown to Irene. Irene's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Janet can know that Irene picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Janet","Irene","Michael"],"index":1172,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8731952906,"difficulty":0.1268047094}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shirley can now know whether Robert can know whether Shirley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Miguel","Shirley"],"index":465,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8243992925,"difficulty":0.1756007075}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Carolyn. Carolyn's card is shown to Christine. Christine's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether Carolyn picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Christine can now know whether Christine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carolyn","Christine","Sharon","James"],"index":5182,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5212432146,"difficulty":0.4787567854}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ronald can now know that Linda can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ronald","Linda"],"index":8525,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9686970115,"difficulty":0.0313029885}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether Keith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Stacy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stacy","Dorothy","Keith"],"index":5474,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9723426104,"difficulty":0.0276573896}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melanie's card is shown to Kenneth. Elizabeth's card is shown to Melanie. Catherine's card is shown to Elizabeth. Kenneth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Melanie does not know whether or not everyone picked a red card. It is publicly announced that Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Kenneth can now know that Catherine can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Catherine","Kenneth","Melanie","Elizabeth"],"index":9483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9868859053,"difficulty":0.0131140947}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Jerry. Jada's card is shown to Jerry. Jada's card is shown to Brian. Jerry's card is shown to Jada. It is publicly announced that someone picked a red card. It is publicly announced that Jerry does not know whether Jerry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows 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:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jerry can now know that Jada can know that Jada picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Brian","Jada"],"index":3556,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9683508277,"difficulty":0.0316491723}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fannie does not know whether or not everyone is thirsty. It is publicly announced that Maria does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Maria can now know that Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Fannie","Maria","Robert"],"index":6192,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9599146843,"difficulty":0.0400853157}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph's forehead is not muddy. It is publicly announced that Jose knows whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] (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) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jose can now know whether Ralph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Salvatore","Jose","Ralph","Haley"],"index":6496,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9616267681,"difficulty":0.0383732319}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marty's card is shown to Gina. Gina's card is shown to Marty. Marty's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Gina does not know whether Gina picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gina can now know whether Elizabeth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gina","Marty","Elizabeth"],"index":5200,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9884595871,"difficulty":0.0115404129}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether Douglas'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 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":"Douglas can now know whether Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Douglas","Michelle"],"index":3041,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.972306788,"difficulty":0.027693212}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kent does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Kent can now know whether Kent's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kent","Loretta","James","Carolyn"],"index":3796,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9232882857,"difficulty":1.9232882857}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Robert. Linda's card is shown to Charles. Mavis's card is shown to Charles. Mavis's card is shown to Linda. Robert's card is shown to Mavis. Linda's card is shown to Mavis. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Mavis does not know whether Charles picked a red card. It is publicly announced that Robert does not know whether Charles picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Linda can now know that Charles can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Charles","Linda","Mavis"],"index":2197,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9744029641,"difficulty":0.0255970359}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Angela. Andrew's card is shown to Angela. Andrew's card is shown to Jeff. Jeff's card is shown to Karen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeff can now know whether Angela can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","Jeff","Karen","Andrew"],"index":8911,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9319877028,"difficulty":0.0680122972}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman 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 3)","n_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":"Delores can now know whether Delores's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Norman","Mildred","Delores"],"index":1210,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9438436031,"difficulty":0.0561563969}
-{"premise":"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 April's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"April can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maude","April","Teresa"],"index":7993,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9742591381,"difficulty":0.0257408619}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bettie knows whether Amina's forehead is muddy.","smcdel_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":"Amina can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bettie","Shondra","Amina"],"index":2219,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9744087458,"difficulty":0.0255912542}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jose can now know that Tom can know that Pamela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tom","Tina","Jose","Pamela"],"index":9496,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9711838365,"difficulty":0.0288161635}
-{"premise":"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 not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Jonathan can now know whether Stephanie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jonathan","Stephanie"],"index":512,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9678370953,"difficulty":0.0321629047}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Joann can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Joann","Eileen"],"index":1845,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9880157113,"difficulty":0.0119842887}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Linda. Cynthia's card is shown to Linda. Linda's card is shown to Cynthia. Timothy's card is shown to Cynthia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether Timothy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Timothy","Leonarda","Cynthia"],"index":689,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6326876283,"difficulty":0.3673123717}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Venessa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows 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":"Venessa 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","John","Venessa"],"index":3352,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9845598936,"difficulty":0.0154401064}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curt's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Curt","Judy"],"index":4074,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9841067791,"difficulty":0.0158932209}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roman does not know whether Daniel is thirsty. It is publicly announced that Phillip does not know whether Agnes is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Phillip can now know that Daniel can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Phillip","Roman","Daniel","Agnes"],"index":1214,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8758248091,"difficulty":0.1241751909}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rene's card is shown to David. Rene's card is shown to John. David's card is shown to Rene. John's card is shown to Rene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rene can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","John","Rene"],"index":421,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9740018845,"difficulty":0.0259981155}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herbert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Herbert can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Stephen","Herbert"],"index":24,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.989302814,"difficulty":0.010697186}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether Linda's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Linda can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Eric","Linda"],"index":7276,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9008408785,"difficulty":0.0991591215}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Norman can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Norman","Craig","James"],"index":1919,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9813646674,"difficulty":0.0186353326}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Corey does not know whether Marsha is thirsty. It is publicly announced that Marsha does not know whether Jose is thirsty. It is publicly announced that Corey is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] Agentd knows that (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Marsha can now know that Corey can know whether Marsha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Corey","Duane","Marsha"],"index":6854,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6915791035,"difficulty":0.3084208965}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Yvonne can now know that Colleen can know that Yvonne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Yvonne","Paul","Colleen"],"index":8867,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9719874859,"difficulty":0.0280125141}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick knows whether or not nobody's forehead is muddy. It is publicly announced that Herbert does not know whether Herbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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) ] 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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know whether Eddie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Herbert","Eddie","Frederick"],"index":1124,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.955968678,"difficulty":1.955968678}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Josefina is not thirsty. It is publicly announced that Robert does not know whether Ronald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Annie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Josefina","Ronald","Annie","Robert"],"index":5856,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9720805287,"difficulty":0.0279194713}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barry knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Barry can now know whether John can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Roderick","Barry"],"index":6085,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9467327595,"difficulty":1.9467327595}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tammy's card is shown to Jessie. Jessie's card is shown to James. Jessie's card is shown to Tammy. James's card is shown to Tammy. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Tammy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessie","James","Tammy"],"index":4604,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.972820282,"difficulty":0.027179718}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosemary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Vera can now know that Rosemary can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Vera","Jeanette","Rosemary"],"index":1679,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9852498174,"difficulty":0.0147501826}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Earline can now know that Andrew is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earline","Frances","Eric","Andrew"],"index":621,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9554044604,"difficulty":0.0445955396}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Henry. Bianca's card is shown to Henry. Henry's card is shown to Michael. Henry's card is shown to Bianca. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darlene can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Henry","Michael","Darlene","Bianca"],"index":7972,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9752134085,"difficulty":0.0247865915}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Phillip's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Phillip can now know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Richard","Phillip"],"index":3771,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9529933929,"difficulty":0.0470066071}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Colleen. Colleen's card is shown to Joseph. Earl's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Colleen","Joseph","Earl"],"index":5011,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9745589495,"difficulty":0.0254410505}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Gus can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Gus","Jennifer","William"],"index":3106,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9735746384,"difficulty":0.0264253616}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cora's card is shown to Deborah. Joseph's card is shown to James. Cora's card is shown to James. Deborah's card is shown to Joseph. James's card is shown to Joseph. Deborah's card is shown to Cora. Joseph's card is shown to Cora. It is publicly announced that someone picked a red card. It is publicly announced that Deborah picked a red card. It is publicly announced that Cora does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Cora can now know that James can know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","James","Joseph","Cora"],"index":76,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6696028113,"difficulty":0.3303971887}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Robert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Marlin","Janna","Robert"],"index":4845,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9861759543,"difficulty":0.0138240457}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley is thirsty. It is publicly announced that Jason knows whether someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Kayla does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jason can now know whether Kayla can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Kayla","Shirley"],"index":3461,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9878189564,"difficulty":0.0121810436}
-{"premise":"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 Kimberely's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Kimberely can now know whether Nellie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kimberely","Nellie"],"index":2383,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8832902312,"difficulty":0.1167097688}
-{"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 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":"Brian can now know that Sarah can know that Tara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sarah","Tara","Brian"],"index":2615,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9709469676,"difficulty":0.0290530324}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Juanita can now know that Glenn can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Juanita","Glenn"],"index":3912,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9879288077,"difficulty":0.0120711923}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Kevin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"William can now know whether Shirley can know whether Shirley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","William","Shirley"],"index":9115,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9108678102,"difficulty":0.0891321898}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joanne does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Joanne can now know whether Linda can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Michael","Joanne"],"index":6319,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5617217422,"difficulty":0.4382782578}
-{"premise":"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 Rubie 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) ] [ ! (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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"James can now know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Rubie","Raymond"],"index":7592,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9774971604,"difficulty":1.9774971604}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Diane. Diane's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Grace does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows 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":"Diane can now know whether Grace picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Diane","Grace"],"index":6876,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.513741672,"difficulty":1.513741672}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (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":"Shawn can now know that Zenaida can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Zenaida","Shawn","Caitlin"],"index":2591,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9894267321,"difficulty":0.0105732679}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Demetria does not know whether Christopher is thirsty. It is publicly announced that Christopher is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! (1|2) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Demetria can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Demetria","Christopher"],"index":3107,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.661606729,"difficulty":1.661606729}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Frances knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Frances can now know that Ruby can know that Kerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruby","Frances","Kerry","Maria"],"index":1237,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9671716094,"difficulty":0.0328283906}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Regena. Margaret's card is shown to Ian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Regena can now know that Margaret can know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Regena","Ian"],"index":570,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6491160393,"difficulty":1.6491160393}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacklyn's card is shown to Steven. Brent's card is shown to Steven. Brent's card is shown to Jacklyn. Jacklyn's card is shown to Brent. It is publicly announced that someone picked a red card. It is publicly announced that Jacklyn knows whether Brent picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Steven can now know that Steven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Jacklyn","Brent"],"index":5045,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9533686638,"difficulty":0.0466313362}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Deborah can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tomeka","Jodi","Deborah","Richard"],"index":3016,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9840188026,"difficulty":0.0159811974}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annette's card is shown to Charity. Tyler's card is shown to Charity. Tyler's card is shown to Annette. Charity's card is shown to Tyler. Annette's card is shown to Tyler. Charity's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether someone picked a red card. It is publicly announced that Tyler does not know whether Tyler picked a red card. It is publicly announced that Tyler knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Charity can now know that Tyler can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charity","Annette","Tyler","David"],"index":7505,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9891979098,"difficulty":0.0108020902}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ann can now know that Annie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Annie","Ann"],"index":107,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9817194343,"difficulty":0.0182805657}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Cody can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Albert","Cody"],"index":294,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9760412574,"difficulty":0.0239587426}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether someone's forehead is muddy. It is publicly announced that Edwin knows whether Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Martha can now know whether Marcia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edwin","Martha","Ronald","Marcia"],"index":1348,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9848841429,"difficulty":0.0151158571}
-{"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":"Connie can now know that Leonard can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Connie","Tara","Leonard","Cora"],"index":6385,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.850371182,"difficulty":0.149628818}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bill does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Nancy can now know that Lucrecia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bill","Nancy","Gloria","Lucrecia"],"index":3440,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9559795856,"difficulty":0.0440204144}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know that Peggy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Adam","Peggy","Laura"],"index":6656,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9817596674,"difficulty":0.0182403326}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bradley can now know whether Patricia can know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Bradley","Jacqueline","Gwen"],"index":4224,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9340704083,"difficulty":1.9340704083}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Edward can now know whether April is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Denise","Edward","Glenn","April"],"index":786,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8675399423,"difficulty":1.8675399423}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Fred can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shelby","Fred","Jennifer","Lucille"],"index":5300,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9870148897,"difficulty":0.0129851103}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beckie's card is shown to Kristi. Donald's card is shown to Beckie. Mathew's card is shown to Beckie. Kristi's card is shown to Donald. Donald's card is shown to Mathew. It is publicly announced that someone picked a red card. It is publicly announced that Mathew does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Mathew can now know that Kristi can know that Beckie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kristi","Beckie","Donald","Mathew"],"index":4721,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9699261189,"difficulty":0.0300738811}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlotte knows whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Charlotte can now know whether Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charlotte","Robert"],"index":9613,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9234892726,"difficulty":0.0765107274}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold is not thirsty. It is publicly announced that David does not know whether Kelly is thirsty. It is publicly announced that Xavier does not know whether Kelly is thirsty. It is publicly announced that David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] Agentb knows whether (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] 0","hypothesis":"David can now know whether Kelly can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","David","Kelly","Xavier"],"index":2882,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9255864024,"difficulty":0.0744135976}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tyler can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julia","Vickie","Tyler"],"index":4971,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8128453493,"difficulty":0.1871546507}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricky's card is shown to Lavonne. Lavonne's card is shown to Jennifer. Ricky's card is shown to Jennifer. Michael's card is shown to Jennifer. Lavonne's card is shown to Ricky. Jennifer's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ricky can now know whether Jennifer can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lavonne","Jennifer","Ricky","Michael"],"index":4442,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9871531129,"difficulty":0.0128468871}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond's forehead is muddy. It is publicly announced that Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Doug can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Doug","Raymond"],"index":6613,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9799210429,"difficulty":0.0200789571}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Georgia can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Georgia","Belen"],"index":300,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9846128225,"difficulty":0.0153871775}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacob does not know whether Jacob's forehead is muddy. It is publicly announced that Erin does not know whether Erin's forehead is muddy. It is publicly announced that Jacob'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 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Erin can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erin","Jacob","Robert"],"index":4804,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9693521857,"difficulty":0.0306478143}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alvin's card is shown to Angela. Jefferson's card is shown to Alvin. Angela's card is shown to Tenesha. Alvin's card is shown to Jefferson. It is publicly announced that someone picked a red card. It is publicly announced that Tenesha does not know whether Jefferson picked a red card. It is publicly announced that Angela picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Tenesha can now know that Alvin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Alvin","Tenesha","Jefferson"],"index":938,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.947685957,"difficulty":0.052314043}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know that Nancy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chad","Nancy","Mark","Eddy"],"index":6047,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9808077216,"difficulty":0.0191922784}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Melanie can now know whether Victor can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Victor","Melanie"],"index":994,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9904044867,"difficulty":0.0095955133}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Anne'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) ] [ ! (Agentb knows whether 3) ] [ ! ~(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) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Becky can now know whether Anne can know whether Anne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Susan","Anne","Becky"],"index":737,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9721730351,"difficulty":0.0278269649}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Vanessa. Raymond's card is shown to Vanessa. John's card is shown to Tyler. Tyler's card is shown to John. John's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Tyler does not know whether or not everyone picked a red card. It is publicly announced that Vanessa does not know whether Tyler picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"John can now know that Raymond picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vanessa","Tyler","John","Raymond"],"index":8355,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9524110556,"difficulty":0.0475889444}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monique's card is shown to Daniel. Monique's card is shown to Mike. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mike can now know that Daniel can know whether Monique picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Mike","Monique"],"index":9133,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6700015068,"difficulty":1.6700015068}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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":"Walter can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Walter","Gary","Fred"],"index":758,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.990085125,"difficulty":0.009914875}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Eula is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gary can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gary","Eula"],"index":7552,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8825634122,"difficulty":0.1174365878}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 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":"Ethel can now know that Carol can know that Nick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ethel","Nick","Carol"],"index":3778,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9715823531,"difficulty":0.0284176469}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Loretta can now know that Loretta is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Loretta","Floyd"],"index":717,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9634681344,"difficulty":0.0365318656}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"John can now know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Frank","Thomas","Joseph","John"],"index":9156,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9849907756,"difficulty":0.0150092244}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan knows whether Walter's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Alan can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Alan","Walter"],"index":4960,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9720119834,"difficulty":0.0279880166}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Charlie is thirsty. It is publicly announced that George is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Charlie can now know whether Paul is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Charlie","George"],"index":8425,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7875774503,"difficulty":0.2124225497}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Jacqueline can now know that Amy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jacqueline","Amy"],"index":865,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9760693908,"difficulty":0.0239306092}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marsha does not know whether or not everyone's forehead is muddy. It is publicly announced that Marsha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (~(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":"Marsha can now know whether Janet can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janet","Marsha"],"index":261,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9751910567,"difficulty":0.0248089433}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nathaniel does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ramon can now know that Kathryn can know that Nathaniel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ramon","Nathaniel","Kathryn"],"index":306,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9699614644,"difficulty":1.9699614644}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Ann can now know whether Megan can know whether Megan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Megan","Araceli","Ann"],"index":997,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.974693954,"difficulty":0.025306046}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"George can now know whether Ethel can know whether George is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Ethel","James"],"index":6667,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8211448193,"difficulty":0.1788551807}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dorothy","Joseph","Maria"],"index":2093,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9864093065,"difficulty":0.0135906935}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Donna can now know whether Alfredo can know that Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alfredo","Donna"],"index":756,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.851439774,"difficulty":0.148560226}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Graciela's card is shown to Michael. Christina's card is shown to Samantha. Graciela's card is shown to Samantha. Michael's card is shown to Christina. Samantha's card is shown to Christina. Michael's card is shown to Graciela. Christina's card is shown to Graciela. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card. It is publicly announced that Graciela does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Graciela can now know that Michael can know whether Samantha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Samantha","Christina","Graciela"],"index":5429,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6681896448,"difficulty":1.6681896448}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henry's card is shown to William. William's card is shown to Shawn. Henry's card is shown to Shawn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Henry can now know whether Henry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Henry","Shawn"],"index":4147,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8473824263,"difficulty":1.8473824263}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wallace knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Wallace can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wallace","Jamie"],"index":3982,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9490264654,"difficulty":0.0509735346}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Mary","Anna","Charles"],"index":4491,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9588780999,"difficulty":0.0411219001}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Lisa. Ryan's card is shown to Eduardo. Mark's card is shown to Eduardo. Ryan's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eduardo can now know whether Ryan can know whether Ryan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Ryan","Eduardo","Mark"],"index":8049,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9113454819,"difficulty":0.0886545181}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Laura can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","Pauline","Charles"],"index":6424,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9750891328,"difficulty":0.0249108672}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Fay. Fay's card is shown to John. John's card is shown to Leslie. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that John picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Fay can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Fay","John","Leslie"],"index":2751,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9479157329,"difficulty":0.0520842671}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 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":"Aaron can now know that Kimberlee can know whether Aaron's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Aaron","Deborah","Kimberlee"],"index":7194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8222010136,"difficulty":0.1777989864}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Connie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Sean","Joseph","Connie"],"index":998,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9877930284,"difficulty":0.0122069716}
-{"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|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":"Eva can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bridgette","Arletha","Eva"],"index":3554,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9793965816,"difficulty":0.0206034184}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maricruz's card is shown to Amanda. Amanda's card is shown to Maricruz. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amanda can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amanda","Maricruz","Virginia"],"index":8483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9877454638,"difficulty":0.0122545362}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joe's card is shown to Raymond. Joe's card is shown to Henry. Raymond's card is shown to Joe. It is publicly announced that someone picked a red card. It is publicly announced that Joe does not know whether Henry picked a red card. It is publicly announced that Raymond does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Henry can now know whether Raymond can know whether Raymond picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raymond","Henry","Joe"],"index":6313,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9517982006,"difficulty":0.0482017994}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Kristopher. Thelma's card is shown to Jodi. Kristopher's card is shown to Josefa. Jodi's card is shown to Josefa. Thelma's card is shown to Josefa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristopher can now know whether Jodi can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kristopher","Jodi","Thelma","Josefa"],"index":3169,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9769514203,"difficulty":0.0230485797}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Isabel can now know whether Paul can know whether Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Isabel","Paul"],"index":8160,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8997298479,"difficulty":0.1002701521}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edith does not know whether Gloria is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Gloria can now know whether James can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edith","James","Gloria"],"index":4866,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9440869093,"difficulty":0.0559130907}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Donald. Teresa's card is shown to James. James's card is shown to Teresa. Donald's card is shown to Ramon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ramon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donald","James","Teresa","Ramon"],"index":4714,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9818398356,"difficulty":0.0181601644}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lori is thirsty. It is publicly announced that Zelma knows whether Lori is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Minnie can now know whether Zelma is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lori","Zelma","Minnie"],"index":6038,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5518454313,"difficulty":0.4481545687}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Lawrence can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clifton","Monica","Mary","Lawrence"],"index":1615,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9792303443,"difficulty":0.0207696557}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 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":"Kelly can now know whether Ronald can know whether Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelly","Ronald","Jayne"],"index":3321,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9164742827,"difficulty":1.9164742827}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Randy can now know whether Kelly can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randy","Kelly"],"index":2327,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9501879811,"difficulty":0.0498120189}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mary can now know whether David can know that Magdalena is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Magdalena","David"],"index":6733,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8679612875,"difficulty":0.1320387125}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Kam can now know whether Philip can know whether Philip is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Philip","Kam","Charles"],"index":8943,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8861240745,"difficulty":0.1138759255}
-{"premise":"There are three 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.","smcdel_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 3)","n_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":"Sue can now know that Cora can know that Sue's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cora","Kathryn","Sue"],"index":7817,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9644645452,"difficulty":0.0355354548}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jennifer can now know whether Judith can know that Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Kristin","Judith","Jennifer"],"index":9528,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.886269033,"difficulty":0.113730967}
-{"premise":"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 Dianne knows 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Dianne can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harvey","Sharon","Dianne"],"index":6683,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.987742424,"difficulty":0.012257576}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellis knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Daniel can now know whether Bessie can know that Bessie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Jerry","Bessie","Ellis"],"index":8292,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8462194204,"difficulty":1.8462194204}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Sharon can now know that Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Marvin","Terry"],"index":2110,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9410024881,"difficulty":0.0589975119}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dianne can now know that Adam can know whether Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adam","Dianne","Barbara"],"index":578,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9783896208,"difficulty":0.0216103792}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Sidney'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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Kimberly can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sidney","Kimberly"],"index":5275,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6414622068,"difficulty":1.6414622068}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know whether Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jason","Laura","Sabrina","Jo"],"index":9245,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9856866002,"difficulty":0.0143133998}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Jeff. Jeff's card is shown to Randy. Sharon's card is shown to Randy. Julie's card is shown to Randy. Sharon's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Jeff knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Sharon can now know whether Randy can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeff","Sharon","Randy","Julie"],"index":510,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9844843745,"difficulty":0.0155156255}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Marian can now know that Joseph can know that Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachele","Marian","Jeffrey","Joseph"],"index":4729,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9665605426,"difficulty":0.0334394574}
-{"premise":"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 knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"John can now know that Daniel can know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","John","Larry"],"index":6686,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9257521629,"difficulty":1.9257521629}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justina can now know that Barbara can know whether Justina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justina","Barbara","Tyrone","Judith"],"index":4198,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9672266841,"difficulty":0.0327733159}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carrie. Carrie's card is shown to Franklin. Carrie's card is shown to Carol. Franklin's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Franklin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Carrie can now know whether Carol can know that Franklin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carrie","Franklin","Carol"],"index":4348,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9618798494,"difficulty":1.9618798494}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold does not know whether Helen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Barry can now know that Helen can know that Helen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harold","Everett","Barry","Helen"],"index":7755,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9719959497,"difficulty":0.0280040503}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas does not know whether Kathleen is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Laurie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathleen","Douglas","Laurie"],"index":5935,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9745315909,"difficulty":1.9745315909}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Erlinda can now know that Erlinda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erlinda","Charles"],"index":691,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9569053054,"difficulty":0.0430946946}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Lynne. Marilyn's card is shown to Lynne. Marilyn's card is shown to Maria. Lynne's card is shown to Marilyn. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 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:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Lynne can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynne","Maria","Marilyn"],"index":9196,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.975214541,"difficulty":0.024785459}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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":"Tom can now know that Louis can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Mark","Tom","Mary"],"index":676,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.985248208,"difficulty":0.014751792}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Anthony can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Pamela","Anthony"],"index":8854,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9470123649,"difficulty":0.0529876351}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jocelyn does not know whether Rosemary is thirsty. It is publicly announced that Rosemary knows whether someone is thirsty. It is publicly announced that Jocelyn does not know whether Rosemary is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Johnnie can now know that Rosemary can know that Johnnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Johnnie","Jocelyn","Rosemary"],"index":7649,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9702723622,"difficulty":0.0297276378}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris knows whether Phyllis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Phyllis can now know whether Misha can know whether Chris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melanie","Misha","Chris","Phyllis"],"index":7328,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.984806776,"difficulty":0.015193224}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann is not thirsty. It is publicly announced that Ann is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(2) ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Kevin can now know that Melissa can know that Ann is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melissa","Ann","Kevin"],"index":8220,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.971460402,"difficulty":0.028539598}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Mark. John's card is shown to Mark. James's card is shown to Craig. James's card is shown to John. Mark's card is shown to James. John's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether Mark picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Craig can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Craig","John","James"],"index":4283,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9550983906,"difficulty":0.0449016094}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abigail knows whether Abigail's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joan can now know that Jerome can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joan","Abigail","Minnie","Jerome"],"index":8454,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.715038836,"difficulty":0.284961164}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Calvin can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chester","Melanie","Calvin","James"],"index":5851,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9875663519,"difficulty":0.0124336481}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isabell is thirsty. It is publicly announced that Edmund knows whether someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Juan does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Isabell can now know whether Edmund can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edmund","Juan","Isabell"],"index":7431,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9852833748,"difficulty":0.0147166252}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry does not know whether Terry's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Terry can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Terry","Leah"],"index":2191,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9761249423,"difficulty":0.0238750577}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows 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":"Dorothy can now know that Edna can know whether Edna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diana","Michael","Edna","Dorothy"],"index":2322,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8529625535,"difficulty":1.8529625535}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilyn knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Marilyn can now know that Edward can know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marilyn","Edward"],"index":5000,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.936257422,"difficulty":0.063742578}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Rachel. Patrick's card is shown to Rachel. Rachel's card is shown to John. Patrick's card is shown to John. Rachel's card is shown to Kevin. Rachel's card is shown to Patrick. Kevin's card is shown to Patrick. It is publicly announced that someone picked a red card. It is publicly announced that Patrick does not know whether Patrick picked a red card. It is publicly announced that Rachel does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Rachel can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rachel","John","Kevin","Patrick"],"index":7406,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.516459167,"difficulty":1.516459167}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether or not everyone's forehead is muddy. It is publicly announced that Katherine knows whether Katherine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Anthony can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anthony","Katherine"],"index":1259,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9886488318,"difficulty":0.0113511682}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Henry can now know whether Carl can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carl","Henry","Todd"],"index":4456,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9822241664,"difficulty":0.0177758336}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lazaro knows whether Annette's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Angelica can now know whether Lazaro can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lazaro","Angelica","Annette","Frank"],"index":2141,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9791364074,"difficulty":0.0208635926}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gilbert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ken can now know that Gilbert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gilbert","Ken"],"index":9288,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9572822452,"difficulty":1.9572822452}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Deborah. Donna's card is shown to Deborah. Donna's card is shown to Dale. Dale's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Dale picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Dale can now know that Deborah can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deborah","Dale","Donna"],"index":3080,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9849424362,"difficulty":0.0150575638}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Debra is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Michael can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ryan","Debra","Michael"],"index":961,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.974729836,"difficulty":0.025270164}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vicente knows whether Vicente's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Brandon can now know that Vicente's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wendy","Vicente","Brandon","Kyle"],"index":6111,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9525640011,"difficulty":0.0474359989}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clifford knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kathleen can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathleen","Clifford","Joseph","James"],"index":6934,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9875487089,"difficulty":0.0124512911}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Anthony does not know whether Leslie is thirsty. It is publicly announced that Jimmie does not know whether Leslie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gladys can now know whether Jimmie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jimmie","Leslie","Gladys","Anthony"],"index":6374,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9863638282,"difficulty":0.0136361718}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Ronald is thirsty. It is publicly announced that Neil does not know whether Ronald is thirsty. It is publicly announced that Neil does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentb knows whether (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Ronald can now know whether Neil can know that Matthew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Ronald","Kevin","Neil"],"index":8606,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9052889943,"difficulty":0.0947110057}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vincent knows whether Mary'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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Vincent can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","Vincent"],"index":8871,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5652774572,"difficulty":1.5652774572}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristine can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joan","Elsie","Kristine","Wallace"],"index":6054,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9899820685,"difficulty":0.0100179315}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brett does not know whether Janice is thirsty. It is publicly announced that Elvira knows whether someone is thirsty. It is publicly announced that Francis does not know whether or not everyone is thirsty. It is publicly announced that Francis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Janice can now know whether Brett can know whether Brett is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Janice","Brett","Elvira"],"index":5699,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9550349712,"difficulty":0.0449650288}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether someone's forehead is muddy. It is publicly announced that Harold knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentb knows whether 1) ] (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)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Harold can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Harold","Luz"],"index":7090,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9684566855,"difficulty":0.0315433145}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peggy knows whether Eric's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Peggy can now know whether Amanda can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bruce","Amanda","Peggy","Eric"],"index":4793,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.987850368,"difficulty":0.012149632}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","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":"Greg can now know that Helen can know that Greg's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Greg","Ernesto","Helen","Brenda"],"index":6100,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9702987075,"difficulty":0.0297012925}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Lacey can know whether Lacey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Marcus","Chase","Lacey"],"index":6783,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8121899366,"difficulty":1.8121899366}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emily does not know whether Ophelia is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Marsha can now know that Emily is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ophelia","Emily","Marsha"],"index":2289,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9515684843,"difficulty":1.9515684843}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amber's card is shown to Harry. Kristin's card is shown to William. Kristin's card is shown to Amber. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Harry can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kristin","Harry","William","Amber"],"index":8051,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9820075631,"difficulty":0.0179924369}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agentb knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Jeremiah can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Reginald","Jeremiah"],"index":640,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9899821877,"difficulty":0.0100178123}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Keith does not know whether Dwayne is thirsty. It is publicly announced that Keith knows whether Keith is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dwayne can now know whether Keith can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dwayne","Keith"],"index":9176,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9614644647,"difficulty":0.0385355353}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peggy knows whether Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Boyd can now know whether Wanda can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wanda","James","Peggy","Boyd"],"index":8555,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9877151847,"difficulty":0.0122848153}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether Bill is thirsty. It is publicly announced that Bill does not know whether Vincent is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Bill can now know whether Bill is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Bill","Vincent"],"index":4417,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7918910384,"difficulty":1.7918910384}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Percy does not know whether Percy's forehead is muddy.","smcdel_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":"Christian can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christian","Jacob","Percy"],"index":1752,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.608702302,"difficulty":0.391297698}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"William can now know that Gail can know that Gail is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Gail","Gregory"],"index":5387,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9728210568,"difficulty":0.0271789432}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Douglas can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Travis","Douglas"],"index":5913,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9888745546,"difficulty":0.0111254454}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samantha does not know whether Maria is thirsty. It is publicly announced that Charles does not know whether Larry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Larry can now know whether Charles can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Samantha","Maria","Larry"],"index":9603,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9652878046,"difficulty":0.0347121954}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephanie's card is shown to Nicholas. Nicholas's card is shown to Stephanie. Timothy's card is shown to Stephanie. Nicholas's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Stephanie knows whether or not nobody picked a red card. It is publicly announced that Nicholas knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Nicholas can now know that Stephanie can know that Nicholas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicholas","Stephanie","Timothy"],"index":3950,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9287592173,"difficulty":1.9287592173}
-{"premise":"There are two 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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jose can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jose","Aurea"],"index":8922,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9735680819,"difficulty":0.0264319181}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Timothy's forehead is muddy. It is publicly announced that Tanya 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 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Tanya can now know that Timothy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tanya","Timothy"],"index":6338,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5425655842,"difficulty":1.5425655842}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bebe is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Jack can now know that Bebe can know whether Jack is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jack","David","Jeanette","Bebe"],"index":2186,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7423174381,"difficulty":0.2576825619}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Abe can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rita","Abe","Danny","Daniel"],"index":5100,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9789990187,"difficulty":0.0210009813}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald does not know whether Ronald's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy. It is publicly announced that Barbara does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know that Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronald","Stephanie","Robert","Barbara"],"index":2719,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9282182455,"difficulty":1.9282182455}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nicholas can now know that Darrell can know that Darrell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicholas","Lori","Darrell"],"index":807,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9728753567,"difficulty":0.0271246433}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to George. George's card is shown to Ashley. Matthew's card is shown to Ashley. Ashley's card is shown to Matthew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Matthew can now know that George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Ashley","Matthew"],"index":597,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9547109604,"difficulty":0.0452890396}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mario knows whether Mario is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jose can now know that Mario can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jose","Mario"],"index":2486,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8447179794,"difficulty":0.1552820206}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cortney's card is shown to Valerie. Kelly's card is shown to Donald. Cortney's card is shown to Donald. Valerie's card is shown to Kelly. Donald's card is shown to Kelly. Valerie's card is shown to Cortney. Kelly's card is shown to Cortney. It is publicly announced that someone picked a red card. It is publicly announced that Valerie picked a red card. It is publicly announced that Cortney does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Donald can now know whether Valerie can know that Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Valerie","Donald","Kelly","Cortney"],"index":6132,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9598774314,"difficulty":0.0401225686}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Micheal knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Micheal can now know that Walter can know that Micheal's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lou","Micheal","Crystal","Walter"],"index":3157,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.967913568,"difficulty":0.032086432}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Richard can now know whether Georgia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Georgia","Michael","Richard","Charles"],"index":8194,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.836045444,"difficulty":0.163954556}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julianne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Wilhelmina can now know whether Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Julia","Wilhelmina","Julianne"],"index":8209,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9748654366,"difficulty":0.0251345634}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debra does not know whether Kathryn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kathryn can now know whether Debra can know whether Kathryn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathryn","Debra","Lori"],"index":5698,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9365561604,"difficulty":0.0634438396}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Kathryn. Kathryn's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Kelly knows whether Kathryn picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kelly can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kathryn","Kelly"],"index":2454,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9881061316,"difficulty":0.0118938684}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Felix knows whether Felix is thirsty. It is publicly announced that Betsy does not know whether Richelle is thirsty. It is publicly announced that Felix is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Richelle can now know that Richelle is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gerald","Felix","Betsy","Richelle"],"index":2092,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9529061317,"difficulty":0.0470938683}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Darlene can now know that Dorothy can know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darlene","Dorothy","James"],"index":2119,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9745284915,"difficulty":0.0254715085}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Darlene is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Darlene can now know whether Arlene can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darlene","Arlene","Jennifer"],"index":7602,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5428800583,"difficulty":0.4571199417}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Harold can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susie","Carrie","Robert","Harold"],"index":941,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.94963938,"difficulty":0.05036062}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita does not know whether Lisa is thirsty. It is publicly announced that Melvin is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Melvin can now know that Lisa can know whether Melvin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melvin","Anita","Lisa"],"index":3406,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5700865388,"difficulty":1.5700865388}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to James. James's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Scott does not know whether Scott picked a red card. It is publicly announced that James knows whether Scott picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Scott can now know that James can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Scott"],"index":2964,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848161936,"difficulty":0.0151838064}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erlinda knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 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) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Nicholas can now know whether Scott's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Erlinda","Markus","Nicholas","Scott"],"index":5573,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9706093669,"difficulty":0.0293906331}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrea knows whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Andrea can now know that Laura can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Craig","Beverly","Andrea","Laura"],"index":1238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9790888429,"difficulty":0.0209111571}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martina does not know whether Martina's forehead is muddy. It is publicly announced that Angela knows whether Aimee's forehead is muddy. It is publicly announced that Jane's forehead is not muddy. It is publicly announced that Angela's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] (Agentb 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 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Angela can now know whether Aimee's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martina","Angela","Jane","Aimee"],"index":367,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.962331593,"difficulty":0.037668407}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Harold can now know that Lori can know that Lori's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Francisco","Harold","Lori"],"index":5169,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9735077024,"difficulty":0.0264922976}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward does not know whether Joe is thirsty. It is publicly announced that Edward does not know whether Joe is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Joe can now know that Edward can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joe","Edward"],"index":122,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9782519341,"difficulty":0.0217480659}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Demetria does not know whether Patricia is thirsty. It is publicly announced that Patricia knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Demetria can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Patricia","Demetria"],"index":6688,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8863773346,"difficulty":1.8863773346}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Johnny. Johnny's card is shown to Pauline. Julie's card is shown to Pauline. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Johnny can now know that Pauline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Johnny","Pauline","Julie"],"index":3474,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9522871375,"difficulty":0.0477128625}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alvin can now know whether Paul can know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Francisco","Helen","Alvin"],"index":3551,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7298372984,"difficulty":0.2701627016}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felicia knows whether Felicia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Alexander can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrea","Felicia","Alexander","David"],"index":9415,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9536027908,"difficulty":0.0463972092}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Dorris can now know that Levi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Levi","Dorris"],"index":4676,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9628534317,"difficulty":0.0371465683}
-{"premise":"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 Helen knows 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 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (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 (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Helen can now know that Leonard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leonard","Helen","Jerry"],"index":8066,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9354115725,"difficulty":0.0645884275}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita does not know whether Rita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rita","Brett","Concetta","Michael"],"index":6641,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9009351134,"difficulty":1.9009351134}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ryan can now know whether Scott can know that Jimmy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jimmy","Scott","Ryan","Anne"],"index":1973,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9449137449,"difficulty":0.0550862551}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joan can now know whether John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Allen","Joan","John"],"index":1177,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9715389013,"difficulty":0.0284610987}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcia does not know whether Marcia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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":"Marcia can now know whether Dale can know that Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcia","Dale","Evelyn","Deborah"],"index":5980,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8866841197,"difficulty":0.1133158803}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shaun knows whether Shaun's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Shaun can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sean","Shaun","Rosemary","Mary"],"index":4936,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9676141739,"difficulty":0.0323858261}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debora knows whether Norma's forehead is muddy. It is publicly announced that Debora'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 3) ] [ ! ~(2) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Thomas can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Debora","Norma"],"index":1355,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9698925018,"difficulty":0.0301074982}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy. It is publicly announced that Shara knows whether Robert's forehead is muddy. It is publicly announced that Deloras's forehead is not muddy. It is publicly announced that Shara's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Shara can now know that Deloras's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Shara","Deloras","Robert"],"index":8269,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9383813143,"difficulty":0.0616186857}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramona knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Barry can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barry","Sterling","Ramona","Gertrude"],"index":6229,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9712178707,"difficulty":0.0287821293}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katie's card is shown to Douglas. Timothy's card is shown to Katie. Katie's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Katie knows whether someone picked a red card. It is publicly announced that Timothy does not know whether or not everyone picked a red card. It is publicly announced that Timothy knows whether or not nobody picked a red card. It is publicly announced that Timothy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Katie can now know whether Katie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Douglas","Katie","Timothy"],"index":4414,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9456412792,"difficulty":0.0543587208}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debra knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Joseph can now know that Debra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Benjamin","Debra","Joseph","Jeanine"],"index":5728,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9285583496,"difficulty":0.0714416504}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Robert can now know that Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Peter"],"index":205,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9561722279,"difficulty":0.0438277721}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abdul's forehead is not muddy. It is publicly announced that Reginald knows whether Reginald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] (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) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Abdul can now know whether Abdul's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brian","Reginald","Abdul","Audrey"],"index":9043,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9612796903,"difficulty":0.0387203097}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Jason can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jason","Ella"],"index":6535,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9810861945,"difficulty":0.0189138055}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Aubrey can now know that Roberto can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laurie","Aubrey","Roberto"],"index":7978,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9893246293,"difficulty":0.0106753707}
-{"premise":"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 Norris's forehead is muddy. It is publicly announced that Norris does not know whether or not everyone's forehead is muddy. It is publicly announced that Norris does not know whether Norris's forehead 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 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Fernando can now know that Wayne can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Fernando","Wayne","Norris","James"],"index":6376,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9710832238,"difficulty":0.0289167762}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fernando does not know whether Diane is thirsty. It is publicly announced that Fernando does not know whether Diane is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Diane can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fernando","Sherwood","Diane","George"],"index":4406,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9743106365,"difficulty":0.0256893635}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Chelsea. Chelsea's card is shown to Norma. Chelsea's card is shown to Mary. Norma's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Norma picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Chelsea can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Chelsea","Norma","Mary"],"index":7518,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.986068368,"difficulty":0.013931632}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellsworth knows whether Ellsworth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Ellsworth can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Valeria","Rory","Ellsworth"],"index":3666,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9892428517,"difficulty":0.0107571483}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eloisa can now know that Sarah can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sarah","Samantha","Eloisa"],"index":1199,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9289284945,"difficulty":0.0710715055}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Katherine can now know whether William can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Katherine"],"index":6626,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5800013542,"difficulty":1.5800013542}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Johnny can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Vanita","Adalberto","Richard"],"index":3036,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9809505939,"difficulty":0.0190494061}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Whitney knows whether or not nobody's forehead is muddy. It is publicly announced that Donald knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Michael can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Whitney","Donald","Michael"],"index":3152,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9683601856,"difficulty":0.0316398144}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mee's card is shown to Christopher. Christopher's card is shown to Mee. Dollie's card is shown to Mee. Mee's card is shown to Dollie. It is publicly announced that someone picked a red card. It is publicly announced that Christopher knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mee can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christopher","Mee","Dollie"],"index":5937,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5960441232,"difficulty":0.4039558768}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicholas is thirsty. It is publicly announced that Eric knows whether Nicholas is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ashley can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nicholas","Eric","Ashley"],"index":2490,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7471820116,"difficulty":0.2528179884}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether or not everyone is thirsty. It is publicly announced that Douglas does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Brenda can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brenda","Douglas","Steven","John"],"index":6379,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.974604845,"difficulty":0.025395155}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen 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":"Carmen can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carmen","Ralph","Matthew"],"index":7087,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9770664573,"difficulty":0.0229335427}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacqueline does not know whether Diane is thirsty. It is publicly announced that Roscoe does not know whether Diane is thirsty. It is publicly announced that Roscoe does not know whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Jacqueline can now know that Diane can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Diane","Jacqueline","Roscoe"],"index":6638,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9772056341,"difficulty":0.0227943659}
-{"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 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":"Alan can now know whether Lorraine can know that Lorraine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Douglas","Lorraine","Alan","Mario"],"index":7914,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6567023396,"difficulty":1.6567023396}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Kevin can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Sara","Arlene","Kevin"],"index":7001,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.980096519,"difficulty":0.019903481}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Jack does not know whether Scott is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Robert can now know that Scott is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Scott","Robert","Jack"],"index":1489,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9586807489,"difficulty":0.0413192511}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy.","smcdel_problem":"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":"Patricia can now know that Nelson can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Luke","Nelson","Patricia"],"index":1562,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9886454344,"difficulty":0.0113545656}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Allen can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Allen","Karine"],"index":8619,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9714400172,"difficulty":0.0285599828}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Minnie. Margaret's card is shown to Minnie. Paul's card is shown to Margaret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Minnie can now know that Paul can know that Minnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paul","Minnie","Margaret"],"index":4167,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9738202095,"difficulty":0.0261797905}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward does not know whether Barbara is thirsty. It is publicly announced that Barbara does not know whether Edward is thirsty. It is publicly announced that Edward does not know whether Milton is thirsty. It is publicly announced that Edward does not know whether Velma is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Velma can now know that Edward can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Barbara","Velma","Milton"],"index":440,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8521604538,"difficulty":0.1478395462}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mollie can now know that Marie can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marie","Gayle","Charles","Mollie"],"index":2739,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9729377627,"difficulty":0.0270622373}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Michael can now know whether Carolyn can know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carolyn","Michael","Gary"],"index":3843,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8108610511,"difficulty":1.8108610511}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to John. Herbert's card is shown to Carol. Gerald's card is shown to Carol. Carol's card is shown to Herbert. Gerald's card is shown to Herbert. John's card is shown to Gerald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know whether Herbert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Carol","Herbert","Gerald"],"index":5271,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8240340352,"difficulty":1.8240340352}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (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":"Susan can now know whether Mark can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Sally","Mark","Judith"],"index":3226,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8409956694,"difficulty":0.1590043306}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Betty can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Betty","Elisa","Leroy","Mike"],"index":3400,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9879016876,"difficulty":0.0120983124}
-{"premise":"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 knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows 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) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jeannie can now know whether Barry can know that Jeannie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Don","Julia","Jeannie","Barry"],"index":9190,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8796405792,"difficulty":1.8796405792}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Crysta. Justin's card is shown to Crysta. Crysta's card is shown to Jonathan. Justin's card is shown to Jonathan. Crysta's card is shown to Justin. Jonathan's card is shown to Justin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (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":"Justin can now know that Justin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Crysta","Jonathan","Justin"],"index":5775,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9544665813,"difficulty":0.0455334187}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (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":"Shawn can now know whether Ronda can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Earl","Shawn","Ronda"],"index":1807,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9647883773,"difficulty":0.0352116227}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Daisey can now know that Susan can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Susan","Daisey"],"index":1250,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9807142615,"difficulty":0.0192857385}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arlene is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Joseph can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Arlene","James","Gay"],"index":6822,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9762794375,"difficulty":0.0237205625}
-{"premise":"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 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jennifer can now know whether Harry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harry","Arthur","Jennifer"],"index":7184,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9325448871,"difficulty":0.0674551129}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carmelo can now know whether Harold can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Carmelo","Harold"],"index":3597,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9894785285,"difficulty":0.0105214715}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that 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":"Brian can now know whether Sharon can know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Victor","Sharon","Brian"],"index":5215,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8532806635,"difficulty":1.8532806635}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles is not thirsty. It is publicly announced that Michael does not know whether Lorraine is thirsty. It is publicly announced that Melvin does not know whether Lorraine is thirsty. It is publicly announced that Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] 0","hypothesis":"Michael can now know that Lorraine can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Michael","Lorraine","Melvin"],"index":800,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9850389957,"difficulty":0.0149610043}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcus's card is shown to Chris. Chris's card is shown to Marcus. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marcus can now know that Stephanie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Chris","Marcus","Stephanie"],"index":2841,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9544104934,"difficulty":0.0455895066}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Jewell is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jewell can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","George","Ruby","Jewell"],"index":4197,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.976053834,"difficulty":0.023946166}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Perry's card is shown to Aurelia. Aurelia's card is shown to Perry. It is publicly announced that someone picked a red card. It is publicly announced that Perry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 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":"Perry can now know that Aurelia can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Aurelia","Perry"],"index":6175,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9801038504,"difficulty":0.0198961496}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Audie can now know whether Margarita can know whether Audie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Audie","Michael","Margarita","James"],"index":5193,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9814497232,"difficulty":0.0185502768}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie knows whether Mary's forehead is muddy. It is publicly announced that Carrie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mary can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Carrie"],"index":6600,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9535105228,"difficulty":0.0464894772}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Alden can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Teresa","Alden"],"index":7300,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.97888273,"difficulty":0.02111727}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Alicia can now know that Terisa can know that Suzette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Suzette","Alicia","Jennifer","Terisa"],"index":4205,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9637460113,"difficulty":0.0362539887}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pedro's card is shown to Johnny. Dixie's card is shown to Mildred. Dixie's card is shown to Pedro. Pedro's card is shown to Dixie. It is publicly announced that someone picked a red card. It is publicly announced that Pedro does not know whether Pedro picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Pedro can now know whether Pedro picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Mildred","Pedro","Dixie"],"index":8229,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5176877975,"difficulty":0.4823122025}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Lizette. Patricia's card is shown to Lizette. Lizette's card is shown to William. Patricia's card is shown to William. Lizette's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether William picked a red card. It is publicly announced that Patricia knows whether Lizette picked a red card. It is publicly announced that Lizette does not know whether Lizette picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(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 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lizette can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lizette","William","Patricia"],"index":3426,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9721627831,"difficulty":0.0278372169}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Corey's card is shown to Jimmy. Jimmy's card is shown to Evelyn. Corey's card is shown to Evelyn. Jimmy's card is shown to Corey. Evelyn's card is shown to Corey. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Corey does not know whether Corey picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Evelyn can now know whether Corey can know that Corey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmy","Evelyn","Corey"],"index":1680,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9529363513,"difficulty":0.0470636487}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Stephanie is thirsty. It is publicly announced that Sharla knows whether or not nobody is thirsty. It is publicly announced that John does not know whether Sharla is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Stephanie can now know whether Sharla is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christine","John","Stephanie","Sharla"],"index":3227,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8736667037,"difficulty":1.8736667037}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Neva can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Eula","Neva"],"index":1543,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9735859036,"difficulty":0.0264140964}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Ivan. Ivan's card is shown to Robert. Ada's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ivan","Robert","Kimberly","Ada"],"index":9252,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.988166213,"difficulty":0.011833787}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marie can now know whether Karen can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marie","Gary","Karen"],"index":1084,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9888005257,"difficulty":0.0111994743}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Roberto can now know whether Marcia can know whether Marcia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Roberto","Marcia"],"index":6914,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9202951193,"difficulty":0.0797048807}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roger's card is shown to Donna. Donna's card is shown to Roger. Roger's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Donna does not know whether Donna picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Donna can now know that Roger can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donna","Roger","Eric"],"index":5178,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9759858251,"difficulty":0.0240141749}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Adam can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Linda","Terence","Adam"],"index":4465,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.7735399008,"difficulty":0.2264600992}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angel does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Angel can now know whether Angel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patricia","Angel"],"index":614,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7993782163,"difficulty":1.7993782163}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phyllis knows whether Phyllis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Nicole can now know that Nicole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicole","Phyllis","Rick","Louise"],"index":2581,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9535309076,"difficulty":0.0464690924}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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 that Qiana can know whether Qiana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mario","Richard","Qiana","Nathan"],"index":4346,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7512217164,"difficulty":0.2487782836}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Lee can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lee","John","Jason","Peter"],"index":2335,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9713543057,"difficulty":0.0286456943}
-{"premise":"There are two 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 Debra does not know whether Debra's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (~(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":"Anita can now know that Debra can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Debra","Anita"],"index":418,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9786328673,"difficulty":0.0213671327}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Grant can now know that Mary can know that Grant's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Grant","Charis","Mary","John"],"index":9507,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9745764136,"difficulty":0.0254235864}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory does not know whether Nathaniel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Gregory can now know whether Maria can know that Gregory is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shantel","Maria","Nathaniel","Gregory"],"index":5608,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8685008287,"difficulty":0.1314991713}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Daniel. Patty's card is shown to Daniel. Daniel's card is shown to Mary. Patty's card is shown to Mary. Mary's card is shown to Patty. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether Patty can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Mary","Patty"],"index":595,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.987024188,"difficulty":0.012975812}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandon does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Brandon knows whether Raguel is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brandon can now know whether Raguel can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raguel","Brandon"],"index":3930,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9748755097,"difficulty":0.0251244903}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandon does not know whether Jose is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Brandon can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Brandon","Jose"],"index":3676,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8831254244,"difficulty":0.1168745756}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eddie knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Eddie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eddie","Ruth","Mary"],"index":2312,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9774007201,"difficulty":0.0225992799}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chris is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Christina can now know that Noelia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Noelia","Chris","Courtney","Christina"],"index":8371,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9518512487,"difficulty":0.0481487513}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Antonia knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Antonia can now know whether Peggy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Antonia","Janet","Peggy"],"index":5593,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5662660599,"difficulty":0.4337339401}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Irene can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Irene","Zachery","William"],"index":7457,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9814763665,"difficulty":0.0185236335}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Verlene's card is shown to Marie. Marie's card is shown to Verlene. It is publicly announced that someone picked a red card. It is publicly announced that Marie knows whether someone picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Verlene can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marie","Verlene"],"index":3398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5962677598,"difficulty":0.4037322402}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Robert. Thomas's card is shown to Josie. Robert's card is shown to Thomas. Josie's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Josie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Josie","Thomas"],"index":389,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8271577358,"difficulty":0.1728422642}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Alice. Donald's card is shown to Alice. Donald's card is shown to Judith. Judith's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc: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:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Judith can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alice","Judith","Donald"],"index":4504,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.972525239,"difficulty":0.027474761}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vera knows whether Robert's forehead is muddy. It is publicly announced that Vera knows whether someone's forehead is muddy. It is publicly announced that Vera's forehead is muddy.","smcdel_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 (1|2|3)) ] [ ! 2 ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Robert can now know whether Christal can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Vera","Christal"],"index":5678,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9837228656,"difficulty":0.0162771344}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Juanita. Amy's card is shown to Juanita. William's card is shown to Amy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Juanita can now know that William can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Juanita","Amy"],"index":4612,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9884485602,"difficulty":0.0115514398}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Billie. Billie's card is shown to Oscar. It is publicly announced that someone picked a red card. It is publicly announced that Gary knows whether someone picked a red card. It is publicly announced that Billie picked a red card. It is publicly announced that Gary does not know whether Gary picked a red card. It is publicly announced that Gary does not know whether Gary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Gary can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Billie","Gary","Oscar"],"index":7456,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9713413715,"difficulty":0.0286586285}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly does not know whether May is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"May can now know that Kelly can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelly","May","Rodney"],"index":4150,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9795228243,"difficulty":0.0204771757}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank does not know whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Barbara can now know that Brittany can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Jerry","Barbara","Brittany"],"index":1246,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9877084494,"difficulty":0.0122915506}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ronald can now know that Kevin can know whether Ronald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Ronald"],"index":4876,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9785705209,"difficulty":0.0214294791}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Krista knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Krista can now know whether Krista's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Barbara","Krista"],"index":1627,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9774581194,"difficulty":1.9774581194}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Maria can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Maria","Jeff"],"index":6081,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9880895019,"difficulty":0.0119104981}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnnie's card is shown to Paul. Paul's card is shown to Johnnie. It is publicly announced that someone picked a red card. It is publicly announced that Johnnie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether 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":"Paul can now know that Johnnie can know whether Johnnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Paul","Johnnie"],"index":7578,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5581499934,"difficulty":1.5581499934}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Marcos can now know that Christina can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marcos","Christina"],"index":2924,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9792530537,"difficulty":0.0207469463}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Jesus is thirsty. It is publicly announced that William knows whether William is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"William can now know whether Jesus can know whether Jesus is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jesus","William"],"index":3732,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9340642691,"difficulty":0.0659357309}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Margaret. Margaret's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Margaret does not know whether Margaret picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Margaret can now know whether Christopher can know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Margaret","Christopher"],"index":3054,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9574682117,"difficulty":1.9574682117}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lynn can now know that Lynn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Constance","Lynn","Joanne","Roxanne"],"index":6935,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9613034725,"difficulty":0.0386965275}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timmy's card is shown to Blanca. Timmy's card is shown to Allyson. Blanca's card is shown to Harold. Allyson's card is shown to Harold. Timmy's card is shown to Harold. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Blanca can now know that Timmy can know whether Allyson picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Blanca","Allyson","Timmy","Harold"],"index":97,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6586371064,"difficulty":1.6586371064}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wiley knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Wiley can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wiley","Brian","Anthony"],"index":4808,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9891477823,"difficulty":0.0108522177}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melba can now know that Rickey can know that Sonny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melba","Tammy","Sonny","Rickey"],"index":804,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9737443328,"difficulty":0.0262556672}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jesus can now know that Jaime can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Phyllis","Jesus","Jaime"],"index":222,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9806489944,"difficulty":0.0193510056}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lizzie knows whether or not everyone's forehead is muddy. It is publicly announced that Lester knows whether Lester's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lester can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lizzie","Lester"],"index":2437,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9686506987,"difficulty":0.0313493013}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Richard can now know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Louis","Richard","Jessie"],"index":2807,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9508502483,"difficulty":0.0491497517}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Denise is not thirsty. It is publicly announced that Denise knows whether or not nobody is thirsty. It is publicly announced that Justin knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Denise can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Denise","Justin"],"index":8718,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9578328133,"difficulty":0.0421671867}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (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":"Kimberly can now know that Marcus can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kimberly","Renita","Marcus"],"index":1726,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8404840827,"difficulty":0.1595159173}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Caroline does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Caroline can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Caroline","Sara"],"index":9510,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9876323938,"difficulty":0.0123676062}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Thomas. Mark's card is shown to Travis. Travis's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Travis","Mark","Steven"],"index":7101,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9583912492,"difficulty":0.0416087508}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether or not everyone'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 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 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) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jessica can now know whether Manuel can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Manuel","Steve","Jessica"],"index":4925,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9869534373,"difficulty":0.0130465627}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donna can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","Cynthia","Claude"],"index":623,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.987280786,"difficulty":0.012719214}
-{"premise":"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 Sheldon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"David can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Keith","Jack","Sheldon"],"index":4185,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9704807997,"difficulty":0.0295192003}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keith's card is shown to Todd. Todd's card is shown to Keith. Todd's card is shown to Adrian. It is publicly announced that someone picked a red card. It is publicly announced that Todd does not know whether Adrian picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Adrian can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Todd","Keith","Adrian"],"index":1444,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9746921659,"difficulty":0.0253078341}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Kristen can now know that Kristen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Kristen","Ruby","Mary"],"index":1117,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9537905455,"difficulty":0.0462094545}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know that William can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Michael","Thomas","Ralph"],"index":7670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9734054804,"difficulty":0.0265945196}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Dean can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dean","Michael"],"index":311,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9731589556,"difficulty":0.0268410444}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Haywood knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Linda can now know that Haywood's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Haywood","Linda","Dennis"],"index":827,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9514809251,"difficulty":0.0485190749}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","John","Madge","Constance"],"index":7759,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9656611085,"difficulty":0.0343388915}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori knows whether Andrew's forehead is muddy. It is publicly announced that Lori does not know whether Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Roxanne can now know whether Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lori","Andrew","Roxanne"],"index":1264,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9463453889,"difficulty":0.0536546111}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Avis can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Robert","Avis","James"],"index":2333,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.955268681,"difficulty":0.044731319}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether Byron is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Mark can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Warren","Steven","Byron","Mark"],"index":9077,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.973590076,"difficulty":0.026409924}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gertrude's card is shown to David. Dominique's card is shown to David. Donald's card is shown to Gertrude. Donald's card is shown to Dominique. David's card is shown to Donald. Dominique's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Gertrude does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Gertrude can now know that Gertrude picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Gertrude","Dominique","Donald"],"index":6707,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9559183717,"difficulty":0.0440816283}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Anna can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anna","Kim","William","Michael"],"index":5809,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9461276531,"difficulty":0.0538723469}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Brian can now know whether William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Rosa","Brian","William"],"index":4637,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8746066689,"difficulty":1.8746066689}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Young's forehead is muddy. It is publicly announced that Young knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Young","Keri"],"index":359,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9691010118,"difficulty":0.0308989882}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter does not know whether Beulah is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Gabrielle can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Beulah","Peter","Gabrielle"],"index":2618,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8853618503,"difficulty":0.1146381497}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bryce can now know that Steven can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roxanne","Bryce","Steven","Beverly"],"index":8966,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9794557095,"difficulty":0.0205442905}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Ashley can now know whether Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["April","Marvin","Ashley","Wanda"],"index":245,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9763289094,"difficulty":1.9763289094}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis does not know whether James is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Dennis can now know whether James can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","James","Gemma"],"index":9358,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5199351907,"difficulty":1.5199351907}
-{"premise":"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 Alvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Jesus can now know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Jesus","Herbert","Alvin"],"index":8659,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9754195213,"difficulty":0.0245804787}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachel's card is shown to Darrell. Rachel's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Darrell does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Darrell can now know whether Robert can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrell","Robert","Evelyn","Rachel"],"index":8687,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9239943027,"difficulty":0.0760056973}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Kim can now know whether Heather can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Kim","Heather"],"index":5463,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9824023843,"difficulty":0.0175976157}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know whether Joanna can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sandra","John","Joanna"],"index":5825,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5966632366,"difficulty":0.4033367634}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lola's card is shown to Thurman. Thurman's card is shown to Lola. It is publicly announced that someone picked a red card. It is publicly announced that Thurman picked a black card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(1&2)) ] 0","hypothesis":"Lola can now know that Thurman can know whether Lola picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thurman","Lola"],"index":4702,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6611328125,"difficulty":0.3388671875}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith does not know whether Edith's forehead is muddy. It is publicly announced that Alton knows whether someone's forehead is muddy. It is publicly announced that Nelda does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nelda can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edith","Elizabeth","Alton","Nelda"],"index":2547,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9707878828,"difficulty":0.0292121172}
-{"premise":"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 Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Laura can now know whether Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Loraine","Martha","Laura"],"index":8978,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9369161725,"difficulty":1.9369161725}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Emma can now know that Scott can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Christopher","Scott","Emma"],"index":6701,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9884499311,"difficulty":0.0115500689}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresa's card is shown to Kendall. Kendall's card is shown to Theresa. Edwin's card is shown to Theresa. Kendall's card is shown to Edwin. It is publicly announced that someone picked a red card. It is publicly announced that Theresa picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Kendall can now know whether Edwin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kendall","Theresa","Edwin"],"index":2067,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7725948691,"difficulty":0.2274051309}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Alex. Alex's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy knows whether Alex picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (~(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":"Alex can now know that Dorothy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alex","Dorothy"],"index":1525,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9813522696,"difficulty":0.0186477304}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Etta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Etta can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Oliver","Kimberly","Etta"],"index":8571,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9875594974,"difficulty":0.0124405026}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Mary. Michael's card is shown to Mary. Robert's card is shown to Mary. Mary's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Randy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Randy","Mary","Michael","Robert"],"index":6644,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9531156421,"difficulty":0.0468843579}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Geraldine can now know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Geraldine","Peter","Donnie","John"],"index":4319,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.952293098,"difficulty":0.047706902}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Louis is thirsty. It is publicly announced that Louis does not know whether James is thirsty. It is publicly announced that James does not know whether Joann is thirsty. It is publicly announced that James does not know whether Victoria is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 3) ] Agentd knows that (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Joann can now know that Louis can know whether Louis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Louis","Victoria","Joann"],"index":7713,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7717887163,"difficulty":1.7717887163}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know whether Jessica can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Barbara","Cynthia","Delores"],"index":4538,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9889454246,"difficulty":0.0110545754}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irene does not know whether Amy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Amy can now know whether Felix can know that Felix is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irene","Amy","Vera","Felix"],"index":6431,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8012060523,"difficulty":1.8012060523}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henry's card is shown to Ellen. Gwendolyn's card is shown to Celestine. Ellen's card is shown to Henry. Gwendolyn's card is shown to Henry. Celestine's card is shown to Gwendolyn. Henry's card is shown to Gwendolyn. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Gwendolyn can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ellen","Celestine","Henry","Gwendolyn"],"index":3004,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9870393872,"difficulty":0.0129606128}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Veronica. Kathryn's card is shown to Linda. Linda's card is shown to Kathryn. It is publicly announced that someone picked a red card. It is publicly announced that Linda knows whether someone picked a red card. It is publicly announced that Kathryn does not know whether or not everyone picked a red card. It is publicly announced that Kathryn knows whether or not nobody picked a red card. It is publicly announced that Kathryn does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Linda can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Veronica","Linda","Kathryn"],"index":8360,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.948328197,"difficulty":0.051671803}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether someone's forehead is muddy.","smcdel_problem":"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":"Karen can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Karen","Tanya","Mark"],"index":78,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9731377363,"difficulty":0.0268622637}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herman's card is shown to Rhonda. Marlene's card is shown to Rhonda. Marlene's card is shown to Herman. Rhonda's card is shown to Marlene. Herman's card is shown to Marlene. It is publicly announced that someone picked a red card. It is publicly announced that Rhonda picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Marlene can now know whether Rhonda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rhonda","Herman","Marlene"],"index":2778,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5016819835,"difficulty":0.4983180165}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Enedina is not thirsty. It is publicly announced that Enedina is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Richard can now know that Enedina can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Enedina","Virginia"],"index":9503,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9706103802,"difficulty":0.0293896198}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Ann. Ann's card is shown to Ricky. Scott's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Ann does not know whether Scott picked a red card. It is publicly announced that Scott knows whether or not nobody picked a red card. It is publicly announced that Ann does not know whether Ann picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Scott can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ann","Scott","Ricky","Jean"],"index":8442,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9609001279,"difficulty":0.0390998721}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heather's card is shown to Jonathan. Jonathan's card is shown to Clara. Heather's card is shown to Clara. Gregory's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clara can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jonathan","Clara","Heather","Gregory"],"index":1703,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9825878739,"difficulty":0.0174121261}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bret knows whether or not nobody is thirsty. It is publicly announced that Bret knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Bret can now know whether Jennifer can know that Bret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bret","Jennifer"],"index":531,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9447187185,"difficulty":1.9447187185}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&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":"Lisa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Lisa","James","Kim"],"index":3545,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9764696956,"difficulty":0.0235303044}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose does not know whether or not everyone is thirsty. It is publicly announced that Sheila does not know whether or not everyone is thirsty. It is publicly announced that Jane does not know whether Connie is thirsty. It is publicly announced that Jose does not know whether Connie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Jose can now know whether Sheila can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","Jane","Sheila","Connie"],"index":9226,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8390499949,"difficulty":0.1609500051}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Natalie's card is shown to Marlene. George's card is shown to Marlene. Mary's card is shown to Marlene. George's card is shown to Natalie. Mary's card is shown to Natalie. Marlene's card is shown to George. Natalie's card is shown to Mary. George's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marlene can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marlene","Natalie","George","Mary"],"index":251,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9891764522,"difficulty":0.0108235478}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether Brenda's forehead is muddy. It is publicly announced that Brenda knows whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brenda can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kenneth","Brenda","Charlie"],"index":2480,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9878831506,"difficulty":0.0121168494}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwight's card is shown to Frances. Dwight's card is shown to Leopoldo. Frances's card is shown to Dwight. It is publicly announced that someone picked a red card. It is publicly announced that Dwight does not know whether Leopoldo picked a red card. It is publicly announced that Frances does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Frances can now know whether Dwight can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frances","Leopoldo","Dwight"],"index":2734,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9882019162,"difficulty":0.0117980838}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann knows whether Ann'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:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Andrew can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrew","Russell","Ann"],"index":4297,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9722136259,"difficulty":0.0277863741}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nathan does not know whether Heather is thirsty. It is publicly announced that David does not know whether Stephanie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Stephanie can now know whether Nathan can know that Nathan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Nathan","Heather","Stephanie"],"index":5385,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8905825615,"difficulty":1.8905825615}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Lloyd. Julia's card is shown to Lloyd. Lloyd's card is shown to Daniel. Julia's card is shown to Daniel. Lloyd's card is shown to Dawn. Lloyd's card is shown to Julia. Dawn's card is shown to Julia. It is publicly announced that someone picked a red card. It is publicly announced that Julia does not know whether Julia picked a red card. It is publicly announced that Lloyd does not know whether Daniel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Julia can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lloyd","Daniel","Dawn","Julia"],"index":2604,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9733563662,"difficulty":0.0266436338}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Harry can now know whether Ron can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Luis","Patricia","Ron","Harry"],"index":6446,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9888989329,"difficulty":0.0111010671}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hazel knows whether Hazel's forehead is muddy. It is publicly announced that Hazel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Hazel can now know whether Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roscoe","Rebecca","Hazel"],"index":4017,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9787147045,"difficulty":0.0212852955}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sharon can now know whether Carl can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jack","Carl","Sharon"],"index":9362,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9876220822,"difficulty":0.0123779178}
-{"premise":"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 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 Paulette does not know whether Paulette's forehead is muddy.","smcdel_problem":"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) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Timothy can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Paulette","Timothy","Kimberly"],"index":6349,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9884974957,"difficulty":0.0115025043}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carey knows whether Joy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Joy can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Carey","Joy"],"index":6122,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9886472821,"difficulty":0.0113527179}
-{"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":"Harry can now know that Dwight can know that Josephine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Josephine","Dwight","Harry"],"index":5089,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9710549712,"difficulty":0.0289450288}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows that 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":"Timothy can now know whether Jesse can know that Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jesse","Timothy","Joseph","Marquerite"],"index":1352,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8948655128,"difficulty":1.8948655128}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know that Trena can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karl","Trena","Mary","Suzanne"],"index":1394,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9653605819,"difficulty":0.0346394181}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Eric can now know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bridget","Connie","Tammy","Eric"],"index":1651,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9579244852,"difficulty":0.0420755148}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Robert can now know whether Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Verna","Crystal","Christopher","Robert"],"index":7261,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9779520631,"difficulty":0.0220479369}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Tajuana. Gloria's card is shown to Tajuana. Gloria's card is shown to Sara. Tajuana's card is shown to Gloria. Sara's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that Tajuana picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Sara can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tajuana","Sara","Gloria"],"index":903,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9860231876,"difficulty":0.0139768124}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Donald's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Donald can now know whether Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Donald","Timothy"],"index":9212,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9801213741,"difficulty":0.0198786259}
-{"premise":"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 Gabriel knows whether someone's forehead is muddy. It is publicly announced that Kristin does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kristin can now know that Kristin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","James","Gabriel","Kristin"],"index":519,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9345492125,"difficulty":0.0654507875}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Delores does not know whether Benjamin is thirsty. It is publicly announced that Delores knows whether or not everyone is thirsty. It is publicly announced that Bobbie knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Benjamin can now know that Benjamin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Benjamin","Bobbie","Delores"],"index":7262,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9288643003,"difficulty":0.0711356997}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Angela. Angela's card is shown to Margaret. Angela's card is shown to Bridget. Angela's card is shown to Paul. Margaret's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Bridget does not know whether Bridget picked a red card. It is publicly announced that Margaret knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb 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:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Bridget can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Margaret","Bridget","Paul"],"index":5808,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9744645357,"difficulty":0.0255354643}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lora can now know whether Rafael can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vera","Lora","Rafael","Patricia"],"index":7241,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9895302653,"difficulty":0.0104697347}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucinda does not know whether or not everyone is thirsty. It is publicly announced that Margret does not know whether Gerald is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Margret can now know that Margret is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gerald","Lucinda","Margret"],"index":1954,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9611808658,"difficulty":0.0388191342}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hubert's card is shown to Lynne. Lynne's card is shown to William. William's card is shown to Hubert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lynne","William","Anthony","Hubert"],"index":4280,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9881207943,"difficulty":0.0118792057}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aimee knows whether Aimee is thirsty. It is publicly announced that Larry is thirsty. It is publicly announced that Aimee is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] [ ! ~(1) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] [ ! ~(1) ] 0","hypothesis":"Aimee can now know that Gary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aimee","Gary","Larry","Amanda"],"index":363,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9499647617,"difficulty":0.0500352383}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cora's card is shown to Julie. Julie's card is shown to Cora. Cora's card is shown to Gilbert. Gilbert's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Margaret does not know whether Julie picked a red card. It is publicly announced that Cora picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] Agentc knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] 0","hypothesis":"Gilbert can now know that Margaret can know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Cora","Gilbert","Margaret"],"index":5781,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9671758413,"difficulty":0.0328241587}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Tammy can now know that Romaine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Valerie","Romaine","Tammy"],"index":9067,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9576387405,"difficulty":0.0423612595}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alden's card is shown to Christopher. Christopher's card is shown to Arlene. Alden's card is shown to Arlene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alden can now know that Arlene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Alden","Arlene"],"index":9068,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9558192492,"difficulty":0.0441807508}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine knows whether Catherine's forehead is muddy. It is publicly announced that Catherine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Christina can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christina","Cheryl","Catherine"],"index":7631,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9871763587,"difficulty":0.0128236413}
-{"premise":"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 Dorothy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Geneva can now know whether Dorothy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Geneva"],"index":2632,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9889716506,"difficulty":0.0110283494}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know that Henry can know whether Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Henry","Margaret"],"index":5741,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.85933429,"difficulty":0.14066571}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Eleanor is thirsty. It is publicly announced that Jesse is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Eleanor can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jesse","Michael","Eleanor"],"index":3918,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9097468257,"difficulty":1.9097468257}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Dexter. Dexter's card is shown to Man. Dexter's card is shown to William. Man's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card. It is publicly announced that Man knows whether Dexter picked a red card. It is publicly announced that William does not know whether William picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Man can now know whether Dexter can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dexter","Man","William"],"index":5777,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9600796103,"difficulty":1.9600796103}
-{"premise":"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 Tommy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Tommy can now know that Linda can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tommy","Linda"],"index":6614,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9765051603,"difficulty":0.0234948397}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cassandra's forehead is muddy. It is publicly announced that Willard knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Leonard can now know that Cassandra can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leonard","Cassandra","Willard"],"index":5204,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9776972532,"difficulty":0.0223027468}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know whether Ken can know that Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Gloria","Ken","Richard"],"index":2115,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6213050485,"difficulty":1.6213050485}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Priscilla. Priscilla's card is shown to Arnold. Priscilla's card is shown to Jonathan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Arnold can now know whether Priscilla can know that Jonathan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Priscilla","Arnold","Jonathan"],"index":1907,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9030804634,"difficulty":1.9030804634}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gregory can now know that Rickey can know whether Gregory is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rickey","Randy","Gregory"],"index":3069,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8885934353,"difficulty":0.1114065647}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Carl can now know whether Delores can know whether Delores's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carl","Delores"],"index":1187,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9717046618,"difficulty":1.9717046618}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Sandra can now know whether Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","David","Arlene"],"index":1829,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.976467073,"difficulty":1.976467073}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Lola can now know whether Lola's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Norman","Robert","Lola","Mireille"],"index":9234,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9759300947,"difficulty":0.0240699053}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald does not know whether Angela is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Donald can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gail","Donald","Angela"],"index":6321,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9746685028,"difficulty":0.0253314972}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tabitha knows whether Rocco's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Tabitha can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vita","Tabitha","Rocco"],"index":2548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9776588082,"difficulty":0.0223411918}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Barbara. Florence's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Barbara picked a red card. It is publicly announced that Barbara picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Charles can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Barbara","Edward","Florence"],"index":4355,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9519522786,"difficulty":0.0480477214}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Eric","Robert"],"index":3703,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9856755137,"difficulty":0.0143244863}
-{"premise":"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 does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 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":"Brandon can now know that Erica can know whether Chance's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandon","Erica","Chance","Cassandra"],"index":8707,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8190721273,"difficulty":0.1809278727}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leo does not know whether or not everyone is thirsty. It is publicly announced that Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] Agentc knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] 0","hypothesis":"Ida can now know that Leo can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Leo","Ida"],"index":6788,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7405767441,"difficulty":1.7405767441}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessica does not know whether Grace is thirsty. It is publicly announced that Jessica knows whether Jessica is thirsty. It is publicly announced that Shawn does not know whether Grace is thirsty. It is publicly announced that Shawn knows whether Shawn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Shawn can now know that Grace can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shawn","Jessica","Grace"],"index":6045,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9788587689,"difficulty":0.0211412311}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Willie can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vickie","Willie","Robert","James"],"index":6356,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9873099327,"difficulty":0.0126900673}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Velma knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Donald can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Donald","Velma","Rachel"],"index":6920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9883239269,"difficulty":0.0116760731}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Manuel can now know that Michelle can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Manuel","Michelle"],"index":3164,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8670372367,"difficulty":0.1329627633}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marlene knows whether someone is thirsty. It is publicly announced that Marlene does not know whether Valerie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Marlene can now know whether Valerie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marlene","Valerie"],"index":2594,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5904106498,"difficulty":0.4095893502}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ramona's card is shown to June. Dean's card is shown to June. Dean's card is shown to Ramona. June's card is shown to Dean. It is publicly announced that someone picked a red card. It is publicly announced that Dean does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"June can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["June","Ramona","Dean"],"index":3777,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9813081622,"difficulty":0.0186918378}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dan does not know whether George is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"George can now know that Dan can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dan","Lewis","George","Kim"],"index":2057,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9785388112,"difficulty":0.0214611888}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Enrique can now know whether John can know that Enrique's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Enrique","Robert","Karen"],"index":2062,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8130578995,"difficulty":1.8130578995}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Frances can know whether Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frances","Ernest","Barbara"],"index":1537,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9735495448,"difficulty":0.0264504552}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ola 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 Ola does not know whether Ola's forehead is muddy.","smcdel_problem":"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) ] [ ! ~(Agenta knows whether 1) ] (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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ola","John","Marilyn"],"index":3805,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9462630749,"difficulty":1.9462630749}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Jason. Ryan's card is shown to Donald. Jason's card is shown to Ryan. Donald's card is shown to Ryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ryan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Donald","Ryan"],"index":4794,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.974034369,"difficulty":0.025965631}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Margaret can now know that Dolores's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Dolores","Ethel"],"index":5104,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.950044632,"difficulty":0.049955368}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hester knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that 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":"Hester can now know that Hester's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Paul","Hester"],"index":2895,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9025324583,"difficulty":0.0974675417}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathie's card is shown to Amanda. Amanda's card is shown to Cathie. It is publicly announced that someone picked a red card. It is publicly announced that Cathie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Amanda can now know that Cathie can know whether Amanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Amanda","Cathie"],"index":3575,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6121944785,"difficulty":0.3878055215}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 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":"Timothy can now know that Phillip can know whether Phillip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Phillip","Charles","Russell"],"index":2241,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7553628683,"difficulty":1.7553628683}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentb knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Hilda can now know whether Robert can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Hilda","Sean","Maria"],"index":7135,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9831866026,"difficulty":0.0168133974}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Jacob. Susan's card is shown to Jacob. Susan's card is shown to Ruth. Jacob's card is shown to Susan. Ruth's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Jacob picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb: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:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Jacob can now know whether Ruth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jacob","Ruth","Susan"],"index":6871,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5160344839,"difficulty":1.5160344839}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Charles can now know that Randall can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randall","Charles"],"index":9370,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9865301847,"difficulty":0.0134698153}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Gary. Diane's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Lillie does not know whether Gary picked a red card. It is publicly announced that Gary picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Gary can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lillie","Gary","William","Diane"],"index":1809,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6104598641,"difficulty":1.6104598641}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows 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":"Marilyn can now know that Jerome can know whether Marilyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elois","Nancy","Jerome","Marilyn"],"index":35,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8589214087,"difficulty":0.1410785913}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alonzo can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Jennifer","Lori","Alonzo"],"index":1893,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9782102704,"difficulty":0.0217897296}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Helen can now know whether Roslyn can know whether Roslyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roslyn","Susan","Helen"],"index":6205,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.980699122,"difficulty":0.019300878}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Cecily is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Cecily can now know whether Lai can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Cecily","Lai"],"index":2691,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9599872828,"difficulty":0.0400127172}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carla's card is shown to Margaret. Margaret's card is shown to Carla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Carla can now know whether Margaret can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Margaret","Carla"],"index":5157,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9892765284,"difficulty":0.0107234716}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janie knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Evelyn can now know that Janie can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Evelyn","Mary","Janie","Kevin"],"index":6677,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9858751893,"difficulty":0.0141248107}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Rachel can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Nicole","Rachel","Derrick"],"index":5986,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9764476418,"difficulty":1.9764476418}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to Mary. Victoria's card is shown to Raymond. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Raymond can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Raymond","Victoria"],"index":5968,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9883864522,"difficulty":0.0116135478}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert does not know whether or not everyone's forehead is muddy. It is publicly announced that Lorinda knows whether 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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Albert can now know whether Lorinda can know whether Lorinda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Albert","Lorinda"],"index":8377,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9760161638,"difficulty":0.0239838362}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Carolyn can now know whether Gloria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gloria","Jane","Carolyn","Sharon"],"index":0,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9795276523,"difficulty":0.0204723477}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Esther can now know whether Ann can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bertha","Esther","Ann","Paul"],"index":7012,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9883396626,"difficulty":0.0116603374}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roger 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 3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Cynthia can now know that Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roger","Cynthia","Mary","Betty"],"index":2684,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9481119514,"difficulty":0.0518880486}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chester does not know whether Chester's forehead is muddy.","smcdel_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)","n_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":"Debra can now know whether Wayne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wayne","Debra","Chester"],"index":9281,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9475083351,"difficulty":0.0524916649}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katelyn knows whether John's forehead is muddy. It is publicly announced that Melissa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Melissa can now know whether Katelyn can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Katelyn","John","Melissa"],"index":3944,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.849960804,"difficulty":0.150039196}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Mindy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Crystal can now know that Jennifer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Crystal","Jennifer","Debra","Mindy"],"index":1946,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.958530426,"difficulty":0.041469574}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Audrey can now know that Robert can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Audrey","Robert"],"index":622,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9894636869,"difficulty":0.0105363131}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annie does not know whether or not everyone's forehead is muddy. It is publicly announced that Annie does not know whether or not everyone's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Charles can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Annie"],"index":5099,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9721820354,"difficulty":0.0278179646}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yvonne's card is shown to Lee. Lee's card is shown to Frank. Lee's card is shown to Yvonne. Frank's card is shown to Yvonne. It is publicly announced that someone picked a red card. It is publicly announced that Lee knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Frank can now know that Lee can know that Lee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lee","Frank","Scott","Yvonne"],"index":1705,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9640837312,"difficulty":0.0359162688}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josephine knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (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 3) ] 0","hypothesis":"Lena can now know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Josephine","John","Lena"],"index":2781,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9465194345,"difficulty":0.0534805655}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josefa's card is shown to Terry. Terry's card is shown to Josefa. It is publicly announced that someone picked a red card. It is publicly announced that Josefa does not know whether or not everyone picked a red card. It is publicly announced that Terry knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Terry can now know that Josefa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Terry","Josefa"],"index":6155,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9519665241,"difficulty":0.0480334759}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clifton knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Clifton can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Clifton","Harry"],"index":771,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9793525338,"difficulty":0.0206474662}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lura 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":"Russ can now know that Lura can know whether Lura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lura","Russ"],"index":2662,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9153621793,"difficulty":1.9153621793}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ida can now know that Arlene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arlene","Ida","Carlos"],"index":6736,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9600741863,"difficulty":0.0399258137}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlene's card is shown to Barbara. Jeremy's card is shown to Marlene. Barbara's card is shown to Leonard. Marlene's card is shown to Jeremy. It is publicly announced that someone picked a red card. It is publicly announced that Leonard does not know whether Jeremy picked a red card. It is publicly announced that Barbara picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Barbara can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barbara","Marlene","Leonard","Jeremy"],"index":3254,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9525690675,"difficulty":1.9525690675}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Frances can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Natasha","Frances","Tobias","Susan"],"index":2956,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9776770473,"difficulty":0.0223229527}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Clarence can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joana","Clarence","Kevin","Jacqueline"],"index":696,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9793528914,"difficulty":0.0206471086}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Sarah can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sarah","Robert","Crystal"],"index":5993,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9813796878,"difficulty":0.0186203122}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Betty. Betty's card is shown to Edward. Edward's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc: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 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know that Betty can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Edward","Mark"],"index":4276,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9793244004,"difficulty":0.0206755996}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raul knows whether Darlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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":"Frank can now know whether Raul can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlene","Raul","Frank","Jennifer"],"index":4446,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9577949047,"difficulty":0.0422050953}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Marvin can now know whether Shirley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marvin","William","Shirley"],"index":7160,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.98715657,"difficulty":0.01284343}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Maryann can now know that Luke can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Luke","Mary","Maryann"],"index":1684,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.942461133,"difficulty":0.057538867}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anne does not know whether Frederick is thirsty. It is publicly announced that Frederick does not know whether or not everyone is thirsty. It is publicly announced that Frederick does not know whether Anne is thirsty. It is publicly announced that Anne is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] Agentc knows that (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] 0","hypothesis":"Frederick can now know that Charles can know that Anne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Katrina","Frederick","Anne"],"index":9455,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9707589746,"difficulty":0.0292410254}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carlos's card is shown to Ollie. Ollie's card is shown to Nathaniel. Ollie's card is shown to Patricia. Ollie's card is shown to Carlos. Nathaniel's card is shown to Carlos. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Patricia picked a red card. It is publicly announced that Nathaniel knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Nathaniel can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ollie","Nathaniel","Patricia","Carlos"],"index":983,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5123611689,"difficulty":1.5123611689}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Donna. Cornelius's card is shown to Donna. Donna's card is shown to Joseph. Jerry's card is shown to Cornelius. Donna's card is shown to Cornelius. Joseph's card is shown to Cornelius. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know whether Donna can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Donna","Joseph","Cornelius"],"index":7270,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.98837924,"difficulty":0.01162076}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maureen can now know that Lucy can know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lucy","Maureen","Kimberly","Billy"],"index":7323,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9729078412,"difficulty":0.0270921588}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Loyd's card is shown to Dorothy. Kenneth's card is shown to Dorothy. Dorothy's card is shown to Loyd. Kenneth's card is shown to Loyd. Dorothy's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Loyd picked a red card. It is publicly announced that Kenneth knows whether Dorothy picked a red card. It is publicly announced that Dorothy does not know whether Dorothy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know whether Loyd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Loyd","Kenneth"],"index":3305,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5967976451,"difficulty":1.5967976451}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Jessica is not thirsty. It is publicly announced that Tina does not know whether Nadine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Nadine can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Nadine","Gregory","Tina"],"index":9432,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9857596755,"difficulty":0.0142403245}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dawn does not know whether Dawn's forehead is muddy. It is publicly announced that Dawn knows whether or not nobody's forehead is muddy. It is publicly announced that Dawn 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) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Forrest can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dawn","Forrest","Robert"],"index":5036,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9886505604,"difficulty":0.0113494396}
-{"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 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":"Sandra can now know whether Betty can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Adam","Lee","Sandra","Betty"],"index":549,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9848232269,"difficulty":0.0151767731}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl does not know whether Carl's forehead is muddy. It is publicly announced that Lillie does not know whether Lillie's forehead is muddy. It is publicly announced that Carl's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Lillie can now know whether Carl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lillie","Carl","Molly"],"index":8363,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9243478179,"difficulty":0.0756521821}
-{"premise":"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. It is publicly announced that Gail 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 whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Gail can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gail","Brian"],"index":2007,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.988853097,"difficulty":0.011146903}
-{"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 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":"Rita can now know whether Phillip can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Tom","Rita","Phillip"],"index":4039,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5978041887,"difficulty":0.4021958113}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to James. James's card is shown to Christopher. Ruth's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Christopher can now know whether James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Christopher","Ruth"],"index":1565,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9845026135,"difficulty":0.0154973865}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ken's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Kayla can now know that Ken's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ken","Kayla"],"index":859,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9557526112,"difficulty":0.0442473888}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nellie can now know that Clara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nellie","Clara","Kaci"],"index":2368,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9803144932,"difficulty":0.0196855068}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antonio does not know whether or not everyone's forehead is muddy. It is publicly announced that Claudia knows whether someone's forehead is muddy. It is publicly announced that Antonio does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Claudia can now know whether Antonio can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Antonio","Claudia"],"index":7788,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9773115516,"difficulty":0.0226884484}
-{"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 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":"Joseph can now know that Wayne can know that Frank's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Frank","Joseph","Wayne"],"index":6023,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.970608592,"difficulty":0.029391408}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nohemi's card is shown to William. William's card is shown to Nohemi. William's card is shown to Richard. Nohemi's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Nohemi","Richard"],"index":4059,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9884141684,"difficulty":0.0115858316}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathy's card is shown to Cathleen. Sharon's card is shown to Cathy. Cathy's card is shown to Sharon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cathleen can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cathleen","Cathy","Sharon","Ruth"],"index":4050,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9883292913,"difficulty":0.0116707087}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jodi's card is shown to Deborah. Deborah's card is shown to Jodi. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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":"Jodi can now know that Deborah can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Deborah","Jodi"],"index":2545,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5159521103,"difficulty":0.4840478897}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeffery can now know that Charlotte is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffery","Cheryl","Charlotte"],"index":3143,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9597678185,"difficulty":0.0402321815}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Pat. Sheila's card is shown to Jamie. Pat's card is shown to Sheila. Pat's card is shown to Julie. Jamie's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Julie does not know whether Sheila picked a red card. It is publicly announced that Sheila does not know whether Sheila picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jamie can now know whether Sheila picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Pat","Jamie","Sheila","Julie"],"index":4626,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5112394691,"difficulty":0.4887605309}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Roberta can now know whether Sarah can know whether Sarah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Jennifer","Roberta"],"index":3301,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9276300073,"difficulty":0.0723699927}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doris does not know whether George is thirsty. It is publicly announced that John does not know whether George is thirsty. It is publicly announced that John does not know whether Elsie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"John can now know whether Elsie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elsie","George","Doris","John"],"index":5757,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9871522784,"difficulty":0.0128477216}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Wallace. Wallace's card is shown to Michael. Michael's card is shown to Elouise. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Elouise can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wallace","Michael","Elouise"],"index":8325,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9867687821,"difficulty":0.0132312179}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"John can now know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Judith","John","Michael"],"index":8725,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9854117036,"difficulty":0.0145882964}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether Michael is thirsty. It is publicly announced that William does not know whether Rosalba is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"William can now know that Michael can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Eric","Michael","Rosalba"],"index":5638,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9864462614,"difficulty":0.0135537386}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeffrey can now know that Nancy can know that Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Jeffrey","Daniel"],"index":3001,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9712642431,"difficulty":0.0287357569}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy knows whether or not everyone's forehead is muddy. It is publicly announced that Susan does not know whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 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) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Susan can now know whether Marla can know that Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marla","Susan","Jimmy"],"index":2477,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.911898613,"difficulty":1.911898613}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether Willie's forehead is muddy. It is publicly announced that Wanda does not know whether Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wanda","Willie","Michael"],"index":7727,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9425666928,"difficulty":0.0574333072}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Barbara can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","James","Joyce","Barbara"],"index":4505,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9736850262,"difficulty":0.0263149738}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Dorothy. Dorothy's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether Walter picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Willie can now know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Willie","Walter"],"index":6113,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9542389512,"difficulty":0.0457610488}
-{"premise":"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 nobody's forehead is muddy. It is publicly announced that Betty knows whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Violet can now know whether Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Violet","Betty","Jaymie"],"index":2113,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.982232213,"difficulty":0.017767787}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Marie is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Marie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marie","Thomas","William"],"index":8259,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9731451869,"difficulty":0.0268548131}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether Constance's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Constance can now know whether Stephen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephen","Joan","Constance"],"index":4443,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9847680926,"difficulty":0.0152319074}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether Rachel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Rachel can now know that Marsha can know that Rachel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marsha","Rachel"],"index":677,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9671305418,"difficulty":0.0328694582}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Wilma. Wilma's card is shown to Adam. Adam's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that Wilma does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Gerald can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wilma","Adam","Gerald"],"index":4019,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9817075133,"difficulty":0.0182924867}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nila can now know whether Booker can know whether Nila's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nila","Booker","Terry","Mamie"],"index":4084,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9806069732,"difficulty":0.0193930268}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Ellen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ellen","Ronald","John","Kerri"],"index":1043,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9793431759,"difficulty":0.0206568241}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Diana. George's card is shown to Juana. Diana's card is shown to George. Juana's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Juana does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc: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:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Juana can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diana","Juana","George"],"index":6591,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5178756118,"difficulty":0.4821243882}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Desmond's card is shown to Claud. Claud's card is shown to Desmond. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Desmond can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Claud","Desmond"],"index":8641,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7549363375,"difficulty":0.2450636625}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fernando's card is shown to Mark. Jerry's card is shown to Fernando. Mayra's card is shown to Jerry. Mark's card is shown to Jerry. It is publicly announced that someone picked a red card. It is publicly announced that Fernando does not know whether or not everyone picked a red card. It is publicly announced that Jerry picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Mark can now know whether Fernando can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mayra","Mark","Fernando","Jerry"],"index":9143,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9690921307,"difficulty":0.0309078693}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Darlene. Bonnie's card is shown to Darlene. Thomas's card is shown to Bonnie. Darlene's card is shown to Bonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Darlene can now know whether Thomas can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Darlene","Bonnie"],"index":8961,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.924834609,"difficulty":0.075165391}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carolyn does not know whether Raymond is thirsty. It is publicly announced that Randy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] 0","hypothesis":"Raymond can now know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Randy","Carolyn"],"index":9042,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9548816085,"difficulty":0.0451183915}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renee knows whether Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Jane can now know that Henry can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Renee","Julie","Henry","Jane"],"index":6964,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9742391109,"difficulty":0.0257608891}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Corinna can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lori","Corinna","Jason","Dean"],"index":9625,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9894024134,"difficulty":0.0105975866}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Patrick can now know that Mary can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lloyd","Patrick","Mae","Mary"],"index":3937,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9863023758,"difficulty":0.0136976242}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that Walter can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Walter","Jessica","James"],"index":3453,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9858065248,"difficulty":0.0141934752}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy.","smcdel_problem":"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 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":"Jennifer can now know that Ross can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ross","Michael","Jennifer"],"index":2743,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.908413589,"difficulty":0.091586411}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Tanya can now know whether Mark can know whether Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mark","Tanya"],"index":7964,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9802696109,"difficulty":0.0197303891}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley does not know whether Veronica is thirsty. It is publicly announced that Mary knows whether someone is thirsty. It is publicly announced that Josephine does not know whether or not everyone is thirsty. It is publicly announced that Josephine does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Veronica can now know that Shirley can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Josephine","Veronica","Shirley","Mary"],"index":2076,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.974774003,"difficulty":0.025225997}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Peter. Peter's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Peter can now know whether Jason can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Peter","Jason"],"index":8863,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9840679169,"difficulty":0.0159320831}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mitzi is thirsty. It is publicly announced that Mitzi does not know whether Ashley is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mitzi can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ashley","Mitzi"],"index":1123,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9746973515,"difficulty":0.0253026485}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Frances can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Frances","Jacqueline"],"index":8861,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9797040224,"difficulty":0.0202959776}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarissa's card is shown to Dawn. Dawn's card is shown to Clarissa. It is publicly announced that someone picked a red card. It is publicly announced that Clarissa knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Dawn can now know that Clarissa can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dawn","Clarissa","Randall"],"index":3553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5872339606,"difficulty":0.4127660394}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristen knows whether Catherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Kristen can now know that Elaine can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kristen","Steven","Elaine","Catherine"],"index":4389,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9861582518,"difficulty":0.0138417482}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Linda. Brian's card is shown to Lucy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Linda can now know that Lucy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Lucy","Brian"],"index":2694,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9826489687,"difficulty":0.0173510313}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Dave can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ana","Dave","Donald","Christopher"],"index":8545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9900152087,"difficulty":0.0099847913}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Howard can now know that Steve can know that Kim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kim","Howard","Frank","Steve"],"index":4981,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9656882286,"difficulty":0.0343117714}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leslie can now know whether Vicky can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leslie","Vicky","Timothy","Hope"],"index":5227,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9888327122,"difficulty":0.0111672878}
-{"premise":"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 Natalie knows whether Harry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Nicole can now know whether Harry can know that Corey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harry","Corey","Natalie","Nicole"],"index":8656,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9111281037,"difficulty":0.0888718963}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Araceli knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Kayla can now know whether Ruth can know that Kayla's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruth","Kayla","Araceli"],"index":6196,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9023026824,"difficulty":1.9023026824}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Addie's card is shown to Frances. Ricardo's card is shown to Frances. Addie's card is shown to Ricardo. Frances's card is shown to Ricardo. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Addie can now know that Frances can know whether Addie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Addie","Frances","Ricardo"],"index":8475,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6460891366,"difficulty":1.6460891366}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason is not thirsty. It is publicly announced that Jason knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Trevor can now know that Jason can know that Debra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Jason","Trevor","Debra"],"index":8652,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9700885415,"difficulty":0.0299114585}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Roger can now know that Rudolph can know that Roger's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rudolph","Betty","Roger"],"index":4204,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9685524106,"difficulty":0.0314475894}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Rebecca. Rebecca's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Linda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 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":"Rebecca can now know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rebecca","Linda"],"index":6984,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5542628765,"difficulty":1.5542628765}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joan knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Cheryl can now know whether Joan can know whether Joan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joan","Cheryl"],"index":9542,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9774582386,"difficulty":0.0225417614}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Anthony can now know that Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Albert","David","Anthony"],"index":8679,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9501764178,"difficulty":0.0498235822}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Philip does not know whether or not everyone is thirsty. It is publicly announced that John does not know whether Mayra is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Philip can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mayra","Philip","John"],"index":3650,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9738407731,"difficulty":0.0261592269}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Florence can now know whether Gertha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Florence","Gertha","Susan","Cassie"],"index":6449,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9092187881,"difficulty":0.0907812119}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paula knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Robin can now know that Robin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paula","Norma","Robin"],"index":2668,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9538289309,"difficulty":0.0461710691}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Donna can now know that Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeanine","Jennifer","Lorenzo","Donna"],"index":3210,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9523685575,"difficulty":0.0476314425}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Iva can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francisco","Michael","Iva","Charles"],"index":1376,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9878079295,"difficulty":0.0121920705}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Vincent can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vincent","Rebecca","George","Deborah"],"index":2670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9775420427,"difficulty":0.0224579573}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leona's card is shown to Walter. Jon's card is shown to Walter. Leona's card is shown to Christopher. Christopher's card is shown to Jon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leona can now know whether Christopher can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Leona","Christopher","Jon"],"index":234,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6209157705,"difficulty":0.3790842295}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Donald","Sheryl","Elana"],"index":9216,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9538519382,"difficulty":0.0461480618}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know whether Rosario can know whether Harriet is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harriet","Rosario","Daniel","Juan"],"index":4823,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8162706494,"difficulty":0.1837293506}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Victor can now know that Donald can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donald","Victor"],"index":6596,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9810692668,"difficulty":0.0189307332}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Alexander. Blanche's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Scott does not know whether Alexander picked a red card. It is publicly announced that Alexander picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Scott can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Scott","Alexander","Eric","Blanche"],"index":7278,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6017822623,"difficulty":1.6017822623}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dave's card is shown to Lisa. Dave's card is shown to Tammy. Dave's card is shown to Amber. Amber's card is shown to Dave. It is publicly announced that someone picked a red card. It is publicly announced that Tammy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Tammy can now know whether Amber can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Tammy","Amber","Dave"],"index":8819,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9897018671,"difficulty":0.0102981329}
-{"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 (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":"Roger can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rea","Roger","Bill","Orville"],"index":7093,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8157798648,"difficulty":0.1842201352}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Vanessa. Stacy's card is shown to Vanessa. Dorothy's card is shown to Stacy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vanessa can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vanessa","Dorothy","Michael","Stacy"],"index":6135,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9547772408,"difficulty":0.0452227592}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Catherine can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eugenie","Vickey","Catherine","Mabel"],"index":469,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9877369404,"difficulty":0.0122630596}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Rose can now know that Corey can know whether Dennis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dennis","Corey","Rose"],"index":2630,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.759399116,"difficulty":1.759399116}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"William can now know that Levi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lenore","William","Levi"],"index":4230,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9094650149,"difficulty":0.0905349851}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angelique is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Michelle can now know that Anthony is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michelle","Anthony","Angelique","Laurence"],"index":4919,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9518902302,"difficulty":0.0481097698}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Colin does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Colin can now know that David can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Kathleen","Colin","Alan"],"index":1671,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9881908894,"difficulty":0.0118091106}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelo's card is shown to Courtney. Robin's card is shown to Janet. Angelo's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Courtney does not know whether or not everyone picked a red card. It is publicly announced that Angelo picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 3 ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Courtney can now know whether Robin can know that Robin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Courtney","Robin","Angelo","Janet"],"index":5680,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.955514729,"difficulty":1.955514729}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Dan is thirsty. It is publicly announced that Brian knows whether Brian is thirsty. It is publicly announced that Meagan does not know whether Dan is thirsty. It is publicly announced that Meagan knows whether Meagan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dan can now know whether Brian can know whether Brian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Meagan","Brian","Dan"],"index":2932,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9459466934,"difficulty":0.0540533066}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeanette can now know that William can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonathan","Jeanette","John","William"],"index":6016,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9895122647,"difficulty":0.0104877353}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos knows whether Shane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Thomas can now know whether Shane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Carlos","Shane"],"index":5161,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9847988486,"difficulty":0.0152011514}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicole does not know whether Janelle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Nicole can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Emily","Janelle","Jerome","Nicole"],"index":6402,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.974655211,"difficulty":0.025344789}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Nancy. Nancy's card is shown to Linda. Nancy's card is shown to Elizabeth. Linda's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether or not everyone picked a red card. It is publicly announced that Linda knows whether Nancy picked a red card. It is publicly announced that Elizabeth does not know whether Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Linda can now know that Nancy can know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Linda","Elizabeth"],"index":3948,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9657562375,"difficulty":0.0342437625}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gavin knows whether Felicia's forehead is muddy. It is publicly announced that Felicia knows whether Felicia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Felicia can now know that Gavin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gavin","Felicia"],"index":6713,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9427505136,"difficulty":0.0572494864}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marla knows whether Sheri's forehead is muddy. It is publicly announced that Sheri knows whether Sheri's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Marla can now know that Marla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marla","Sheri"],"index":360,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9442282915,"difficulty":0.0557717085}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynda's card is shown to Brenda. Brenda's card is shown to Lynda. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Lynda can now know that Brenda can know that Brenda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brenda","Lynda"],"index":1235,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9722033739,"difficulty":0.0277966261}
-{"premise":"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 Williams'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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Williams can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Williams","John"],"index":1591,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5657801032,"difficulty":1.5657801032}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melva knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Corey can now know that Melva can know that Melva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Melva","Corey"],"index":7343,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9307954907,"difficulty":0.0692045093}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Donald's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Donald can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Donald","Alvin"],"index":2121,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.988417685,"difficulty":0.011582315}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Crystal can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daisy","Crystal","Tracy"],"index":7329,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9883643389,"difficulty":0.0116356611}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Toni does not know whether Franklin is thirsty. It is publicly announced that Franklin does not know whether or not everyone is thirsty. It is publicly announced that Franklin does not know whether Toni is thirsty. It is publicly announced that Toni is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] 0","hypothesis":"Tiffanie can now know whether Franklin can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tiffanie","Janet","Franklin","Toni"],"index":9136,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9858071804,"difficulty":0.0141928196}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shaun's card is shown to Mary. Mary's card is shown to Shaun. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Shaun can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Shaun"],"index":1556,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.555187583,"difficulty":1.555187583}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (~(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":"Wyatt can now know whether Annie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wyatt","Annie","Cortney","Deanna"],"index":6728,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9645039439,"difficulty":0.0354960561}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Cameron can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cameron","Ronald","Johnathon","Mary"],"index":5056,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.884041965,"difficulty":0.115958035}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Krystal's card is shown to Thomas. Thomas's card is shown to Lola. Thomas's card is shown to Angie. Thomas's card is shown to Krystal. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Lola","Angie","Krystal"],"index":5509,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.817050457,"difficulty":0.182949543}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Vincent can now know that Arthur can know whether Vincent is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Arthur","Vincent"],"index":1162,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8742545843,"difficulty":0.1257454157}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tommy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Tommy can now know whether Camille can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Camille","Tommy"],"index":4405,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9879897237,"difficulty":0.0120102763}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Renae is thirsty. It is publicly announced that Renae does not know whether or not everyone is thirsty. It is publicly announced that Renae does not know whether Richard is thirsty. It is publicly announced that Richard is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] Agentd knows that (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] 0","hypothesis":"Richard can now know that Ashley can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ashley","Mary","Renae","Richard"],"index":5184,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9687916636,"difficulty":0.0312083364}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Laura. Laura's card is shown to Genevieve. Laura's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether Walter picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Walter can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","Genevieve","Walter"],"index":1852,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9730238318,"difficulty":0.0269761682}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Hector's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ernesto can now know that Tracey can know that Ernesto's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hector","Barbara","Tracey","Ernesto"],"index":1618,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9659233689,"difficulty":0.0340766311}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know whether Myles can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nikki","Myles","Laura","Cynthia"],"index":6907,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8855147362,"difficulty":0.1144852638}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeffrey can now know that Marc can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frances","Jeffrey","Marc"],"index":2797,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9816717505,"difficulty":0.0183282495}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bruce","Robert","Carolynn"],"index":5533,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9782429934,"difficulty":0.0217570066}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Deborah can now know that Yolanda can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Troy","Yolanda","Margaret","Deborah"],"index":1874,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9660835862,"difficulty":0.0339164138}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eugene knows whether or not nobody is thirsty. It is publicly announced that Eugene knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Eugene can now know whether Richard can know whether Eugene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Eugene","Richard"],"index":1643,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9709141254,"difficulty":1.9709141254}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Hassan. Melissa's card is shown to Hassan. Joe's card is shown to Hassan. Melissa's card is shown to Michael. Joe's card is shown to Michael. Hassan's card is shown to Melissa. Joe's card is shown to Melissa. Michael's card is shown to Joe. It is publicly announced that someone picked a red card. It is publicly announced that Melissa does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc 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:3,4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Hassan can now know that Melissa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hassan","Michael","Melissa","Joe"],"index":3408,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9764896035,"difficulty":0.0235103965}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Michael can now know whether Denise can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Denise","Michael"],"index":1665,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.925586164,"difficulty":0.074413836}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Bertha. Agnes's card is shown to Bertha. Bertha's card is shown to John. Bertha's card is shown to Agnes. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know whether Agnes can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bertha","John","Agnes"],"index":5270,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9260281324,"difficulty":0.0739718676}
-{"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 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":"Jessie can now know that Scott can know that Scott's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Jessie","Kay","Josh"],"index":5012,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.971211791,"difficulty":0.028788209}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalie's card is shown to Jill. Jill's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Rosalie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Jill can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jill","Charles","Rosalie"],"index":347,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9516381025,"difficulty":0.0483618975}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Chad can now know whether Norma can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Chad","Norma"],"index":8879,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9903206229,"difficulty":0.0096793771}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lydia does not know whether Lydia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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) ] 0","hypothesis":"King can now know that Lydia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lydia","Dean","King","Nicole"],"index":8676,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7034577727,"difficulty":0.2965422273}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Angela. Elma's card is shown to Angela. Elma's card is shown to Daniel. Daniel's card is shown to Elma. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Daniel can now know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Daniel","Elma"],"index":1509,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5027042627,"difficulty":1.5027042627}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Nancy can now know whether Grace can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Marco","Grace"],"index":7021,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9840841889,"difficulty":0.0159158111}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Paulette. Paulette's card is shown to Mary. Mary's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Juan does not know whether Paulette picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Mary can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paulette","Mary","Juan","John"],"index":5093,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9738070965,"difficulty":0.0261929035}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric does not know whether Eric's forehead is muddy. It is publicly announced that Sergio does not know whether Sergio's forehead is muddy. It is publicly announced that Eric'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 2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] (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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Maria can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sergio","Eric","Maria"],"index":2577,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9718613029,"difficulty":0.0281386971}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Rita can now know whether Ray can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rita","Ray"],"index":2697,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9660924673,"difficulty":0.0339075327}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Samantha's forehead is muddy. It is publicly announced that Jennifer's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(2) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Donald can now know whether Samantha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Jennifer","Samantha"],"index":284,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9669203162,"difficulty":0.0330796838}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"John can now know whether Sandra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Debra","Sandra","John"],"index":7086,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8487362862,"difficulty":0.1512637138}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Grace. Grace's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Grace can now know whether David can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Grace","David"],"index":5862,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8645671606,"difficulty":1.8645671606}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Madeleine does not know whether Justin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Thomas can now know that Justin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Madeleine","Jerry","Thomas"],"index":7413,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9584159851,"difficulty":0.0415840149}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether Cheryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Cheryl can now know that Norma can know whether Norma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Sunny","Norma","David"],"index":1906,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9776510596,"difficulty":0.0223489404}
-{"premise":"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 Thelma knows whether Larry's forehead is muddy. It is publicly announced that Thelma knows 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)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Larry can now know that Larry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Thelma","Larry"],"index":4915,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9343402982,"difficulty":0.0656597018}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Abby can now know whether Abby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ronald","Abby"],"index":6598,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9804756045,"difficulty":0.0195243955}
-{"premise":"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 Douglas knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentb 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) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ryan can now know that Elizabeth can know that Ryan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","Ryan","Douglas","Tina"],"index":8005,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9636322856,"difficulty":0.0363677144}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert knows whether Robert is thirsty. It is publicly announced that Barbara does not know whether Thomas is thirsty. It is publicly announced that Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Barbara can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Robert","Barbara","Thomas"],"index":8914,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9722065926,"difficulty":0.0277934074}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Richard can now know that Rene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rene","Richard","Andre","Terri"],"index":728,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9530205727,"difficulty":0.0469794273}
-{"premise":"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 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 (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Robert can now know that Phil can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Robert","Phil"],"index":7625,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8455087543,"difficulty":0.1544912457}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to John. John's card is shown to Nickolas. Frank's card is shown to Nickolas. John's card is shown to Frank. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Frank can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Nickolas","Frank"],"index":1544,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9883025289,"difficulty":0.0116974711}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deloris is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Deloris can now know whether Daniel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deloris","Michael","Daniel"],"index":534,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.824768126,"difficulty":0.175231874}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Earl's card is shown to Darlene. Darlene's card is shown to Earl. Marie's card is shown to Earl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Darlene can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Darlene","Earl","Marie"],"index":2919,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9754930139,"difficulty":0.0245069861}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Neal's card is shown to Cody. Cody's card is shown to Neal. It is publicly announced that someone picked a red card. It is publicly announced that Neal does not know whether Neal picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Neal can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cody","Neal"],"index":2341,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7260229588,"difficulty":0.2739770412}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Vera. Marcie's card is shown to Vera. Vera's card is shown to Patrick. Marcie's card is shown to Patrick. Patrick's card is shown to Marcie. It is publicly announced that someone picked a red card. It is publicly announced that Marcie does not know whether Vera picked a red card. It is publicly announced that Vera knows whether Marcie picked a red card. It is publicly announced that Marcie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Patrick can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vera","Patrick","Marcie"],"index":5313,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9712793827,"difficulty":0.0287206173}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy knows whether Clyde's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kelly can now know that Tim can know that Jimmy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clyde","Jimmy","Tim","Kelly"],"index":6714,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9647868872,"difficulty":0.0352131128}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Basil knows whether Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brenda can now know whether Basil can know that Maranda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Basil","Brenda","Maranda"],"index":6053,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9672630429,"difficulty":0.0327369571}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&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 whether Ila can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ila","William","Annie","Ernesto"],"index":3363,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5712783337,"difficulty":0.4287216663}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Lawrence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Ross picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Ross","Lawrence"],"index":6590,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9523403645,"difficulty":0.0476596355}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Kelly. Kelly's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Kelly can now know whether John can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kelly","John"],"index":6716,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9499853253,"difficulty":0.0500146747}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcos's card is shown to Elizabeth. Elizabeth's card is shown to Marcos. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Marcos can now know that Elizabeth can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elizabeth","Marcos"],"index":9387,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.97770679,"difficulty":0.02229321}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Stephen can now know that Judy can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Judy","Stephen"],"index":1058,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9561700821,"difficulty":0.0438299179}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmen's card is shown to Nickolas. Carmen's card is shown to Katie. Nickolas's card is shown to Carmen. Lorena's card is shown to Carmen. Nickolas's card is shown to Lorena. Carmen's card is shown to Lorena. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lorena can now know that Katie can know whether Carmen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nickolas","Katie","Carmen","Lorena"],"index":3605,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6169036031,"difficulty":1.6169036031}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (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) ] [ ! 2 ] 0","hypothesis":"Larry can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","James","Larry","Forrest"],"index":3798,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.970576942,"difficulty":0.029423058}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Patricia can now know whether Larry can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carmen","Larry","Patricia","Ruth"],"index":4023,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9336128831,"difficulty":1.9336128831}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Byron's card is shown to Andrew. Andrew's card is shown to Byron. It is publicly announced that someone picked a red card. It is publicly announced that Andrew knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (~(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":"Andrew can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Andrew","Byron"],"index":4439,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9735907912,"difficulty":0.0264092088}
-{"premise":"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 or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Clara can now know whether Shirley can know whether Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clara","Shirley","Ronald"],"index":2790,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9836681485,"difficulty":0.0163318515}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luella does not know whether or not everyone is thirsty. It is publicly announced that Lloyd knows whether Lloyd is thirsty. It is publicly announced that Marcus does not know whether Lloyd is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Joshua can now know whether Luella can know whether Joshua is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcus","Luella","Lloyd","Joshua"],"index":5947,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9480343461,"difficulty":0.0519656539}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Timothy can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Paul","Timothy"],"index":2010,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9806736708,"difficulty":0.0193263292}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ciera","David","Richard","Howard"],"index":3975,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9897924662,"difficulty":0.0102075338}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Paul can now know that Catalina can know that Catalina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Catalina","Paul"],"index":5793,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9730705619,"difficulty":0.0269294381}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sara can now know that Emma can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emma","John","Linda","Sara"],"index":93,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9877940416,"difficulty":0.0122059584}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bonnie does not know whether Melissa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Melissa can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clarence","Victor","Melissa","Bonnie"],"index":103,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.987616241,"difficulty":0.012383759}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jasmine does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Phyllis can now know whether Carl can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Phyllis","Carl","Margaret","Jasmine"],"index":4618,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5439454317,"difficulty":0.4560545683}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ryan can now know whether Maria can know whether Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Maria","Ryan","Troy"],"index":2849,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7546693683,"difficulty":0.2453306317}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Rafael can now know that Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Sharon","Jesse","Rafael"],"index":1972,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9565268755,"difficulty":0.0434731245}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Bonnie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Peter","Jose","Bonnie","Michael"],"index":2060,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9893305302,"difficulty":0.0106694698}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jared is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Jared can now know that Christopher can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jared","Christopher","Linda"],"index":3197,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.985042274,"difficulty":0.014957726}
-{"premise":"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 knows whether Gina's forehead is muddy. It is publicly announced that Keith does not know whether Keith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows 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 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Keith can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Keith","Gina","Diane"],"index":4402,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.971147716,"difficulty":0.028852284}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence knows whether Florence's forehead is muddy. It is publicly announced that Florence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Steve can now know that Florence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Steve","Florence"],"index":2690,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9458471537,"difficulty":0.0541528463}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether Russell's forehead is muddy. It is publicly announced that Eugene knows whether or not nobody's forehead is muddy. It is publicly announced that Russell knows whether Russell's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Eugene can now know that Russell can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Russell","Eugene"],"index":3929,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9410865307,"difficulty":0.0589134693}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Trent can now know that Wilburn can know that Trent is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Wilburn","Trent"],"index":2619,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9737707973,"difficulty":0.0262292027}
-{"premise":"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 Ella 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) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Betty can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betty","Ella","Linda"],"index":361,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7193487287,"difficulty":1.7193487287}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether 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 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":"Kathy can now know whether Kathy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Estefana","Kathy"],"index":5686,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9783096313,"difficulty":1.9783096313}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Katherine. Katherine's card is shown to Lori. Katherine's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Linda can now know that Katherine can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katherine","Lori","Linda"],"index":729,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9892725945,"difficulty":0.0107274055}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvester knows whether Theron's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Sylvester can now know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Theron","Sylvester","William","Anthony"],"index":1589,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9854626656,"difficulty":0.0145373344}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Mary. Nancy's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Mary","Nancy","Cory"],"index":5296,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9877446294,"difficulty":0.0122553706}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Suzanne can now know that Ashley can know whether Ashley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Suzanne","Ashley"],"index":6564,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9813036919,"difficulty":0.0186963081}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra does not know whether Sandra's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Andrea can now know whether Sandra can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorcas","Sandra","Andrea","Eric"],"index":7568,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9665997624,"difficulty":0.0334002376}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Jeanette. Erica's card is shown to Johnathan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jason can now know that Johnathan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeanette","Jason","Erica","Johnathan"],"index":4834,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.95449543,"difficulty":0.04550457}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathryn does not know whether James is thirsty. It is publicly announced that James does not know whether Ruby is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Kathryn can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathryn","James","Ruby"],"index":766,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9777416587,"difficulty":0.0222583413}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Nathan can now know whether Ruth can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ruth","Nathan"],"index":1582,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8795362115,"difficulty":0.1204637885}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Trinidad's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Katherine can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Trinidad","Katherine","Clifford","Helen"],"index":2693,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.97946769,"difficulty":0.02053231}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kevin can now know that Millie can know that Kevin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Millie","Joseph"],"index":4429,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9740684032,"difficulty":0.0259315968}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kate 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 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":"Hipolito can now know whether Kate's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Hipolito","Kate"],"index":1524,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9744599462,"difficulty":0.0255400538}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clifford can now know whether Stephen can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clifford","Stephen","Walter","Jessica"],"index":461,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9876975417,"difficulty":0.0123024583}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sandra can now know that Bruce can know that Bruce's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mike","John","Sandra","Bruce"],"index":2560,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9665829539,"difficulty":0.0334170461}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catherine does not know whether or not everyone is thirsty. It is publicly announced that Wilma does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Wilma can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Catherine","Wilma","Josh","Charles"],"index":2008,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9743065834,"difficulty":0.0256934166}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Albertina can now know whether Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kevin","Albertina"],"index":6753,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.984944284,"difficulty":0.015055716}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresa's card is shown to Leola. Leola's card is shown to Theresa. It is publicly announced that someone picked a red card. It is publicly announced that Leola knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (~(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":"Leola can now know whether Theresa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leola","Theresa"],"index":7504,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9843834639,"difficulty":0.0156165361}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Edward can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Christine","Alison","Edward"],"index":611,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.971837163,"difficulty":0.028162837}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cary knows whether Leslie'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":"Cary can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Leslie","Cary"],"index":8565,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9746843576,"difficulty":0.0253156424}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether Anne's forehead is muddy. It is publicly announced that Anne knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Frank can now know that Frank's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frank","Anne","Linda"],"index":6887,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9422543645,"difficulty":0.0577456355}
-{"premise":"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 Barbara's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Barbara can now know whether Mary can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alice","Mary","Barbara"],"index":9533,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9824206233,"difficulty":0.0175793767}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Helen. Helen's card is shown to John. Helen's card is shown to Robert. John's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","John","Robert"],"index":8945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8536834121,"difficulty":0.1463165879}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"James can now know that Earl can know that Earl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Michael","Earl"],"index":3391,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9735656977,"difficulty":0.0264343023}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Muriel can now know that Donald can know that Muriel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Muriel","Donald","Wilbert","Christopher"],"index":9103,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9742102623,"difficulty":0.0257897377}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andre's card is shown to Erica. Erica's card is shown to Martha. It is publicly announced that someone picked a red card. It is publicly announced that Andre does not know whether Erica picked a red card. It is publicly announced that Erica does not know whether Martha picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Andre can now know that Andre picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andre","Erica","Martha"],"index":7250,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9571731687,"difficulty":0.0428268313}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to James. James's card is shown to Lawrence. James's card is shown to Donna. Lawrence's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Keith can now know whether James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Lawrence","Keith","Donna"],"index":6304,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9892147183,"difficulty":0.0107852817}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Yolanda can now know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brock","Yolanda","Edna","Scott"],"index":3195,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9628527164,"difficulty":0.0371472836}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lamont's card is shown to Lynwood. Gary's card is shown to Lamont. Lynwood's card is shown to Gary. Lamont's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lynwood can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lynwood","Lamont","Gary"],"index":8222,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9882709384,"difficulty":0.0117290616}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Lydia. Jennie's card is shown to Lydia. Ronald's card is shown to John. Lydia's card is shown to Jennie. Lydia's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Lydia knows whether or not everyone picked a red card. It is publicly announced that Ronald knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Jennie can now know whether Lydia can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lydia","John","Jennie","Ronald"],"index":7958,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9765269756,"difficulty":0.0234730244}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Thelma is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Thelma","Joy","Andrew"],"index":9107,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9288964868,"difficulty":0.0711035132}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Margarita can know whether Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margarita","Bonnie","Patricia","Joseph"],"index":7811,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9763394594,"difficulty":0.0236605406}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roberta knows whether or not nobody is thirsty. It is publicly announced that Roberta is thirsty. It is publicly announced that Juan does not know whether Georgina is thirsty. It is publicly announced that Juan does not know whether Georgina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Georgina can now know that Roberta is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Georgina","Juan","Roberta"],"index":1712,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9438704252,"difficulty":1.9438704252}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roberto knows whether or not nobody is thirsty. It is publicly announced that Roberto is thirsty. It is publicly announced that Betty does not know whether Megan is thirsty. It is publicly announced that Betty does not know whether Megan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Roberto can now know whether Roberto is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Megan","Betty","Roberto"],"index":7585,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5195625424,"difficulty":0.4804374576}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tina's card is shown to Violet. Violet's card is shown to Tina. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Violet can now know that Tina can know whether Violet picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Violet","Tina"],"index":4842,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6757993698,"difficulty":0.3242006302}
-{"premise":"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 knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Catherine can now know that Sandra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Erik","Catherine","Sandra","Sara"],"index":382,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6022660136,"difficulty":1.6022660136}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margie does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ann can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Margie","Ann"],"index":7709,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9735701084,"difficulty":0.0264298916}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Flora knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Carmen can now know whether Pamela is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carmen","Flora","Pamela","Dana"],"index":8301,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.879998982,"difficulty":1.879998982}
-{"premise":"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 knows whether Lillian's forehead is muddy. It is publicly announced that Frankie's forehead is muddy.","smcdel_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 whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Lillian can now know whether Frankie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bernard","Frankie","Lillian"],"index":3361,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9588144422,"difficulty":1.9588144422}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that Lonnie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Lonnie","Mary","Robert"],"index":4536,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9798852205,"difficulty":0.0201147795}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Bart can now know that Kimberly can know that Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bart","Kimberly"],"index":7823,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9728558064,"difficulty":0.0271441936}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zita's card is shown to Magda. Natalie's card is shown to Magda. Magda's card is shown to Zita. Natalie's card is shown to Zita. Magda's card is shown to Natalie. Zita's card is shown to Natalie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Natalie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Magda","Zita","Natalie"],"index":2824,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8659371734,"difficulty":0.1340628266}
-{"premise":"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 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) ] [ ! (Agenta knows whether 4) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Fred can now know whether Fred's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fred","John","Rosemarie","Jessica"],"index":1650,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9734991193,"difficulty":1.9734991193}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aline knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Allison can now know whether Nick can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alonzo","Nick","Allison","Aline"],"index":3561,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9892349839,"difficulty":0.0107650161}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"William can now know that Carlos can know that Carlos is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carlos","William"],"index":8142,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9692792892,"difficulty":0.0307207108}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Andrew. Andrew's card is shown to Nicholas. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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":"Nicholas can now know that Andrew can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrew","Nicholas"],"index":4106,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9777141809,"difficulty":0.0222858191}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Asia knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lynda can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Asia","Lynda","Leo"],"index":5307,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9823303223,"difficulty":0.0176696777}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leonard's card is shown to Ross. Ross's card is shown to Leonard. It is publicly announced that someone picked a red card. It is publicly announced that Ross knows whether someone picked a red card. It is publicly announced that Ross does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ross can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ross","Leonard"],"index":5720,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9898938537,"difficulty":0.0101061463}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Wade. Kenneth's card is shown to Wade. Kenneth's card is shown to Carol. Wade's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Wade does not know whether Wade picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Wade can now know that Carol can know that Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wade","Carol","Kenneth"],"index":5496,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9696471095,"difficulty":0.0303528905}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Adriane can now know whether Susan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Antonia","Adriane","Dennis"],"index":8225,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9811035395,"difficulty":0.0188964605}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 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":"Carolyn can now know whether Marge can know whether Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Carolyn","Marge"],"index":1031,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9535611272,"difficulty":0.0464388728}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Lucille. Lucille's card is shown to Holly. Lucille's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 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:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lucille can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lucille","Holly","Joseph"],"index":8061,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7032391429,"difficulty":0.2967608571}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether or not everyone is thirsty. It is publicly announced that Jared knows whether Jared is thirsty. It is publicly announced that Esther does not know whether Jared is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jared can now know whether Esther can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Esther","Dorothy","Jared","Patrick"],"index":1801,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9848255515,"difficulty":0.0151744485}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keith's card is shown to Kevin. Keith's card is shown to Dennis. Kevin's card is shown to Keith. Janice's card is shown to Keith. Kevin's card is shown to Janice. Keith's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janice can now know whether Keith can know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Dennis","Keith","Janice"],"index":1200,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9229719639,"difficulty":0.0770280361}
-{"premise":"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 Keith knows whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Betty can now know whether Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Teresa","Betty","Keith"],"index":6197,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9692187905,"difficulty":1.9692187905}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Missy's card is shown to Saul. Richard's card is shown to John. Saul's card is shown to Richard. John's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Saul can now know whether Saul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Saul","John","Missy","Richard"],"index":5950,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8452390432,"difficulty":0.1547609568}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Elaine knows whether Bonnie's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Bonnie can now know whether Bonnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elaine","Bonnie"],"index":5915,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9802866578,"difficulty":0.0197133422}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lori's card is shown to Warren. Daniel's card is shown to Warren. Daniel's card is shown to Lori. Lori's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Lori picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Daniel can now know whether Lori can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Warren","Lori","Daniel"],"index":1714,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7360436916,"difficulty":0.2639563084}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sean's card is shown to Lyle. Raymond's card is shown to Sean. Sean's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Lyle picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Lyle can now know that Sean can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lyle","Sean","Raymond"],"index":581,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9765600562,"difficulty":0.0234399438}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether Jeremy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kathy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeremy","Kathy","James","Gloria"],"index":1384,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9747993946,"difficulty":0.0252006054}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"James can now know whether Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Brian","James"],"index":1375,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9841863513,"difficulty":0.0158136487}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether John is thirsty. It is publicly announced that Anthony knows whether Anthony is thirsty. It is publicly announced that Billie does not know whether John is thirsty. It is publicly announced that Billie knows whether Billie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Anthony can now know that Billie can know whether Billie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Billie","Anthony","John"],"index":2083,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6418161392,"difficulty":1.6418161392}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marilyn's card is shown to Ryan. Ryan's card is shown to Marilyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] (Agentb knows whether (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Marilyn can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ryan","Marilyn"],"index":6084,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8902564645,"difficulty":0.1097435355}
-{"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 (~(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":"Sandra can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Grover","Julie","Sandra","Victor"],"index":7489,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.979383409,"difficulty":0.020616591}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felix's card is shown to Paul. Paul's card is shown to Sherry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paul can now know that Felix can know that Felix picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Felix","Diane","Sherry"],"index":8530,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9723063707,"difficulty":0.0276936293}
-{"premise":"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 Don knows whether Willie's forehead is muddy. It is publicly announced that Don knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Don can now know whether Don's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Don","Willie"],"index":4856,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9512053728,"difficulty":1.9512053728}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathaniel's card is shown to Thomas. Nathaniel's card is shown to Clifton. Thomas's card is shown to Cheri. Clifton's card is shown to Cheri. Nathaniel's card is shown to Cheri. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know that Nathaniel can know that Cheri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Clifton","Nathaniel","Cheri"],"index":7013,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9727888107,"difficulty":0.0272111893}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 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":"Lori can now know whether Nicole can know whether Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicole","Lori","Woodrow"],"index":3387,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9358784556,"difficulty":0.0641215444}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lois can now know that Bryce can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Laura","Lois","Bryce"],"index":269,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.981084168,"difficulty":0.018915832}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sadie's card is shown to Dorothy. Dorothy's card is shown to Lorraine. Dorothy's card is shown to Sadie. Lorraine's card is shown to Sadie. It is publicly announced that someone picked a red card. It is publicly announced that Lorraine does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 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:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sadie can now know that Lorraine can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Lorraine","Sadie"],"index":2085,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9780235887,"difficulty":0.0219764113}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Joseph can now know that Justin can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Justin","Joseph"],"index":6917,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9747524858,"difficulty":0.0252475142}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Stanley can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Stanley","Mary"],"index":7708,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8484041691,"difficulty":0.1515958309}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Aja. Aja's card is shown to Joseph. Sung's card is shown to Joseph. Joseph's card is shown to Sung. It is publicly announced that someone picked a red card. It is publicly announced that Sung knows whether Joseph picked a red card. It is publicly announced that Sung picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Joseph can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Aja","Joseph","Sung"],"index":8839,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9718526006,"difficulty":0.0281473994}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Laura can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Adrienne","Laura"],"index":3925,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9393110871,"difficulty":0.0606889129}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows whether (Agenta knows that 1)","n_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":"Margert can now know whether John can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Brian","Margert"],"index":3181,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8221640587,"difficulty":0.1778359413}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Renee can now know whether Jessica can know that Jessica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessica","John","Miranda","Renee"],"index":9270,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7102863193,"difficulty":1.7102863193}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bob can now know that Mary can know that Lisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bob","Mary","David","Lisa"],"index":2885,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9750282764,"difficulty":0.0249717236}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Alfonso can now know whether Florence can know that Florence is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alfonso","Florence","August"],"index":3140,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8401969075,"difficulty":1.8401969075}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jane can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Timothy","Jane","Christopher"],"index":4723,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9854089618,"difficulty":0.0145910382}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Deborah. Ruth's card is shown to Andre. Ruth's card is shown to Sean. Sean's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Andre knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Sean can now know that Andre can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Andre","Sean","Ruth"],"index":7407,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9763180614,"difficulty":0.0236819386}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cherie's card is shown to Mamie. Mamie's card is shown to Cherie. Mamie's card is shown to Susan. Cherie's card is shown to Susan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Susan can now know that Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mamie","Cherie","Susan"],"index":4648,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9560887814,"difficulty":0.0439112186}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kurt's card is shown to Gene. Deborah's card is shown to Kurt. Gene's card is shown to Kurt. It is publicly announced that someone picked a red card. It is publicly announced that Gene does not know whether Kurt picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Deborah can now know that Gene can know that Deborah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Deborah","Gene","Kurt"],"index":2623,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9683355689,"difficulty":0.0316644311}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"James can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charlene","James","Michelle"],"index":3853,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7504656315,"difficulty":1.7504656315}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Bruce can now know whether Donald can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bruce","Donald"],"index":3901,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.989503026,"difficulty":0.010496974}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Barbara can now know whether Sandra can know that Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sandra","Barbara"],"index":8681,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9689362049,"difficulty":0.0310637951}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Claudine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Debra can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Debra","Albert","Claudine","Marlin"],"index":7573,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9838961363,"difficulty":0.0161038637}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Michelle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stanley","Daniel","Michelle","Helen"],"index":5376,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9806597829,"difficulty":0.0193402171}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to James. Daniel's card is shown to James. James's card is shown to Evelyn. Daniel's card is shown to Evelyn. James's card is shown to Mary. James's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card. It is publicly announced that Daniel does not know whether or not everyone picked a red card. It is publicly announced that Evelyn picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(2) ] (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Evelyn","Mary","Daniel"],"index":8287,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9867053628,"difficulty":0.0132946372}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald does not know whether or not everyone is thirsty. It is publicly announced that Lisa does not know whether Julia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Donald can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Lisa","Julia"],"index":5390,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9765709639,"difficulty":0.0234290361}
-{"premise":"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 or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nina can now know that Thelma can know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thelma","Nina","Jackie","Betty"],"index":8336,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9656440616,"difficulty":0.0343559384}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Ryan. Ryan's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Dennis does not know whether Dennis picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 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":"Dennis can now know that Ryan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ryan","Dennis"],"index":7920,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9550246596,"difficulty":1.9550246596}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Walter can now know whether Laura can know that Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Laura","Walter"],"index":2847,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9520742297,"difficulty":0.0479257703}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terrence can now know that Nelly can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nelly","Terrence","Kristine"],"index":7396,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9779524207,"difficulty":0.0220475793}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jackson does not know whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Barbara can now know whether Ashley is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Ashley","Jackson","Harold"],"index":2160,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8838610053,"difficulty":0.1161389947}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willis's card is shown to Andrew. Charlette's card is shown to Andrew. Richard's card is shown to Andrew. Charlette's card is shown to Willis. Richard's card is shown to Willis. Andrew's card is shown to Charlette. Willis's card is shown to Richard. Charlette's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlette can now know whether Charlette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Willis","Charlette","Richard"],"index":9624,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7935788035,"difficulty":0.2064211965}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elise's card is shown to Philip. Brian's card is shown to Philip. Elise's card is shown to Yesenia. Yesenia's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Yesenia can now know whether Philip can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Philip","Elise","Yesenia","Brian"],"index":8564,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9872342944,"difficulty":0.0127657056}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beatrice knows whether or not everyone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Beatrice can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Beatrice","James"],"index":5576,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9445744753,"difficulty":0.0554255247}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clarissa does not know whether or not everyone is thirsty. It is publicly announced that Helen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] 0","hypothesis":"Helen can now know whether Clarissa can know whether Nellie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Clarissa","Nellie"],"index":9353,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9514151216,"difficulty":0.0485848784}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that Helen knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"James can now know that Roy can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roy","Helen","James"],"index":8110,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9632436037,"difficulty":0.0367563963}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Cecil can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Griselda","Lori","Cecil","Angela"],"index":3153,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9894912243,"difficulty":0.0105087757}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian knows whether someone is thirsty. It is publicly announced that Brian knows whether Daniel is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brian can now know that Daniel can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daniel","Brian"],"index":9475,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.806665957,"difficulty":1.806665957}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Russell can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Russell","Margaret","Troy"],"index":8492,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9753677249,"difficulty":0.0246322751}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Ryan can now know whether Helen can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Manuel","Linda","Ryan"],"index":2117,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8562139273,"difficulty":0.1437860727}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard knows whether or not everyone's forehead is muddy. It is publicly announced that Chris does not know whether Chris's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Howard can now know that Chris can know whether Chris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Chris","Howard"],"index":7455,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8179110885,"difficulty":1.8179110885}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bessie's card is shown to Michael. Michael's card is shown to Barbara. Bessie's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bessie can now know whether Michael can know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Bessie","Barbara"],"index":2348,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9109551311,"difficulty":0.0890448689}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether Jarrod's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Anna can now know that Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Ashley","Anna","Jarrod"],"index":4209,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9465458989,"difficulty":0.0534541011}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Jessica. Jessica's card is shown to Betty. Stephen's card is shown to Betty. Betty's card is shown to Stephen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Betty can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessica","Betty","Stephen"],"index":3383,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.883395493,"difficulty":0.116604507}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sanford's card is shown to Lucille. Lucille's card is shown to Sanford. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Lucille can now know whether Lucille picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lucille","Sanford"],"index":6473,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5990810394,"difficulty":0.4009189606}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Donna can now know that Mary can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Erin","Stanley","Donna","Mary"],"index":7138,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9801294208,"difficulty":0.0198705792}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Matthew can now know that Edgar's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Walter","Edgar","Matthew"],"index":7510,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9559634328,"difficulty":0.0440365672}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joe can now know that Ronald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jean","Joe","Nancy","Ronald"],"index":342,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9792681932,"difficulty":0.0207318068}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Rosy does not know whether Rosy's forehead is muddy.","smcdel_problem":"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 2) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Rosy can now know that Jose can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Rosy","Jose"],"index":1101,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9881287217,"difficulty":0.0118712783}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ross can now know whether Mark can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ross","Douglas","Mark","Sadie"],"index":7397,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.98826015,"difficulty":0.01173985}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Diane. Juan's card is shown to Solomon. Mike's card is shown to Solomon. Mike's card is shown to Juan. Diane's card is shown to Mike. Juan's card is shown to Mike. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Mike does not know whether Solomon picked a red card. It is publicly announced that Diane does not know whether Solomon picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Diane can now know whether Juan can know that Mike picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diane","Solomon","Juan","Mike"],"index":584,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9563743472,"difficulty":1.9563743472}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Jerry can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Martha","Jerry","Robert"],"index":3427,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8644395471,"difficulty":0.1355604529}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Daniel's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Daniel can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Daniel","Pamela"],"index":7560,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9781253934,"difficulty":0.0218746066}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Harold's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Joe can now know that Michael can know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Matthew","Joe","Michael","Harold"],"index":1811,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9658871293,"difficulty":0.0341128707}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenell's card is shown to Grace. Dana's card is shown to Grace. Dana's card is shown to Jenell. Grace's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Dana does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jenell can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Grace","Jenell","Dana"],"index":643,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9812877774,"difficulty":0.0187122226}
-{"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 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":"Kevin can now know whether Maria can know whether Reginald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terence","Kevin","Reginald","Maria"],"index":5662,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9462332726,"difficulty":0.0537667274}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Perry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Tiffany can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathy","Perry","Tiffany"],"index":7253,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9756134152,"difficulty":0.0243865848}
-{"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":"Renee can now know that Consuelo can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Jeannine","Renee","Consuelo"],"index":789,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9693112969,"difficulty":0.0306887031}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Katrina can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Katrina","Jack","Matthew"],"index":602,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9671461582,"difficulty":0.0328538418}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Joseph. Amy's card is shown to Kenneth. Kenneth's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Amy does not know whether Amy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kenneth can now know that Joseph can know whether Amy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Kenneth","Amy"],"index":9559,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5021264553,"difficulty":0.4978735447}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon does not know whether Shannon's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Shannon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Shannon","Michael"],"index":9509,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9542122483,"difficulty":0.0457877517}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Eula can now know whether Mark can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","James","Eula","Mark"],"index":5338,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9041485786,"difficulty":0.0958514214}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amber's card is shown to Randall. Philip's card is shown to Amber. Randall's card is shown to Philip. Amber's card is shown to Philip. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Philip can now know whether Randall can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Randall","Amber","Philip"],"index":3023,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9360393882,"difficulty":0.0639606118}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Roberto can now know that Matthew can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Matthew","Roberto"],"index":1042,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9793961048,"difficulty":0.0206038952}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Mabel. Linda's card is shown to Mabel. Richard's card is shown to Rufus. Rufus's card is shown to Richard. Richard's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Rufus does not know whether or not everyone picked a red card. It is publicly announced that Mabel does not know whether Rufus picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mabel can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mabel","Rufus","Richard","Linda"],"index":3768,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9786800146,"difficulty":0.0213199854}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tomas knows whether Tomas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tomas","Robert","Arden","Charles"],"index":459,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8682733774,"difficulty":0.1317266226}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stacy can now know that Terry can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joann","Stacy","Christopher","Terry"],"index":4964,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8486413956,"difficulty":0.1513586044}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to David. Susan's card is shown to David. David's card is shown to Irene. David's card is shown to Susan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Irene","Susan"],"index":7634,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9890493155,"difficulty":0.0109506845}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (~(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":"Leonel can now know that Marjorie can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leonel","Marjorie","Mable","Catherine"],"index":5827,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9856782556,"difficulty":0.0143217444}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis does not know whether Octavia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Michael can now know whether George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Dennis","George","Octavia"],"index":1222,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8916264772,"difficulty":0.1083735228}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Velma does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 (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":"Velma can now know whether Kenneth can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irene","Kenneth","Velma","Rosalinda"],"index":4888,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9880850911,"difficulty":0.0119149089}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sam's card is shown to Melissa. Melissa's card is shown to Sam. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Melissa knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Sam can now know that Melissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Melissa","Sam"],"index":9394,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.885591507,"difficulty":0.114408493}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Curtis can now know whether Aileen can know whether Curtis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Curtis","Aileen"],"index":5363,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.91500175,"difficulty":1.91500175}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bobbie can now know that Rosemary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bobbie","Kristen","Laurie","Rosemary"],"index":3276,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9625921249,"difficulty":0.0374078751}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adolfo's card is shown to Jennifer. Todd's card is shown to Richard. Todd's card is shown to Adolfo. Adolfo's card is shown to Todd. It is publicly announced that someone picked a red card. It is publicly announced that Adolfo does not know whether Adolfo picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Richard can now know whether Todd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jennifer","Richard","Adolfo","Todd"],"index":6383,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5695384741,"difficulty":1.5695384741}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy. It is publicly announced that Patricia knows whether Patricia'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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Amanda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Amanda","Susan"],"index":7681,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9681981206,"difficulty":1.9681981206}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"James can now know whether Victor can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Victor","James"],"index":4426,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9697381258,"difficulty":0.0302618742}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeannette does not know whether Lauren is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Maria can now know whether Jeannette is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mildred","Jeannette","Lauren","Maria"],"index":5696,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8728935122,"difficulty":0.1271064878}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Steven. Steven's card is shown to Edward. Joseph's card is shown to Edward. Edward's card is shown to Joseph. Joseph's card is shown to Edwin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edwin can now know that Joseph can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Edward","Joseph","Edwin"],"index":1814,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.98083812,"difficulty":0.01916188}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Larry","Richard","Robert"],"index":4231,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9791425467,"difficulty":0.0208574533}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathey knows whether Kathey is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kathey can now know whether Melody can know that Kathey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Melody","Kathey"],"index":8349,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9082409739,"difficulty":1.9082409739}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Michael. Rita's card is shown to Alicia. Rose's card is shown to Alicia. Alicia's card is shown to Rita. Rose's card is shown to Rita. Michael's card is shown to Rose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Alicia","Rita","Rose"],"index":5586,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9528771043,"difficulty":0.0471228957}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shante's card is shown to Karen. Shante's card is shown to Jennifer. Karen's card is shown to Shante. It is publicly announced that someone picked a red card. It is publicly announced that Shante does not know whether Jennifer picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know whether Shante can know that Karen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Jennifer","Shante"],"index":8561,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9650771618,"difficulty":1.9650771618}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Jerry. Lois's card is shown to Jerry. Lois's card is shown to Daniel. Daniel's card is shown to Lois. It is publicly announced that someone picked a red card. It is publicly announced that Daniel knows whether Lois picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Jerry can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jerry","Daniel","Lois"],"index":9591,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9883905649,"difficulty":0.0116094351}
-{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Diane can now know that Christopher can know whether Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Diane","Christopher","Lawrence"],"index":4300,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9299226403,"difficulty":1.9299226403}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beatrice can now know whether Theresa can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","Beatrice","Isaac","Theresa"],"index":9608,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9536753893,"difficulty":0.0463246107}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erica is not thirsty. It is publicly announced that Erica knows whether or not nobody is thirsty. It is publicly announced that Rudy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Rudy can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Erica","Rudy"],"index":1322,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.98825562,"difficulty":0.01174438}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bessie's card is shown to Andrew. Andrew's card is shown to Bessie. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Andrew can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andrew","Bessie"],"index":4068,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9747700691,"difficulty":0.0252299309}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hugo knows whether or not everyone's forehead is muddy. It is publicly announced that Nathaniel knows whether Nathaniel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Hugo can now know that Nathaniel can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hugo","Nathaniel"],"index":7425,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9820808768,"difficulty":0.0179191232}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Elaine can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joe","Elaine","Terry"],"index":291,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9881520867,"difficulty":0.0118479133}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Mary can now know whether Christopher is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Christopher","Patricia"],"index":8623,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.814522922,"difficulty":0.185477078}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether or not everyone's forehead is muddy. It is publicly announced that Michael knows whether Michael'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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Kevin can now know that Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Kevin","Mark"],"index":8885,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9358290434,"difficulty":1.9358290434}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irish's card is shown to Eugene. Eugene's card is shown to Irish. It is publicly announced that someone picked a red card. It is publicly announced that Irish does not know whether Irish picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Irish can now know that Eugene can know whether Eugene picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eugene","Irish"],"index":493,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5475972891,"difficulty":0.4524027109}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandy can now know that Christopher can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nicholas","Zoila","Brandy","Christopher"],"index":6845,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9315491915,"difficulty":0.0684508085}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiana knows whether Cynthia's forehead is muddy. It is publicly announced that Cynthia knows whether Tiana's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Cynthia can now know that Amy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tiana","Cynthia","Amy"],"index":2061,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9400846958,"difficulty":0.0599153042}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Myrtle can now know that Roger can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Myrtle","Roger","Michael"],"index":9269,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.97445786,"difficulty":0.02554214}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that April does not know whether April's forehead is muddy. It is publicly announced that Ida knows whether April's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Morton can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Morton","April","Ida"],"index":4986,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9707650542,"difficulty":0.0292349458}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rodney can now know that Andrew can know that Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leo","Andrew","Rodney"],"index":3632,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9742023349,"difficulty":0.0257976651}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillian knows whether Jesse's forehead is muddy. It is publicly announced that Alice's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Jesse can now know that Virginia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Virginia","Lillian","Jesse","Alice"],"index":8610,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9840659499,"difficulty":0.0159340501}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether someone is thirsty. It is publicly announced that Christy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Nelson can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Nelson","Christy"],"index":5475,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9890028238,"difficulty":0.0109971762}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theodore does not know whether Donna is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Donna can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Donna","Theodore"],"index":9175,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9739537239,"difficulty":0.0260462761}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Latoya knows whether Gladys's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Marie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Latoya","Gladys","Judy"],"index":2236,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9704148769,"difficulty":0.0295851231}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Johnny's forehead 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)","n_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":"Mari can now know whether Maureen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maureen","Johnny","Mari"],"index":1065,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9507683516,"difficulty":0.0492316484}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheree's card is shown to Clifford. Clifford's card is shown to Sheree. Marcus's card is shown to Sheree. Sheree's card is shown to Marcus. Sheree's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Sheree does not know whether Sheree picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Marcus can now know that Frank can know whether Clifford picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clifford","Sheree","Marcus","Frank"],"index":5454,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5398920774,"difficulty":1.5398920774}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Geraldine. Sandra's card is shown to Gloria. Richard's card is shown to Sandra. It is publicly announced that someone picked a red card. It is publicly announced that Richard picked a black card. It is publicly announced that Geraldine does not know whether Sandra picked a red card. It is publicly announced that Geraldine does not know whether Gloria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Geraldine can now know that Gloria can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Geraldine","Gloria","Sandra","Richard"],"index":5771,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9741988182,"difficulty":0.0258011818}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Anna can now know whether Toni can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Toni","Jessie","Anna","Leland"],"index":8705,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9897518158,"difficulty":0.0102481842}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie knows whether Heather's forehead is muddy. It is publicly announced that Jamie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(2) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Jamie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lucille","Jamie","Heather"],"index":8067,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9821718335,"difficulty":0.0178281665}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachael's card is shown to Diana. Rachael's card is shown to Gary. Rachael's card is shown to Robert. Robert's card is shown to Rachael. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd: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:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know that Diana can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diana","Gary","Robert","Rachael"],"index":3203,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6277511716,"difficulty":0.3722488284}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Trina's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Trina can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Trina","Frederick"],"index":2260,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9753934741,"difficulty":0.0246065259}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Eugene can now know whether Diana is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bettina","George","Eugene","Diana"],"index":8422,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8695957661,"difficulty":1.8695957661}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Barry. Barry's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Patricia can now know that Barry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Barry","Patricia"],"index":2130,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9494951367,"difficulty":0.0505048633}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jeffrey can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffrey","Dale","Gerald","Carol"],"index":8625,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9879773259,"difficulty":0.0120226741}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Denise can now know that Wilbur can know that Wilbur is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harold","Denise","Gabriele","Wilbur"],"index":7919,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9753907323,"difficulty":0.0246092677}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Susan can now know that Jennie can know that Celeste's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","Jennie","Celeste","Nichole"],"index":9316,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9674212337,"difficulty":0.0325787663}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 1)","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 Mark can know that Becky's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Becky","Mary","Mark","Rose"],"index":839,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9718135595,"difficulty":0.0281864405}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether Jaime is thirsty. It is publicly announced that Jaime does not know whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Barbara can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Jaime","Christopher"],"index":794,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8280829787,"difficulty":0.1719170213}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shawn can now know whether Anthony can know that Shawn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Max","Scott","Anthony","Shawn"],"index":2860,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9384115338,"difficulty":0.0615884662}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elliot's card is shown to Gene. Gene's card is shown to Eleanor. Gene's card is shown to Elliot. Eleanor's card is shown to Elliot. It is publicly announced that someone picked a red card. It is publicly announced that Elliot does not know whether or not everyone picked a red card. It is publicly announced that Eleanor knows whether Gene picked a red card. It is publicly announced that Elliot does not know whether Elliot picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Eleanor can now know whether Gene can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gene","Eleanor","Elliot"],"index":5546,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9884722829,"difficulty":0.0115277171}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether Kathy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kimberly can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kathy","Kimberly"],"index":9401,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9877858162,"difficulty":0.0122141838}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ida can now know that Patrick can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Candice","Ida","Doris","Patrick"],"index":1046,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9872122407,"difficulty":0.0127877593}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Stacey can now know that Sophie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thelma","Michael","Sophie","Stacey"],"index":4254,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9574460387,"difficulty":0.0425539613}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Stephen can now know that Leticia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Leticia","Stephen"],"index":456,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9571214914,"difficulty":0.0428785086}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katharine knows whether someone's forehead is muddy. It is publicly announced that Eileen knows whether Lynne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Katharine can now know that Eileen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eileen","Lynne","Katharine","John"],"index":3574,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9324263334,"difficulty":0.0675736666}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(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":"Tracy can now know that Melissa can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stanley","Melissa","Tracy"],"index":9409,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6831393242,"difficulty":1.6831393242}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Ada. Lisa's card is shown to Rosalie. Cecilia's card is shown to Lisa. Rosalie's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rosalie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ada","Cecilia","Rosalie","Lisa"],"index":3116,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9759742618,"difficulty":0.0240257382}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rafael does not know whether Lynette is thirsty. It is publicly announced that Jason does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Lynette can now know that Rafael can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rafael","James","Jason","Lynette"],"index":9244,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9777078032,"difficulty":0.0222921968}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Anthony is thirsty. It is publicly announced that Kurt knows whether or not nobody is thirsty. It is publicly announced that Brian does not know whether Kurt is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kurt can now know that Franklin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Franklin","Brian","Anthony","Kurt"],"index":1514,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9307260513,"difficulty":0.0692739487}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marissa's card is shown to Gloria. Gloria's card is shown to Todd. Marissa's card is shown to Todd. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gloria can now know that Marissa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gloria","Marissa","Todd"],"index":2149,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9883384109,"difficulty":0.0116615891}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Veronica. Veronica's card is shown to Patricia. Genevieve's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Veronica can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Veronica","Patricia","Genevieve"],"index":779,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8352271318,"difficulty":0.1647728682}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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)) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that John can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","John","Margret","Douglas"],"index":2941,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9825146794,"difficulty":0.0174853206}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julia does not know whether Sharon is thirsty. It is publicly announced that Julia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] 0","hypothesis":"Sharon can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Charles","Julia"],"index":8655,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.798597157,"difficulty":0.201402843}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffery's card is shown to Jacalyn. Jacalyn's card is shown to Jeffery. It is publicly announced that someone picked a red card. It is publicly announced that Jacalyn knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Jeffery can now know whether Jacalyn can know that Jacalyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jacalyn","Jeffery"],"index":773,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9789500237,"difficulty":1.9789500237}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether or not everyone is thirsty. It is publicly announced that Allison is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"May can now know whether Allison can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["May","John","Allison"],"index":6174,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9701523781,"difficulty":0.0298476219}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doris does not know whether Stephen is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Doris can now know whether Stephen can know that Doris is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Doris","Stephen"],"index":5751,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8467037082,"difficulty":0.1532962918}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Betty can now know whether John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Betty","Francis"],"index":8578,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9761824608,"difficulty":0.0238175392}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Sarah can now know whether Sarah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sarah","Lewis","John"],"index":6128,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8081279993,"difficulty":1.8081279993}
-{"premise":"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 Marie knows whether Harry's forehead is muddy. It is publicly announced that Marie knows whether Carmen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Harry can now know that Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carmen","Marie","Harry"],"index":7046,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9321505427,"difficulty":0.0678494573}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanna knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Joanna can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Joanna"],"index":3188,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9687649012,"difficulty":0.0312350988}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gene does not know whether Horace is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Horace can now know that Gene can know that Brenda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacob","Brenda","Horace","Gene"],"index":2512,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9705294371,"difficulty":0.0294705629}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jane can now know whether Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jane","Natasha","Maria","Clarence"],"index":6769,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9742876887,"difficulty":0.0257123113}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to James. Juan's card is shown to Arnold. Lois's card is shown to Arnold. Juan's card is shown to Lois. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Arnold can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Juan","Arnold","Lois"],"index":3043,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9321087599,"difficulty":0.0678912401}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Ivory can know that Ivory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gregory","Mark","Ivory","William"],"index":8993,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9758478999,"difficulty":0.0241521001}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Ruby is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Maria can now know whether Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Maria","Ruby","Michelle"],"index":4171,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8666444421,"difficulty":1.8666444421}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allan's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Allan can now know that Jane can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Allan","Jane"],"index":3469,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9801484942,"difficulty":0.0198515058}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacy knows whether Stacy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Deanna can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Deanna","Kenneth","Stacy"],"index":4450,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9731128216,"difficulty":0.0268871784}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Theresa","Joseph"],"index":3172,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9636880755,"difficulty":0.0363119245}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tara knows whether Tara is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Edwin can now know whether Tara can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edwin","Tara"],"index":53,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9511706829,"difficulty":0.0488293171}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryn's card is shown to Nelia. Nelia's card is shown to Darrell. Nelia's card is shown to Lance. Kathryn's card is shown to Lance. Nelia's card is shown to Kathryn. Darrell's card is shown to Kathryn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darrell can now know whether Kathryn can know that Kathryn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nelia","Darrell","Lance","Kathryn"],"index":5707,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8775784969,"difficulty":0.1224215031}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jovita's forehead is muddy. It is publicly announced that Douglas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Kelvin can now know whether Douglas can know whether Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelvin","Jovita","Douglas"],"index":133,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.982591331,"difficulty":0.017408669}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Scott","Erick","Ronald"],"index":5214,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9632948041,"difficulty":0.0367051959}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chester knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Chester can now know whether Yolanda can know whether Danny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danny","Pauline","Yolanda","Chester"],"index":9524,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9873419404,"difficulty":0.0126580596}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ron's card is shown to Garth. Sara's card is shown to Garth. Ron's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Garth can now know that Ron picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ron","Garth","Sara"],"index":3862,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9554787874,"difficulty":0.0445212126}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Stacy can now know that Susanne can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stacy","Susanne","Amber"],"index":8186,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9856282473,"difficulty":0.0143717527}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Corrine can now know that Johnny can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicholas","Johnny","Tammie","Corrine"],"index":7054,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9889999032,"difficulty":0.0110000968}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Amy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Steven can now know that William can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Amy","Sharon","William"],"index":2816,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9877893925,"difficulty":0.0122106075}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Troy can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Troy"],"index":2441,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9879879951,"difficulty":0.0120120049}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether Logan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mike can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mike","Sarah","Logan"],"index":732,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9877397418,"difficulty":0.0122602582}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diane knows whether Diane is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Marc can now know that Debbie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diane","Marc","Jerome","Debbie"],"index":6127,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9565544128,"difficulty":0.0434455872}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 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":"Wilhelmina can now know that Dorothy can know that Wilhelmina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","Cassie","Wilhelmina","Joshua"],"index":3855,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9725952744,"difficulty":0.0274047256}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura does not know whether Jeffrey is thirsty. It is publicly announced that Laura is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Jeffrey can now know that Jeffrey is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yvonne","Jeffrey","Laura"],"index":3580,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9532112479,"difficulty":0.0467887521}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martin knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Edward can now know that Bobby can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Molly","Bobby","Martin","Edward"],"index":6495,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9884872437,"difficulty":0.0115127563}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ellen's card is shown to Gladys. Gladys's card is shown to Ellen. It is publicly announced that someone picked a red card. It is publicly announced that Ellen knows whether Ellen picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 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":"Gladys can now know whether Ellen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gladys","Ellen"],"index":8330,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7167915702,"difficulty":0.2832084298}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Derrick knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Vada can now know whether Derrick can know whether Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clyde","Vada","Carolyn","Derrick"],"index":1633,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9668702483,"difficulty":0.0331297517}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristi does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kristi can now know whether Kristi is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Kristi","John","Jewell"],"index":3035,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8859519958,"difficulty":1.8859519958}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ted does not know whether Mercedes is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Dennis can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Ted","Dennis","Mercedes"],"index":1613,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9746693969,"difficulty":0.0253306031}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to William. David's card is shown to William. William's card is shown to Robert. William's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Robert","David"],"index":6830,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9560935497,"difficulty":0.0439064503}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathryn does not know whether Rita is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Rita can now know that Robert can know whether Rita is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathryn","Rita","Robert"],"index":8165,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8177964091,"difficulty":0.1822035909}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Alan. Alan's card is shown to Harry. Elizabeth's card is shown to Harry. Harry's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Harry can now know that Alan can know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alan","Harry","Elizabeth"],"index":6460,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9709638357,"difficulty":0.0290361643}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Steven. Steven's card is shown to Irene. Eartha's card is shown to Irene. Irene's card is shown to Eartha. Eartha's card is shown to Amanda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amanda can now know that Irene can know that Eartha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Irene","Eartha","Amanda"],"index":11,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9735965133,"difficulty":0.0264034867}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earl knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Earl can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kristin","Earl"],"index":7044,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8575791121,"difficulty":0.1424208879}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Patricia. Patricia's card is shown to Marc. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Nancy can now know that Patricia can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Nancy","Marc"],"index":2417,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9888600111,"difficulty":0.0111399889}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyle's forehead is muddy. It is publicly announced that Kyle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Betty can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Betty","Kyle"],"index":3335,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9749061465,"difficulty":0.0250938535}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Lawrence's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Lawrence can now know that Thomas can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lawrence","Thomas","Donna"],"index":8815,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9812984467,"difficulty":0.0187015533}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy 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":"Tammy can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tammy","Ernest"],"index":8663,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9488350749,"difficulty":1.9488350749}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Michael can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Keith"],"index":2657,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.978261292,"difficulty":0.021738708}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","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":"Josefina can now know whether Teresa can know whether Josefina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Josefina","Sandra","Teresa"],"index":2445,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9381300807,"difficulty":0.0618699193}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elton does not know whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"William can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Thomas","Micheal","Elton"],"index":2745,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9588332772,"difficulty":0.0411667228}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rita's card is shown to Lori. Lori's card is shown to Grace. Rita's card is shown to Grace. Grace's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Grace does not know whether Grace picked a red card. It is publicly announced that Grace knows whether someone picked a red card. It is publicly announced that Lori does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Grace can now know whether Lori picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lori","Grace","Rita"],"index":5946,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6695665717,"difficulty":0.3304334283}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Randall can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Randall","Vincent","Gwendolyn"],"index":3091,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9785504341,"difficulty":0.0214495659}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Vincent. Vincent's card is shown to Garry. Paula's card is shown to Garry. Vincent's card is shown to Paula. Garry's card is shown to Paula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vincent can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Vincent","Garry","Paula"],"index":112,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.981646359,"difficulty":0.018353641}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gregory can now know that Joseph can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gregory","Kenneth","Joseph"],"index":4425,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9795714617,"difficulty":0.0204285383}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samantha's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Samantha can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Samantha","Joann","John","Domonique"],"index":3256,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9752419591,"difficulty":0.0247580409}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bob does not know whether or not everyone is thirsty. It is publicly announced that Scott does not know whether Erin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Bob can now know that Scott is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bob","Scott","Jack","Erin"],"index":6245,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9587356448,"difficulty":0.0412643552}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Josephine can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harriet","Josephine","Eugene","William"],"index":7730,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9758821726,"difficulty":0.0241178274}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Bonnie can now know that William can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Bonnie","Kim","William"],"index":5494,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9720467329,"difficulty":0.0279532671}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alex does not know whether Tabatha is thirsty. It is publicly announced that Alex is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 3 ] 0","hypothesis":"Tabatha can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tabatha","Thomas","Alex"],"index":4733,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9734115005,"difficulty":0.0265884995}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jean can now know whether Jean is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerard","Matthew","Maura","Jean"],"index":1883,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.828823328,"difficulty":1.828823328}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Adam can now know that Juan can know that Brad's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juan","Brad","Adam"],"index":393,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9727832079,"difficulty":0.0272167921}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether Marilyn's forehead is muddy. It is publicly announced that Marilyn knows whether Marilyn's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jessica can now know whether Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jessica","Marilyn"],"index":3288,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9855583906,"difficulty":0.0144416094}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 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":"Teresa can now know whether David can know that Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Teresa","Jonathan","Steven"],"index":7384,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7036839724,"difficulty":1.7036839724}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Spencer knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows 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":"Angel can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Spencer","Leslie","Angel"],"index":4805,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9887350202,"difficulty":0.0112649798}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert is not thirsty. It is publicly announced that Robert knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Dean can now know that Robert can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Robert","Dean","Vivian"],"index":5001,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9779592752,"difficulty":0.0220407248}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Harlan. James's card is shown to Harlan. Harlan's card is shown to Edward. James's card is shown to Edward. Edward's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Harlan can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harlan","Edward","James"],"index":3330,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9558457136,"difficulty":0.0441542864}
-{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Teresa can now know whether Coy can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joshua","Coy","Teresa"],"index":3327,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9881159067,"difficulty":0.0118840933}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josephine knows whether or not everyone's forehead is muddy. It is publicly announced that Brenda does not know whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 2) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Louis can now know that Brenda can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louis","Brenda","Josephine"],"index":1826,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5137000084,"difficulty":1.5137000084}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessie can now know that Grace can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Grace","Mark","Jessie"],"index":8853,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9796651006,"difficulty":0.0203348994}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paula can now know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Paula","Jason"],"index":8491,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.96189785,"difficulty":0.03810215}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know whether Mike can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Harold","Mike"],"index":8760,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9882802963,"difficulty":0.0117197037}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 1)","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":"Sean can now know that Frank can know that Frances's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frances","Mui","Frank","Sean"],"index":2033,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9714238048,"difficulty":0.0285761952}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know whether Ethel can know that Ethel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Joe","Ethel","Vanessa"],"index":1446,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6740831733,"difficulty":1.6740831733}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Selina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gloria can now know that Selina can know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Selina","Gloria"],"index":1416,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.839142561,"difficulty":0.160857439}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Linda. Linda's card is shown to Russell. Randy's card is shown to Russell. Linda's card is shown to Randy. Russell's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Randy does not know whether Randy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Russell can now know that Randy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Russell","Randy"],"index":6162,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9744338989,"difficulty":0.0255661011}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tommie's card is shown to Harry. Harry's card is shown to Tommie. It is publicly announced that someone picked a red card. It is publicly announced that Harry does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Harry can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harry","Tommie"],"index":1709,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.988840282,"difficulty":0.011159718}
-{"premise":"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 Tia's forehead is muddy. It is publicly announced that Elsie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] [ ! ~(4) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Tia can now know whether Shirley can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Fred","Tia","Elsie"],"index":1160,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9538095593,"difficulty":0.0461904407}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sue's card is shown to Mary. Mary's card is shown to Sylvia. Sue's card is shown to Sylvia. Mary's card is shown to Emily. Emily's card is shown to Sue. It is publicly announced that someone picked a red card. It is publicly announced that Sylvia knows whether someone picked a red card. It is publicly announced that Sylvia picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"Emily can now know that Emily picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Sylvia","Emily","Sue"],"index":8004,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9359312057,"difficulty":0.0640687943}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elsie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 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":"Jean can now know that Herman can know that Bobby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Herman","Jean","Bobby","Elsie"],"index":5888,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9649198651,"difficulty":0.0350801349}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hubert is not thirsty. It is publicly announced that Jama is not thirsty. It is publicly announced that Hubert does not know whether Mario is thirsty. It is publicly announced that Mario knows whether Mario is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] Agenta knows that (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Maurice can now know that Jama can know whether Hubert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maurice","Hubert","Jama","Mario"],"index":2974,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7034180164,"difficulty":1.7034180164}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adam knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jared can now know whether Adam is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Adam","Jared"],"index":6282,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7550296783,"difficulty":0.2449703217}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicolas does not know whether Nicolas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nicolas can now know that Alice can know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Kenneth","Nicolas","Alice"],"index":8055,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8337879777,"difficulty":0.1662120223}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Manuel can now know whether Allen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Manuel","Allen"],"index":1802,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9856821895,"difficulty":0.0143178105}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucinda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 (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":"Carolyn can now know that Michael can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lucinda","Michael","Carolyn","Adele"],"index":8339,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8239657283,"difficulty":1.8239657283}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kate does not know whether Omar is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Betty can now know whether Betty is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Omar","Kate","Betty"],"index":6420,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8636857867,"difficulty":1.8636857867}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristin does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Kristin can now know that Andrea can know that Andrea is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Andrea","Michael","Kristin"],"index":8743,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9714765549,"difficulty":0.0285234451}
-{"premise":"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)) ] (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":"Jeffrey can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Albert","Patricia","Jeffrey"],"index":6607,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5557106733,"difficulty":1.5557106733}
-{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows whether 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 Erika can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Erika"],"index":795,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.94390589,"difficulty":0.05609411}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Susan is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Susan can now know whether Susan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Susan","Charles"],"index":7140,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8620114923,"difficulty":1.8620114923}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Cathy can now know that Joseph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Cathy","Steven","Walter"],"index":8869,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9831856489,"difficulty":0.0168143511}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renda's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Paul can now know whether Renda can know that Renda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Renda","John"],"index":1702,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9710808396,"difficulty":0.0289191604}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marlene knows whether Raymond's forehead is muddy. It is publicly announced that Raymond knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Marlene can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marlene","Raymond"],"index":2204,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9741137624,"difficulty":0.0258862376}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rose does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ina can now know that Chad can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Ina","Mary","Chad"],"index":8383,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9776278138,"difficulty":0.0223721862}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Richard can now know that Jean can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Jean"],"index":5436,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9865891933,"difficulty":0.0134108067}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joyce can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Renae","Sarah","Joyce","Sandra"],"index":2168,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9762810469,"difficulty":0.0237189531}
-{"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":"Eunice can now know whether Stephanie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stephanie","Theodore","Barbara","Eunice"],"index":778,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5677055717,"difficulty":0.4322944283}
-{"premise":"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 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":"Norma can now know whether Nathaniel can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nathaniel","Norma"],"index":3981,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9866589308,"difficulty":0.0133410692}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Doris. William's card is shown to Doris. William's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Kevin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Doris can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Doris","Kevin","William"],"index":2050,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9749296904,"difficulty":0.0250703096}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether or not everyone is thirsty. It is publicly announced that Joshua does not know whether or not everyone is thirsty. It is publicly announced that Grady does not know whether Aaron is thirsty. It is publicly announced that Mark does not know whether Aaron is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows that (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Aaron can now know that Joshua can know whether Grady is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Grady","Joshua","Aaron"],"index":8274,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7873134017,"difficulty":0.2126865983}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Martha. Esther's card is shown to Martha. Esther's card is shown to William. William's card is shown to Esther. It is publicly announced that someone picked a red card. It is publicly announced that William picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"William can now know whether Esther can know whether Esther picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martha","William","Esther"],"index":2603,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9478861094,"difficulty":0.0521138906}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Susan. Robert's card is shown to Susan. Robert's card is shown to Lisa. Lisa's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Robert can now know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Lisa","Robert"],"index":7814,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9512940645,"difficulty":0.0487059355}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Kelly. Martin's card is shown to Kelly. Dana's card is shown to Kelly. Martin's card is shown to Mary. Dana's card is shown to Mary. Kelly's card is shown to Martin. Mary's card is shown to Dana. Martin's card is shown to Dana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dana can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kelly","Mary","Martin","Dana"],"index":5505,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9892487526,"difficulty":0.0107512474}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillian knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Lillian can now know whether David can know that Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Ruth","Jean","Lillian"],"index":7108,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8951370716,"difficulty":0.1048629284}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 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":"Ernest can now know that Richard can know whether Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Brenda","Ernest"],"index":8593,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8926817179,"difficulty":0.1073182821}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leslie does not know whether Janet is thirsty. It is publicly announced that Janet does not know whether Catherine is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Leslie can now know whether Leslie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leslie","Janet","Catherine"],"index":8078,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8103621602,"difficulty":1.8103621602}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Dan. Dan's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Dan does not know whether Dan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dan can now know whether Brian can know whether Dan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dan","Brian"],"index":7165,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9518400431,"difficulty":0.0481599569}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Irene can now know that Evelyn can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Irene","Evelyn","Patricia"],"index":5372,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9297884107,"difficulty":0.0702115893}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Adelaide can now know whether Patrick can know whether Adelaide's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Adelaide","Patrick"],"index":8580,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9812763929,"difficulty":0.0187236071}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Winston can now know that Gary can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Winston","Lisa","Gary"],"index":9195,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9778792262,"difficulty":0.0221207738}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara knows whether Tamara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Timothy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Tamara","Senaida","Timothy"],"index":5552,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9771561623,"difficulty":0.0228438377}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laurie's card is shown to Maurice. Rosa's card is shown to Maurice. William's card is shown to Maurice. Laurie's card is shown to William. Rosa's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Laurie knows whether William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Rosa can now know whether Laurie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laurie","Rosa","Maurice","William"],"index":6838,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7606174946,"difficulty":1.7606174946}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter does not know whether Dominic is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Dominic can now know that Stephen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Peter","Stephen","Nicholas","Dominic"],"index":2830,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9754312038,"difficulty":0.0245687962}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alyssa's card is shown to Marisol. Daniel's card is shown to Robert. Daniel's card is shown to Alyssa. Alyssa's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Alyssa does not know whether Alyssa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Daniel can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marisol","Robert","Alyssa","Daniel"],"index":543,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9812781215,"difficulty":0.0187218785}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Simone is thirsty. It is publicly announced that James does not know whether Simone is thirsty. It is publicly announced that James does not know whether Danielle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agenta knows that (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Danielle can now know that James can know that Simone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Danielle","Simone","Maria","James"],"index":2686,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9701551795,"difficulty":0.0298448205}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Dustin can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Benjamin","Christopher","Dustin","Francisco"],"index":3191,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9754164815,"difficulty":0.0245835185}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Yesenia can now know whether Brian can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Yesenia","Brian","Betty","Pamela"],"index":1209,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9897742271,"difficulty":0.0102257729}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Denise. Denise's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Denise knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Mark can now know whether Denise can know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Denise","Mark"],"index":63,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9827439189,"difficulty":0.0172560811}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Carol. Michael's card is shown to Carol. Carol's card is shown to Linda. Michael's card is shown to Linda. Linda's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Carol picked a red card. It is publicly announced that Carol knows whether Michael picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Linda can now know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Linda","Michael"],"index":4108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6018076539,"difficulty":0.3981923461}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monte's card is shown to Ruth. Ruth's card is shown to Monte. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether or not everyone picked a red card. It is publicly announced that Ruth knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(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":"Ruth can now know whether Ruth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ruth","Monte"],"index":98,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.964064002,"difficulty":1.964064002}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Laila can now know that Shannon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Nathan","Shannon","Laila"],"index":7420,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9567977786,"difficulty":0.0432022214}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cleo does not know whether Jonathan is thirsty. It is publicly announced that Margery is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Cleo can now know whether Margery can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margery","Cleo","Jonathan"],"index":4564,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9846878648,"difficulty":0.0153121352}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Michael. Kenneth's card is shown to Cheryl. Elizabeth's card is shown to Cheryl. Kenneth's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Kenneth can know that Cheryl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Kenneth","Cheryl","Elizabeth"],"index":3552,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9728605747,"difficulty":0.0271394253}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debra is not thirsty. It is publicly announced that Michael does not know whether Roxanne is thirsty. It is publicly announced that Wilma does not know whether Roxanne is thirsty. It is publicly announced that Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] Agentb knows that (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] 0","hypothesis":"Michael can now know that Roxanne can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Michael","Roxanne","Wilma"],"index":2201,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6976261139,"difficulty":1.6976261139}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leanne does not know whether Carol is thirsty. It is publicly announced that Carol knows whether someone is thirsty. It is publicly announced that Leanne does not know whether Carol is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Carol can now know that Leanne can know whether Yvonne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Yvonne","Leanne","Carol"],"index":1861,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5911415815,"difficulty":0.4088584185}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Brian. Jillian's card is shown to Rosie. Brian's card is shown to Jillian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rosie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Rosie","Rebecca","Jillian"],"index":8731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9742709398,"difficulty":0.0257290602}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Shaun. Shaun's card is shown to Manuel. It is publicly announced that someone picked a red card. It is publicly announced that Shaun knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Manuel can now know whether Shaun can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shaun","Manuel"],"index":7066,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9777925014,"difficulty":0.0222074986}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Katherina. Jonathan's card is shown to Donna. Katherina's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jonathan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jonathan","Katherina","Donna"],"index":3765,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9736001492,"difficulty":0.0263998508}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Robert can now know whether Dolores's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Magaret","Dolores","Robert","Richard"],"index":3134,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9845013022,"difficulty":0.0154986978}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Christine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Heather can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Heather","Christine","Donald"],"index":7065,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9731944203,"difficulty":0.0268055797}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Rachel. David's card is shown to Jon. Rachel's card is shown to David. Regina's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Regina does not know whether or not everyone picked a red card. It is publicly announced that Regina does not know whether Regina picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Rachel can now know that Regina can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachel","Regina","Jon","David"],"index":8685,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9739444852,"difficulty":0.0260555148}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Virgil can now know that Karina can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karina","Mabel","Virgil"],"index":2369,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9816530347,"difficulty":0.0183469653}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Thomas can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thomas","James"],"index":9228,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9877436161,"difficulty":0.0122563839}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Dorothy. Dorothy's card is shown to Theresa. Dorothy's card is shown to Dennis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Theresa can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Theresa","Dennis"],"index":562,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.883228898,"difficulty":0.116771102}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brittany 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 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":"Corrine can now know that Brittany's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brittany","Corrine","Rosanna"],"index":2538,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9559273124,"difficulty":0.0440726876}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Mary. Mary's card is shown to Joseph. Edward's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Edward picked a red card. It is publicly announced that Edward knows whether or not nobody picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Edward","Joseph","James"],"index":2907,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9227026105,"difficulty":1.9227026105}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tabitha's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Monica can now know that Tabitha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angelina","Monica","Julia","Tabitha"],"index":2318,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9560877681,"difficulty":0.0439122319}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adam does not know whether or not everyone's forehead is muddy. It is publicly announced that Mildred knows whether someone's forehead is muddy. It is publicly announced that Adam does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Adam can now know whether Mildred can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Adam","Mildred"],"index":1686,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9871569276,"difficulty":0.0128430724}
-{"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":"Bonnie can now know that Christian can know that Bonnie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bertha","Christian","Bonnie","James"],"index":9598,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9715350866,"difficulty":0.0284649134}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Ray can now know that Susan can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Susan","Ray"],"index":4272,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9794638157,"difficulty":0.0205361843}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anita's card is shown to Thomas. Thomas's card is shown to Anita. It is publicly announced that someone picked a red card. It is publicly announced that Thomas knows whether someone picked a red card. It is publicly announced that Thomas picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Anita can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thomas","Anita"],"index":712,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9865379333,"difficulty":0.0134620667}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deana does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Muriel can now know whether Caroline can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Caroline","Lizzie","Deana","Muriel"],"index":3377,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7567572594,"difficulty":1.7567572594}
-{"premise":"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 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 Rachel does not know whether Rachel's forehead is muddy.","smcdel_problem":"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) ] [ ! ~(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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Craig can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rachel","William","Craig"],"index":6898,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9706027508,"difficulty":0.0293972492}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether Candelaria's forehead is muddy. It is publicly announced that Helen knows whether someone's forehead is muddy. It is publicly announced that Helen's forehead is muddy.","smcdel_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 (1|2|3)) ] [ ! 2 ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Helen can now know that Candelaria can know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Candelaria","Helen","Cherly"],"index":6221,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9574591517,"difficulty":1.9574591517}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynda's card is shown to Charles. Brittany's card is shown to Charles. Lynda's card is shown to Merrill. Merrill's card is shown to Brittany. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Merrill can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Lynda","Merrill","Brittany"],"index":7289,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9815214276,"difficulty":0.0184785724}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ed can now know that Linda can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ed","Deborah","Linda"],"index":1850,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9870564938,"difficulty":0.0129435062}
-{"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 whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlene can now know that Russell can know whether Russell's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Russell","Charlene","Edmond"],"index":192,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8013547063,"difficulty":1.8013547063}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Eloisa. Donald's card is shown to Elissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eloisa can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Eloisa","Elissa"],"index":8958,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9887164831,"difficulty":0.0112835169}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Neville can now know whether Michael can know whether Mollie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Neville","Mollie","Louie","Michael"],"index":1364,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9820819497,"difficulty":0.0179180503}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows 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":"Brandon can now know whether John can know that Walter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Walter","John","Brandon"],"index":3627,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7139612436,"difficulty":0.2860387564}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Adam can now know that Elias's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adam","Howard","Elias","Emily"],"index":855,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9541775584,"difficulty":0.0458224416}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alisa knows whether Stella's forehead is muddy. It is publicly announced that Alisa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Donald can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alisa","Donald","Stella"],"index":6526,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.930416584,"difficulty":0.069583416}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Lydia. Lydia's card is shown to Howard. It is publicly announced that someone picked a red card. It is publicly announced that Howard does not know whether Howard picked a red card. It is publicly announced that Lydia knows whether Howard picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Lydia can now know that Howard can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lydia","Howard"],"index":3842,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9858533144,"difficulty":0.0141466856}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicholas does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"David can now know whether Janet can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicholas","David","Janet"],"index":4091,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9857769608,"difficulty":0.0142230392}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Nicholas can now know that Oscar can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Eva","Oscar","Nicholas"],"index":341,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8362844586,"difficulty":0.1637155414}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know whether Harry can know that Harry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harry","Williams","Helen","Effie"],"index":7889,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9370119572,"difficulty":0.0629880428}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Christopher can now know whether Andrew can know whether Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Andrew","Christopher"],"index":8268,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9820437431,"difficulty":1.9820437431}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Brian can now know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Robert","Jennifer","Brian"],"index":8938,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9733610153,"difficulty":0.0266389847}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ralph knows whether or not nobody is thirsty. It is publicly announced that Ralph is thirsty. It is publicly announced that Micah does not know whether Woodrow is thirsty. It is publicly announced that Micah does not know whether Woodrow is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Woodrow can now know that Woodrow is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Woodrow","Micah","Ralph"],"index":7530,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.94713521,"difficulty":0.05286479}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Corey can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Corey","Christina"],"index":5331,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9776212573,"difficulty":1.9776212573}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Terry does not know whether or not everyone is thirsty. It is publicly announced that Lawanda does not know whether or not everyone is thirsty. It is publicly announced that Judy does not know whether Irma is thirsty. It is publicly announced that Terry does not know whether Irma is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Judy can now know that Lawanda can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terry","Judy","Lawanda","Irma"],"index":6562,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.953355968,"difficulty":0.046644032}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Parker's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Karla can now know that Karla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Parker","Anita","John","Karla"],"index":5677,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9590357542,"difficulty":0.0409642458}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Kenneth. Carrie's card is shown to Kenneth. Carrie's card is shown to Evelyn. Fred's card is shown to Carrie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know that Fred can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Fred","Evelyn","Carrie"],"index":6632,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9816799164,"difficulty":0.0183200836}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Terry. Terry's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Mary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Terry can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Terry","Evelyn","Mary"],"index":9111,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9783802629,"difficulty":0.0216197371}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Nicholas. Michael's card is shown to Melissa. Lois's card is shown to Melissa. Melissa's card is shown to Lois. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Nicholas can now know whether Melissa can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Nicholas","Melissa","Lois"],"index":2449,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8663748503,"difficulty":1.8663748503}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earl knows whether Earl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Johnny","Earl","Sylvia","John"],"index":2408,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9877517223,"difficulty":0.0122482777}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Herbert does not know whether Derek is thirsty. It is publicly announced that Herbert does not know whether Derek is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Derek can now know whether Herbert can know whether Sandra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Derek","Sandra","Frank","Herbert"],"index":5553,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9343659878,"difficulty":0.0656340122}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Martin can now know that Billy can know that Martin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pauline","Jason","Martin","Billy"],"index":3884,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9728416204,"difficulty":0.0271583796}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy. It is publicly announced that Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Joseph can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arnold","Darin","Joseph"],"index":2989,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9782887697,"difficulty":0.0217112303}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esther's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Jonathan can now know that Mark can know whether Esther's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Esther","Mark","Jonathan"],"index":3538,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8895040751,"difficulty":0.1104959249}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows whether (Agentb knows that 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":"Rosa can now know whether Charles can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Charles","Dorothy","Rosa"],"index":4035,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8432587981,"difficulty":0.1567412019}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Maria. Jason's card is shown to Joey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Adam can now know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maria","Adam","Jason","Joey"],"index":5872,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.851072073,"difficulty":1.851072073}
-{"premise":"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 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 Gregory does not know 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) ] [ ! ~(Agenta 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gregory can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gregory","Kathy","Cynthia"],"index":3460,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9891642928,"difficulty":0.0108357072}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alexandria does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"William can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["William","Alexandria"],"index":8443,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9882048368,"difficulty":0.0117951632}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mindy's forehead is not muddy. It is publicly announced that Melvin knows whether Melvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mindy can now know whether Melvin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rufus","Melvin","Mindy","Lisa"],"index":1837,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9650789499,"difficulty":0.0349210501}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Edward. Billy's card is shown to Edward. Edward's card is shown to Billy. It is publicly announced that someone picked a red card. It is publicly announced that Billy picked a black card. It is publicly announced that Edward does not know whether Edward picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Edward can now know that Larry can know that Edward picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edward","Larry","Billy"],"index":7081,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9684643745,"difficulty":0.0315356255}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Cliff can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cliff","Steven"],"index":780,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8339297175,"difficulty":0.1660702825}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Jasmine can now know whether Thomas can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Jasmine"],"index":1666,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9817544818,"difficulty":0.0182455182}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 3)","n_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":"Joshua can now know that Joshua's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Connie","Michael","Joshua"],"index":8332,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9613221884,"difficulty":0.0386778116}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Joe can now know whether Eloise can know that Eloise's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joe","Eloise","Michael"],"index":2387,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9524902105,"difficulty":0.0475097895}
-{"premise":"There are three 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 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 3)","n_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":"Pearl can now know that Mitsuko can know whether Marco's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pearl","Mitsuko","Marco"],"index":5409,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8560497761,"difficulty":0.1439502239}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 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":"Margaret can now know that Joshua can know whether Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Joshua","Margaret"],"index":7899,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8535254002,"difficulty":0.1464745998}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelley's forehead is not muddy. It is publicly announced that Judy knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Susan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Judy","Kelley","Tomiko"],"index":9439,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.975323379,"difficulty":0.024676621}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Noble does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mary can now know whether John can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","John","Noble"],"index":5895,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9115384817,"difficulty":0.0884615183}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debbie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Debbie can now know whether Jason can know that Debbie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Debbie","Elinor","Jason"],"index":735,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8829901814,"difficulty":0.1170098186}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jill knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agenta knows that 3)","n_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":"Jill can now know whether Kristi can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kristi","Jill","John"],"index":2362,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.926195085,"difficulty":0.073804915}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jason knows whether Libby's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Libby can now know whether Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jason","Libby"],"index":9194,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9819303155,"difficulty":0.0180696845}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Janette. Patricia's card is shown to Adela. Janette's card is shown to Patricia. Adela's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eva can now know that Eva picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janette","Adela","Eva","Patricia"],"index":8604,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9546561241,"difficulty":0.0453438759}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Susan can now know that Sherry can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Susan","Sherry"],"index":6278,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9630583525,"difficulty":0.0369416475}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anna does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jose can now know that Anna can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anna","Megan","Jose","Patrick"],"index":4639,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.816259861,"difficulty":0.183740139}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael knows whether Michael is thirsty. It is publicly announced that Carolyn is thirsty. It is publicly announced that Michael is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] [ ! ~(1) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] [ ! ~(1) ] 0","hypothesis":"Stanley can now know whether Carolyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Stanley","Carolyn","Helen"],"index":764,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6192333698,"difficulty":0.3807666302}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steve knows whether Steve is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that Steve can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Steve","Mary"],"index":3701,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7549925447,"difficulty":0.2450074553}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josephine's card is shown to Lyle. Robert's card is shown to Lyle. Edgar's card is shown to Lyle. Robert's card is shown to Josephine. Edgar's card is shown to Josephine. Lyle's card is shown to Robert. Edgar's card is shown to Robert. Josephine's card is shown to Edgar. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Josephine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Robert can now know whether Josephine can know that Edgar picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lyle","Josephine","Robert","Edgar"],"index":241,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9601626396,"difficulty":0.0398373604}
-{"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 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":"Virginia can now know whether Stephanie can know whether Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Herbert","Virginia","Dorothy","Stephanie"],"index":6161,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9279174805,"difficulty":1.9279174805}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debbie's card is shown to Henry. Henry's card is shown to Debbie. It is publicly announced that someone picked a red card. It is publicly announced that Henry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that 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":"Debbie can now know that Henry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Henry","Debbie"],"index":4572,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9487515688,"difficulty":0.0512484312}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"James can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Frances","James"],"index":5042,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9877825379,"difficulty":0.0122174621}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gail knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Wayne can now know that Paul can know that Gail's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wayne","Gail","Paul","Ignacia"],"index":4864,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9659175873,"difficulty":0.0340824127}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terry can now know that Don can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Don","Terry","Darlene"],"index":2795,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9786431193,"difficulty":0.0213568807}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramon knows whether or not everyone's forehead is muddy. It is publicly announced that Jody does not know whether Jody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jody can now know that Ramon can know whether Ramon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Malissa","Jody","Ramon"],"index":6339,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7899347544,"difficulty":0.2100652456}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emily's card is shown to Ella. Roberta's card is shown to Ella. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emily can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Emily","Ella","Roberta","Ronald"],"index":6371,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9731442928,"difficulty":0.0268557072}
-{"premise":"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 Bert knows whether or not everyone's forehead is muddy. It is publicly announced that Bert does not know whether Bert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (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 (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Karen can now know whether Karen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Bert","Mary"],"index":8490,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9095389843,"difficulty":0.0904610157}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose does not know whether Terri is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Aaron can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Terri","Constance","Jose","Aaron"],"index":6428,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9803299904,"difficulty":0.0196700096}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edith does not know whether Donald is thirsty. It is publicly announced that Edith is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Charles can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Donald","Edith"],"index":2666,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9723703861,"difficulty":0.0276296139}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ginger can now know whether Jeanne can know whether Pamela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pamela","Vernon","Ginger","Jeanne"],"index":636,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8489355445,"difficulty":0.1510644555}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nathan is not thirsty. It is publicly announced that Nathan is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(2) ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Karen can now know that Kelvin can know whether Kelvin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelvin","Nathan","Karen"],"index":1687,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7020682693,"difficulty":1.7020682693}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Michael. Ryan's card is shown to Michael. Robert's card is shown to Michael. Michael's card is shown to Kimberly. Ryan's card is shown to Kimberly. Robert's card is shown to Kimberly. Michael's card is shown to Ryan. Robert's card is shown to Ryan. Ryan's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card. It is publicly announced that Kimberly does not know whether Kimberly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agentd knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Robert can now know that Ryan can know whether Kimberly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Kimberly","Ryan","Robert"],"index":765,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6263260841,"difficulty":1.6263260841}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know whether Duane can know whether Duane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Ronald","Duane"],"index":8040,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.981351912,"difficulty":0.018648088}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Kristine. Kristine's card is shown to Louann. Kristine's card is shown to Timothy. Louann's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Louann does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Kristine can now know that Louann can know whether Timothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kristine","Louann","Timothy"],"index":2334,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5618393421,"difficulty":1.5618393421}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Lois can now know that Samuel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Katie","Carlos","Lois","Samuel"],"index":4307,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9552032351,"difficulty":0.0447967649}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stella can now know whether Kevin can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cassie","Kevin","Stella","Kathleen"],"index":3020,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9896140695,"difficulty":0.0103859305}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Maurice is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Patricia can now know that Imelda can know that Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Maurice","Imelda","Joseph"],"index":270,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.970760107,"difficulty":0.029239893}
-{"premise":"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's forehead is muddy. It is publicly announced that Mike does not know whether Mike'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)","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":"Dwight can now know whether Mike can know that Mike's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mike","Dwight"],"index":6781,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8836496472,"difficulty":0.1163503528}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karon's card is shown to Jennifer. Jennifer's card is shown to Catherine. Karon's card is shown to Catherine. Jennifer's card is shown to Karon. Catherine's card is shown to Karon. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Karon does not know whether Karon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Catherine can now know that Jennifer can know whether Karon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Catherine","Karon"],"index":6603,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6665657759,"difficulty":0.3334342241}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Dorothy. James's card is shown to Dorothy. Kathleen's card is shown to Michael. Michael's card is shown to Kathleen. Michael's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Dorothy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dorothy","Michael","Kathleen","James"],"index":1383,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9880638719,"difficulty":0.0119361281}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ron's card is shown to Diane. Maria's card is shown to Diane. Diane's card is shown to Ron. Diane's card is shown to Maria. Ron's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ron can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diane","Ron","Maria"],"index":7398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9813388586,"difficulty":0.0186611414}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Keith knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Keith can now know that Craig can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Keith","Craig"],"index":5812,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6788814664,"difficulty":1.6788814664}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether someone's forehead is muddy. It is publicly announced that Catherine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"Sergio can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alvin","Catherine","Debra","Sergio"],"index":3618,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9819390178,"difficulty":0.0180609822}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jonathan can now know whether Nancy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicholas","Nancy","David","Jonathan"],"index":4179,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9806804061,"difficulty":0.0193195939}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Anna can now know that Pamela can know whether Pamela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Christopher","Anna","Pamela"],"index":3324,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9815373421,"difficulty":0.0184626579}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Ashley. Daryl's card is shown to Ashley. Daryl's card is shown to Michael. Ashley's card is shown to Daryl. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Daryl can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ashley","Michael","Daryl"],"index":1734,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5654886365,"difficulty":1.5654886365}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Tommie can now know that Chris can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tommie","Chris"],"index":1949,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9819975495,"difficulty":0.0180024505}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Audrey can now know whether Tyler can know whether Kathryn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathryn","Tyler","Audrey"],"index":5023,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9825789928,"difficulty":0.0174210072}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Daniel can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","David","Steven","Daniel"],"index":4600,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9312707186,"difficulty":0.0687292814}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carla knows whether Carla is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carla can now know that Robert can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carla","Robert"],"index":5133,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9870807528,"difficulty":0.0129192472}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know that Marilyn can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marilyn","Maria","James","Lynn"],"index":9048,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.978887856,"difficulty":0.021112144}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Rudolph. Ashely's card is shown to Shannon. Shannon's card is shown to Ashely. Lisa's card is shown to Ashely. It is publicly announced that someone picked a red card. It is publicly announced that Rudolph does not know whether Shannon picked a red card. It is publicly announced that Shannon does not know whether Shannon picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Rudolph does not know whether Ashely picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Rudolph can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rudolph","Shannon","Ashely","Lisa"],"index":8369,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9776582718,"difficulty":0.0223417282}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"George can now know that Jamie can know whether Jamie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jamie","George"],"index":1192,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9819263816,"difficulty":0.0180736184}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shawn can now know whether Kimberly can know whether Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shawn","Kimberly","Leonard"],"index":4682,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9809290767,"difficulty":0.0190709233}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia knows whether Charlie's forehead is muddy. It is publicly announced that Charlie knows whether Julia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Charlie can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julia","Charlie","Thomas"],"index":2398,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9171282649,"difficulty":0.0828717351}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan 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 Ryan does not know whether Ryan's forehead is muddy.","smcdel_problem":"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) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Geraldine can now know whether Geraldine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ryan","Geraldine","Gregory"],"index":1468,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9295312762,"difficulty":0.0704687238}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Dennis. Stephen's card is shown to Kenneth. Kenneth's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether Stephen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Dennis can now know that Kenneth can know whether Stephen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dennis","Kenneth","Stephen"],"index":4620,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.529671669,"difficulty":0.470328331}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Jeffrey can now know that Rosa can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Richard","Rosa","George"],"index":8405,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9777948856,"difficulty":0.0222051144}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chris does not know whether Calvin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Brian can now know whether Chris can know that Calvin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chris","Brian","Kristen","Calvin"],"index":3599,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8776883483,"difficulty":0.1223116517}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kristina can now know whether Dallas can know that Dallas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dallas","Kristina","Erin"],"index":7351,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9464564323,"difficulty":0.0535435677}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that David is not thirsty. It is publicly announced that Sandra does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Sandra can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","William","Dorothy","Sandra"],"index":1878,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9781905413,"difficulty":0.0218094587}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Cierra. Otis's card is shown to Cierra. Cierra's card is shown to Karen. Otis's card is shown to Mary. Cierra's card is shown to Otis. Mary's card is shown to Otis. It is publicly announced that someone picked a red card. It is publicly announced that Cierra knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (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:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Otis can now know that Cierra can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cierra","Karen","Mary","Otis"],"index":6732,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9524919391,"difficulty":0.0475080609}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shane's card is shown to Veronica. Veronica's card is shown to Shane. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Veronica can now know whether Shane can know whether Shane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Veronica","Shane"],"index":1563,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9457005858,"difficulty":0.0542994142}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Freddie. Freddie's card is shown to Elizabeth. Krystal's card is shown to Elizabeth. Freddie's card is shown to Krystal. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Krystal can now know that Freddie can know that Freddie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Freddie","Elizabeth","Krystal"],"index":7789,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9712821245,"difficulty":0.0287178755}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lana knows whether Elizabeth's forehead is muddy. It is publicly announced that Lana knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Lana can now know that Lana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lana","Kay","Elizabeth"],"index":3963,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8787643313,"difficulty":0.1212356687}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether Deidra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] (Agentc knows that 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 4) ] 0","hypothesis":"Cynthia can now know that Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eugene","Tenisha","Cynthia","Deidra"],"index":7266,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9496882558,"difficulty":0.0503117442}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth's forehead is not muddy. It is publicly announced that Jeffrey knows whether Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentb knows whether 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) ] [ ! ~(3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jeffrey can now know that Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Miriam","Jeffrey","Ruth","Herman"],"index":9099,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.948413372,"difficulty":1.948413372}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether someone's forehead is muddy.","smcdel_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":"Kenneth can now know that Albert can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Albert","Raymond","Kenneth"],"index":7564,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.988570869,"difficulty":0.011429131}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ross can now know whether Francis can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellen","Ross","Francis"],"index":5228,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9835538864,"difficulty":0.0164461136}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Megan knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Lisa can now know whether Megan can know that Megan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lisa","Megan"],"index":5562,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8842110038,"difficulty":0.1157889962}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW 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":"Michelle can now know whether Vanessa can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Robert","Vanessa","Kimberly"],"index":6544,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9855632782,"difficulty":0.0144367218}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Melissa. Melissa's card is shown to Benjamin. Ronald's card is shown to Benjamin. Benjamin's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ronald can now know that Benjamin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melissa","Benjamin","Ronald"],"index":8746,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9815480709,"difficulty":0.0184519291}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Kimberly. Ron's card is shown to Kimberly. Kimberly's card is shown to Thomas. Ron's card is shown to Madeline. Kimberly's card is shown to Ron. Madeline's card is shown to Ron. It is publicly announced that someone picked a red card. It is publicly announced that Kimberly knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] Agentd knows that (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Ron can now know that Kimberly can know whether Ron picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Thomas","Madeline","Ron"],"index":1095,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9575792551,"difficulty":0.0424207449}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Marcia. Marcia's card is shown to Joseph. Joseph's card is shown to Leland. It is publicly announced that someone picked a red card. It is publicly announced that Leland does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know whether Marcia can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marcia","Joseph","Leland"],"index":3149,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9894233346,"difficulty":0.0105766654}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Tamara can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Sherie","Tamara"],"index":4562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9795423746,"difficulty":0.0204576254}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 1)","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":"Sandy can now know that Peter's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Peter","Sandy"],"index":237,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9419521689,"difficulty":0.0580478311}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ross does not know whether Edward is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Edward can now know whether Ross is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Ross","Edward","Jody"],"index":4057,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8998326659,"difficulty":0.1001673341}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Keith does not know whether or not everyone is thirsty. It is publicly announced that James knows whether James is thirsty. It is publicly announced that Hector does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Keith can now know that Yvonne can know that Keith is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hector","Keith","James","Yvonne"],"index":7454,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9690167904,"difficulty":1.9690167904}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Michael can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Steven","Michael","Jane"],"index":8315,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8391721249,"difficulty":0.1608278751}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Elmer. Diane's card is shown to Dawn. Dawn's card is shown to Diane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Diane can now know that Elmer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elmer","Dawn","Diane","Andrew"],"index":3480,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9509994388,"difficulty":0.0490005612}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina's forehead is muddy. It is publicly announced that 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 ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Tina can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Tina"],"index":7895,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9750695229,"difficulty":0.0249304771}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Robert can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Kristen","Elizabeth"],"index":1590,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9844113588,"difficulty":0.0155886412}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Stephen can now know whether Johnny can know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnny","Stephen","Harold","Linda"],"index":7921,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9865793586,"difficulty":0.0134206414}
-{"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 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":"Laura can now know that Kenneth can know that Erik's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Tonya","Erik","Laura"],"index":1041,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9714639783,"difficulty":0.0285360217}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Allen can now know that Brenda can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stella","Brenda","Allen"],"index":8831,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.987406671,"difficulty":0.012593329}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether someone's forehead is muddy.","smcdel_problem":"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)","n_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":"Donald can now know whether Justin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Justin","Doris","Donald"],"index":7316,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.971356988,"difficulty":0.028643012}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know whether James can know that Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Katherine","James","Jeanette"],"index":2717,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8718019128,"difficulty":0.1281980872}
-{"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 (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":"Mildred can now know that James can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Myrtle","James","Pamela","Mildred"],"index":1133,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9870958328,"difficulty":0.0129041672}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Geraldine can now know that Maria can know whether Geraldine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","William","Geraldine","Louis"],"index":3057,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9757644534,"difficulty":0.0242355466}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willis knows whether someone's forehead is muddy. It is publicly announced that Holly knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Dorothy can now know that Willis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Holly","Dorothy","Willis","Guadalupe"],"index":295,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9321067929,"difficulty":0.0678932071}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","David"],"index":394,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9709739685,"difficulty":0.0290260315}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sylvia's card is shown to John. George's card is shown to John. Linda's card is shown to Sylvia. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether George picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"John can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","John","Sylvia","George"],"index":9626,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9727056026,"difficulty":0.0272943974}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Edgar does not know whether Wayne is thirsty. It is publicly announced that Chrystal does not know whether Wayne is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Wayne can now know that Glenda can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chrystal","Wayne","Glenda","Edgar"],"index":105,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9648824334,"difficulty":0.0351175666}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dottie knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Timothy can now know whether Dottie can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Dottie","Timothy","Aimee"],"index":4498,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9743484259,"difficulty":0.0256515741}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miguel knows whether Debora's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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) ] 0","hypothesis":"Debora can now know whether Edward can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debora","Miguel","Edward","Jorge"],"index":726,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9885801673,"difficulty":0.0114198327}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Keith knows whether Keith is thirsty. It is publicly announced that Christina is thirsty. It is publicly announced that Keith is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] [ ! ~(1) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] [ ! ~(1) ] 0","hypothesis":"Cheryl can now know whether Keith is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Keith","Cheryl","Christina","Mauro"],"index":9314,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5563537478,"difficulty":0.4436462522}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caterina's card is shown to James. John's card is shown to James. James's card is shown to Caterina. John's card is shown to Caterina. It is publicly announced that someone picked a red card. It is publicly announced that Caterina does not know whether Caterina picked a red card. It is publicly announced that James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Caterina can now know that James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Caterina","John"],"index":8910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9743902087,"difficulty":0.0256097913}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Mary can now know whether Ann can know whether Ann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Mary","Ann","Edward"],"index":2297,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9852870703,"difficulty":0.0147129297}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Rosa can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pamela","Rosa","James"],"index":4941,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9746679068,"difficulty":0.0253320932}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judy does not know whether Michael is thirsty. It is publicly announced that Deanna does not know whether Aaron is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Judy can now know that Michael can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deanna","Judy","Michael","Aaron"],"index":8029,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9787114263,"difficulty":0.0212885737}
-{"premise":"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 Steven knows whether Florence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 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) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Joel can now know that Steven can know that Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florence","David","Steven","Joel"],"index":286,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9640907049,"difficulty":0.0359092951}
-{"premise":"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 John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kari can now know that Virginia can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Virginia","Kari","James"],"index":7927,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9871195555,"difficulty":0.0128804445}
-{"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)","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":"Adrian can now know whether Mae can know whether Mildred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mildred","Adrian","Fermin","Mae"],"index":6571,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9501043558,"difficulty":0.0498956442}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Leola can now know whether Constance can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Yvonne","Leola","Constance"],"index":4124,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9883279204,"difficulty":0.0116720796}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karl knows whether Michael's forehead is muddy. It is publicly announced that Phillip's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] [ ! ~(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) ] [ ! (Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Phillip can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","Karl","Michael","Phillip"],"index":2300,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9787142873,"difficulty":0.0212857127}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrew can now know that Donna can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donna","Jason","Cynthia","Andrew"],"index":6397,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9322984815,"difficulty":0.0677015185}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Mary. Mary's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Mary can now know that Laura can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Laura"],"index":1211,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9701554179,"difficulty":0.0298445821}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Michael. Michael's card is shown to Wayne. Orval's card is shown to Wayne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Orval can now know whether Michael can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Orval","Wayne"],"index":3506,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8872253895,"difficulty":0.1127746105}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clelia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Kristi can now know that Clelia can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clelia","Michelle","Kristi"],"index":3039,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.7142352462,"difficulty":0.2857647538}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Rosa can now know whether Anne can know that Anne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Anne","Rosa"],"index":5629,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8709656596,"difficulty":1.8709656596}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Shelia can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shelia","David","Steven"],"index":3468,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9590328932,"difficulty":0.0409671068}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether Jane can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jane","Richard","Dorothy"],"index":2742,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9673432112,"difficulty":0.0326567888}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacy does not know whether or not everyone is thirsty. It is publicly announced that Franklin does not know whether Melanie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Franklin can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stacy","Franklin","Mark","Melanie"],"index":4719,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9875417352,"difficulty":0.0124582648}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Larry can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Larry","Amanda"],"index":1683,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9887048602,"difficulty":0.0112951398}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Linda can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wanda","Linda","Nathan","Ruth"],"index":4987,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9804852009,"difficulty":0.0195147991}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Allison is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mary can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Allison","James","Mary"],"index":3949,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9733641744,"difficulty":0.0266358256}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether Donna's forehead is muddy. It is publicly announced that Donna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Donna can now know that Mario's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laurie","Mario","Donna"],"index":4271,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.945622623,"difficulty":0.054377377}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heidi is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Patti can now know whether Dorthy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Patti","Dorthy","Heidi"],"index":8795,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9819227457,"difficulty":0.0180772543}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernice knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bernice","Robert"],"index":5876,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9788503051,"difficulty":0.0211496949}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Susan can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Susan","Roger"],"index":867,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9775286317,"difficulty":0.0224713683}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Janet. Janet's card is shown to Cheryl. Paul's card is shown to Cheryl. Jimmy's card is shown to Cheryl. Janet's card is shown to Paul. Cheryl's card is shown to Jimmy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cheryl can now know whether Janet can know that Janet picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janet","Cheryl","Paul","Jimmy"],"index":4875,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8959568143,"difficulty":0.1040431857}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bruce does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Bruce can now know that Bruce is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ebony","Bruce"],"index":5513,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9571166635,"difficulty":1.9571166635}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Bobby can now know that John can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Harry","Erik","Bobby"],"index":4281,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7528411746,"difficulty":1.7528411746}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeff's card is shown to Alyssa. Thomas's card is shown to Alyssa. Jeff's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alyssa can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeff","Alyssa","Thomas"],"index":8686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9879585505,"difficulty":0.0120414495}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathleen does not know whether Vonda is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kathleen can now know whether Kathleen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vonda","Kathleen"],"index":1936,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8687078357,"difficulty":1.8687078357}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Gladys can now know that Carol can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gladys","Carol"],"index":8720,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9798588753,"difficulty":0.0201411247}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Christina can now know that Juan can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Juan","Christina"],"index":6730,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.984351635,"difficulty":0.015648365}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Beatrice does not know whether Joshua is thirsty. It is publicly announced that Joshua does not know whether or not everyone is thirsty. It is publicly announced that Joshua does not know whether Beatrice is thirsty. It is publicly announced that Beatrice is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(4) ] 0","hypothesis":"Beatrice can now know that Sabrina can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Damion","Sabrina","Joshua","Beatrice"],"index":4632,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9777040482,"difficulty":0.0222959518}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward does not know whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Edward can now know whether Pamela can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Esther","Linda","Edward","Pamela"],"index":4138,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9866906404,"difficulty":0.0133093596}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Dorothea. Dorothea's card is shown to Donna. David's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothea can now know that Donna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothea","David","Donna"],"index":8189,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.954228878,"difficulty":0.045771122}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Trenton knows whether someone's forehead is muddy. It is publicly announced that Holly knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Holly","William","Trenton","Troy"],"index":6692,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9645709395,"difficulty":0.0354290605}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margarete's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Cynthia can now know that Margarete can know that Margarete's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Margarete","Cynthia"],"index":5290,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9705256224,"difficulty":0.0294743776}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alton's card is shown to Daniel. Daniel's card is shown to Alton. Daniel's card is shown to Bryan. Alton's card is shown to Bryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Daniel can now know that Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","Alton","Bryan"],"index":1689,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9567149878,"difficulty":0.0432850122}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Billy does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Kristy can now know whether Billy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristy","Billy","Charles"],"index":6257,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.871989131,"difficulty":0.128010869}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Stacie. Patricia's card is shown to Stacie. Stacie's card is shown to Sharon. Patricia's card is shown to Joshua. Stacie's card is shown to Patricia. Joshua's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Stacie knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Sharon can now know whether Joshua can know whether Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stacie","Sharon","Joshua","Patricia"],"index":3932,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9766228199,"difficulty":0.0233771801}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Janice can now know that Joseph can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Janice","Joseph"],"index":4807,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9746755958,"difficulty":0.0253244042}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelo's card is shown to Elizabeth. Elizabeth's card is shown to Patricia. Edna's card is shown to Angelo. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Edna picked a red card. It is publicly announced that Edna knows whether or not nobody picked a red card. It is publicly announced that Elizabeth does not know whether Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Patricia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Edna","Patricia","Angelo"],"index":8589,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9425150156,"difficulty":0.0574849844}
-{"premise":"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 Leonard's forehead is muddy.","smcdel_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":"Lena can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amy","Lena","Leonard"],"index":2757,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9742212296,"difficulty":0.0257787704}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hannah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 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":"Brent can now know whether Hannah can know whether Hannah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alma","Hannah","Brian","Brent"],"index":458,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9596586227,"difficulty":0.0403413773}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred's forehead is muddy. It is publicly announced that Fred's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Marybeth can now know whether Marybeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marybeth","Tammy","Fred"],"index":9114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9574129581,"difficulty":0.0425870419}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dawn is thirsty. It is publicly announced that Dawn does not know whether Monica is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jason can now know whether Monica can know whether Jason is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ann","Monica","Dawn","Jason"],"index":9119,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9099959135,"difficulty":0.0900040865}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Danny can now know that Jennifer can know that Danny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Walter","Jennifer","Danny"],"index":8494,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9725964069,"difficulty":0.0274035931}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theresa does not know whether Paul is thirsty. It is publicly announced that Paul is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Theresa can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Theresa","Paul"],"index":7460,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9756934047,"difficulty":0.0243065953}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is not thirsty. It is publicly announced that Christie is not thirsty. It is publicly announced that James does not know whether Adeline is thirsty. It is publicly announced that Adeline knows whether Adeline is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Adeline can now know that Ana can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ana","James","Christie","Adeline"],"index":9032,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7538733482,"difficulty":1.7538733482}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Amy can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olga","Amy","Neal","Michael"],"index":2436,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9347011447,"difficulty":0.0652988553}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Armando can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Armando","Amy","Ross"],"index":5527,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9898501635,"difficulty":0.0101498365}
-{"premise":"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 Soledad knows whether Shawna's forehead is muddy. It is publicly announced that Soledad knows whether Jacob's forehead is muddy.","smcdel_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) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Soledad can now know that Soledad's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jacob","Soledad","Shawna"],"index":1766,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9321015477,"difficulty":0.0678984523}
-{"premise":"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 Andrea's forehead is muddy. It is publicly announced that Matthew does not know whether Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Andrea can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Andrea","Ray"],"index":8356,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5850313902,"difficulty":1.5850313902}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Jason. Jason's card is shown to Sonia. Margaret's card is shown to Sonia. Kevin's card is shown to Sonia. Jason's card is shown to Margaret. Sonia's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jason can now know whether Sonia can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Sonia","Margaret","Kevin"],"index":7974,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9897453189,"difficulty":0.0102546811}
-{"premise":"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 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) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Winifred can now know that Charles can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charles","Winifred"],"index":8821,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.927231431,"difficulty":0.072768569}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Adrian. Adrian's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Virginia knows whether Adrian picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Virginia can now know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Adrian","Virginia"],"index":6740,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7890818119,"difficulty":0.2109181881}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carol","Richard"],"index":1586,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9772601724,"difficulty":0.0227398276}
-{"premise":"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 whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Demetria can now know whether Myrna can know whether Myrna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Myrna","Demetria"],"index":3882,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9736775756,"difficulty":1.9736775756}
-{"premise":"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 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 (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":"Dirk can now know that Kenneth can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dirk","Kenneth","Alfred"],"index":3393,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9882235527,"difficulty":0.0117764473}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 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":"Delbert can now know whether Claude can know that Delbert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolina","Claude","Rachel","Delbert"],"index":4047,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7060115933,"difficulty":1.7060115933}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Paul does not know whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 2) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Laura can now know whether Aaron can know that Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laura","Paul","Aaron"],"index":6770,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8863845468,"difficulty":0.1136154532}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Loretta knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ashley can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ashley","Loretta","Trent","Michelle"],"index":5548,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8268458843,"difficulty":1.8268458843}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Steven can now know that Antonio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sarah","Steven","Antonio","Stephen"],"index":5914,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9526967406,"difficulty":0.0473032594}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andre knows whether Andre's forehead is muddy. It is publicly announced that Andre's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Andre can now know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Duane","Andre"],"index":5078,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9780848026,"difficulty":0.0219151974}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Earline does not know whether Jenny is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Bernard can now know whether Jenny can know that Earline is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earline","Latisha","Bernard","Jenny"],"index":8611,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8839800954,"difficulty":0.1160199046}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Nicole can now know whether Terrence can know that Nicole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Terrence","Nicole"],"index":1340,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9413875937,"difficulty":0.0586124063}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edward can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Douglas","Abbey","Leisa","Edward"],"index":6464,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9354348183,"difficulty":0.0645651817}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Delia can now know whether Agnes can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Delia","Juanita","Agnes"],"index":2412,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9883737564,"difficulty":0.0116262436}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alyssa's card is shown to Ronald. Ronald's card is shown to William. Ronald's card is shown to Charlie. Alyssa's card is shown to Charlie. Ronald's card is shown to Alyssa. William's card is shown to Alyssa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Alyssa can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","William","Charlie","Alyssa"],"index":4596,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8873159885,"difficulty":1.8873159885}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Heath is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Irene can now know whether Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Heath","Mary","Irene"],"index":7803,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7240957022,"difficulty":1.7240957022}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shirley can now know whether Joyce can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Joyce","Robert"],"index":5426,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9552441239,"difficulty":0.0447558761}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin knows whether Sharlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Benjamin can now know that Jesus can know whether Jesus's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Benjamin","Julie","Sharlene","Jesus"],"index":3086,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9553058743,"difficulty":0.0446941257}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Jean is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Jo can now know whether William can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Jean","Jo"],"index":8880,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9875291586,"difficulty":0.0124708414}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that Brian can know that Sanford's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Sanford","Brian"],"index":4129,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9739547372,"difficulty":0.0260452628}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Casey. Casey's card is shown to Andrea. Philip's card is shown to Andrea. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Philip can now know whether Casey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Casey","Philip","Andrea"],"index":1595,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6417647004,"difficulty":0.3582352996}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"James can now know whether Kyle can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kyle","James"],"index":7797,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9325966239,"difficulty":0.0674033761}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Dianne can now know that Dianne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dianne","Anthony"],"index":7671,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9640359282,"difficulty":0.0359640718}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott is thirsty. It is publicly announced that Virginia knows whether someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Samuel does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Samuel can now know whether Virginia can know that Virginia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Virginia","Samuel","Scott"],"index":5032,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9599655271,"difficulty":1.9599655271}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Vernon 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":["James","Glenn","Anna","Vernon"],"index":95,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8624891043,"difficulty":0.1375108957}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fannie's card is shown to Eddie. Jamie's card is shown to Eddie. Jamie's card is shown to Fannie. Eddie's card is shown to Jamie. It is publicly announced that someone picked a red card. It is publicly announced that Jamie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Fannie can now know whether Eddie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eddie","Fannie","Jamie"],"index":8678,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5466778278,"difficulty":0.4533221722}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Leslie can now know whether Heath can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leslie","Heath"],"index":4722,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9088732004,"difficulty":0.0911267996}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Gary. Ann's card is shown to Maria. Gary's card is shown to Ann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know whether Gary can know whether Maria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Maria","Ann"],"index":1447,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9005616903,"difficulty":0.0994383097}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Dustin. Dustin's card is shown to Pauline. Dustin's card is shown to Patricia. Robert's card is shown to Patricia. Dustin's card is shown to Robert. Pauline's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Pauline can know that Pauline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dustin","Pauline","Patricia","Robert"],"index":2893,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9716290236,"difficulty":0.0283709764}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cornelia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Linda can now know that Camila can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Cornelia","Camila","Joe"],"index":4935,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9769118428,"difficulty":0.0230881572}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clelia can now know that Robin can know whether Numbers is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tomas","Clelia","Numbers","Robin"],"index":9363,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8656140566,"difficulty":0.1343859434}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Loretta can now know that Jimmie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jimmie","Loretta","Lillian"],"index":1654,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9469385743,"difficulty":0.0530614257}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Douglas is thirsty. It is publicly announced that Douglas is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that John does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"John can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Douglas","Nancy","John","Richard"],"index":7365,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9597804546,"difficulty":0.0402195454}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tony can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Raymond","Tony"],"index":2906,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9778757095,"difficulty":0.0221242905}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (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":"Mark can now know that Angel can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Angel","Larry","Clifford"],"index":4558,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9866734743,"difficulty":0.0133265257}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Katherine can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brendan","Katherine","Michael"],"index":8469,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9879948497,"difficulty":0.0120051503}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentd knows whether 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":"Donna can now know whether Jim's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Jim","Linda","Donna"],"index":8395,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9355658293,"difficulty":0.0644341707}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Betty can now know whether Buck can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Stella","Buck"],"index":4070,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9096176624,"difficulty":0.0903823376}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows whether (Agentc knows 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":"Delmar can now know whether Jerry can know that Jerry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Delmar","Raymond","Jerry"],"index":8448,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8307699561,"difficulty":0.1692300439}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Meredith's card is shown to Robert. Lee's card is shown to Robert. Robert's card is shown to Meredith. Pam's card is shown to Meredith. Robert's card is shown to Lee. Meredith's card is shown to Lee. Robert's card is shown to Pam. Meredith's card is shown to Pam. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Pam picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Lee can now know that Pam can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Meredith","Lee","Pam"],"index":216,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.972556591,"difficulty":0.027443409}
-{"premise":"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 muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Rachel can now know that Karen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Millie","Lindsey","Rachel"],"index":9266,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9551995397,"difficulty":1.9551995397}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Lynda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"John can now know whether Lynda can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Melissa","Lynda","Victoria"],"index":4455,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9861153364,"difficulty":0.0138846636}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nadia knows whether Marshall's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Nadia can now know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marshall","Nadia","Daniel","Elmer"],"index":6176,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9527434707,"difficulty":0.0472565293}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eddie does not know whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Barbara can now know that Eddie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adrian","Barbara","Eddie"],"index":3704,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9712786078,"difficulty":0.0287213922}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Patsy. Manuel's card is shown to Patsy. Patsy's card is shown to Manuel. Patsy's card is shown to Eugene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Albert can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patsy","Albert","Manuel","Eugene"],"index":91,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8854140043,"difficulty":0.1145859957}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Byron knows whether Colleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Andrea can now know that Byron can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Colleen","Byron","Andrea","Alexander"],"index":3721,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9736402631,"difficulty":0.0263597369}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Walter. Walter's card is shown to Edward. Willie's card is shown to Edward. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Walter can now know whether Willie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Walter","Edward","Willie"],"index":5087,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8414080143,"difficulty":0.1585919857}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie knows whether Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Bobby can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Connie","Joseph","Terry","Bobby"],"index":1205,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9748441577,"difficulty":0.0251558423}
-{"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 (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":"Diana can now know that Bonita can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bonita","Diana","Sharon","Carolyn"],"index":2514,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9787389636,"difficulty":0.0212610364}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Courtney. Nancy's card is shown to Courtney. David's card is shown to Adam. Courtney's card is shown to Nancy. Courtney's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Courtney knows whether or not everyone picked a red card. It is publicly announced that David knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Nancy can now know that Adam can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Courtney","Adam","Nancy","David"],"index":8550,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9802952409,"difficulty":0.0197047591}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Billy. Billy's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether (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":"Billy can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Billy","Michael"],"index":1294,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9879351854,"difficulty":0.0120648146}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Jeff. Sarah's card is shown to Jeff. Sarah's card is shown to Sheila. Jeff's card is shown to Sarah. Sheila's card is shown to Sarah. Jeff's card is shown to Jon. It is publicly announced that someone picked a red card. It is publicly announced that Jon knows whether someone picked a red card. It is publicly announced that Sarah does not know whether Sarah picked a red card. It is publicly announced that Sarah knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Sarah can now know that Sheila can know whether Sheila picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeff","Sheila","Sarah","Jon"],"index":6847,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6505855322,"difficulty":1.6505855322}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeannie's card is shown to Kurt. Sharleen's card is shown to Ronald. Kurt's card is shown to Jeannie. Sharleen's card is shown to Jeannie. Ronald's card is shown to Sharleen. Jeannie's card is shown to Sharleen. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jeannie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kurt","Ronald","Jeannie","Sharleen"],"index":3146,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9740600586,"difficulty":0.0259399414}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Lisa. Lisa's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Karen knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether (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":"Karen can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lisa","Karen"],"index":6399,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9891222119,"difficulty":0.0108777881}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samuel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Samuel can now know that Katrina can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Samuel","Katrina","Dolores"],"index":8891,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9788609147,"difficulty":0.0211390853}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hilde's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Rose can now know that Rose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Rose","Pedro","Hilde"],"index":2667,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9568295479,"difficulty":0.0431704521}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Richard. Daniel's card is shown to Linda. Richard's card is shown to Daniel. Linda's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb: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:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Linda can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Linda","Daniel"],"index":8228,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9516335726,"difficulty":0.0483664274}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Micheal does not know whether Micheal's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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)) ] Agentb knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Micheal can now know that Donald can know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Micheal","William","Donald"],"index":869,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7342785001,"difficulty":1.7342785001}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vivian knows whether Corey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Sandra can now know that Corey can know that Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vivian","Christopher","Corey","Sandra"],"index":7882,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9668236971,"difficulty":0.0331763029}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Robert. William's card is shown to Dee. William's card is shown to Elaine. It is publicly announced that someone picked a red card. It is publicly announced that Dee does not know whether Dee picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"William can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Robert","Dee","Elaine"],"index":5945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9728338122,"difficulty":0.0271661878}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Lorenza can now know that Peggy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peggy","Stacy","Lorenza"],"index":2243,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9116451144,"difficulty":0.0883548856}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jake's card is shown to Alison. Jake's card is shown to Dennis. Yolanda's card is shown to Dennis. Yolanda's card is shown to Jake. Alison's card is shown to Yolanda. Jake's card is shown to Yolanda. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Yolanda does not know whether Dennis picked a red card. It is publicly announced that Alison does not know whether Dennis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dennis can now know that Alison can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alison","Dennis","Jake","Yolanda"],"index":3479,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9858773947,"difficulty":0.0141226053}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Stella can now know that Stella's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jack","Stella"],"index":5583,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9593756795,"difficulty":0.0406243205}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Jim. Steve's card is shown to Michael. Michael's card is shown to Steve. Michael's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Donna picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Donna can now know that Steve picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jim","Michael","Steve","Donna"],"index":8737,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9528250694,"difficulty":0.0471749306}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Juan can now know that Tim can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tim","Juan","Jacob"],"index":6465,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9877259135,"difficulty":0.0122740865}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy's forehead is muddy. It is publicly announced that Troy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Kenneth can now know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Stephanie","Troy"],"index":2167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9525053501,"difficulty":0.0474946499}
-{"premise":"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 knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentb knows 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":"David can now know whether Christopher can know that Vernon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Christopher","Vernon"],"index":6891,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8683125973,"difficulty":0.1316874027}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Dennis is thirsty. It is publicly announced that Linda knows whether or not nobody is thirsty. It is publicly announced that David does not know whether Linda is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Emily can now know that Linda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Emily","David","Dennis","Linda"],"index":488,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9323992729,"difficulty":0.0676007271}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juanita can now know that Maria can know that Juanita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Juanita","Alex","William"],"index":5082,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9741780162,"difficulty":0.0258219838}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paulette can now know that Jason can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Constance","Jason","Dorothy","Paulette"],"index":7686,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9794685245,"difficulty":0.0205314755}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerry knows whether someone's forehead is muddy. It is publicly announced that Doris knows whether Melvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Melvin can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Doris","Melvin","Kerry","Joseph"],"index":3421,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9228690267,"difficulty":0.0771309733}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isabell does not know whether Helen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Bruce can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Isabell","Carissa","Helen","Bruce"],"index":3525,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8830877542,"difficulty":0.1169122458}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Liliana knows whether Stella's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Liliana can now know that Wilma can know that Gloria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Wilma","Liliana","Stella"],"index":6999,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9655478001,"difficulty":0.0344521999}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Curtis does not know whether Herbert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Mark can now know whether Mark is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","Curtis","Herbert","Eric"],"index":1313,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8984590173,"difficulty":1.8984590173}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sidney knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Sidney can now know whether Steve's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sidney","Steve"],"index":8902,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9861140847,"difficulty":0.0138859153}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bonnie does not know whether Howard is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Hazel can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hazel","Bonnie","Howard"],"index":143,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9872271419,"difficulty":0.0127728581}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Kelly can now know that Viola can know that Viola's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stacey","Richard","Viola","Kelly"],"index":6967,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9660209417,"difficulty":0.0339790583}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is thirsty. It is publicly announced that David does not know whether Doug is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Michael can now know that David can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Doug","David","Aaron"],"index":247,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9855258465,"difficulty":0.0144741535}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Minnie can now know whether Dustin can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dustin","James","Minnie"],"index":3790,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8728337884,"difficulty":0.1271662116}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Tamica can now know whether Vicki's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tamica","Vicki","Kent","Laura"],"index":8338,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9857712984,"difficulty":0.0142287016}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy knows whether someone is thirsty. It is publicly announced that Timothy does not know whether John is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Timothy can now know whether John can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Timothy","John"],"index":5642,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9868810177,"difficulty":0.0131189823}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Michael. Gary's card is shown to Mary. Michael's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Mary","Gary"],"index":1646,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9716381431,"difficulty":0.0283618569}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Shyla is not thirsty. It is publicly announced that Mary does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Mary can now know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shyla","Elizabeth","Nicole","Mary"],"index":6529,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9580672383,"difficulty":0.0419327617}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (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":"Tammy can now know whether Victor can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Tammy","Victor"],"index":1908,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8905556202,"difficulty":0.1094443798}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Betty can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olive","James","Betty","Constance"],"index":4785,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9870095253,"difficulty":0.0129904747}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","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":"Michael can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Barbara"],"index":2918,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9759830236,"difficulty":0.0240169764}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Terri. Karen's card is shown to Todd. Todd's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Todd knows whether someone picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card. It is publicly announced that Karen knows whether or not nobody picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know that Todd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Terri","Todd","Karen"],"index":7383,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8975465894,"difficulty":1.8975465894}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Joe. Chris's card is shown to William. Joe's card is shown to Chris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joe can now know that William can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joe","William","Chris"],"index":5799,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9820603132,"difficulty":0.0179396868}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Michael can now know that Ann can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Ann"],"index":5910,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9793455601,"difficulty":0.0206544399}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori knows whether Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Beatrice can now know that Lori can know that Lori's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frances","Patricia","Lori","Beatrice"],"index":4227,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9685634375,"difficulty":0.0314365625}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy. It is publicly announced that Janette knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Janette can now know that Maurice can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maurice","Joseph","Janette"],"index":9280,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9658335447,"difficulty":1.9658335447}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ashley does not know whether Martin is thirsty. It is publicly announced that Daniel is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Ashley can now know that Martin can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Ashley","Martin"],"index":695,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9775811434,"difficulty":0.0224188566}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine knows whether someone's forehead is muddy. It is publicly announced that George knows whether Roy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Roy can now know that Flora's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Roy","Katherine","Flora"],"index":2422,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9289554358,"difficulty":0.0710445642}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to David. David's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Michael","Jesus"],"index":3593,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9753072858,"difficulty":0.0246927142}
-{"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 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Freda","Jean","Laura"],"index":5218,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.92509377,"difficulty":1.92509377}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Shannon. Sherry's card is shown to Shannon. Shannon's card is shown to Luke. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shannon can now know whether Shannon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shannon","Luke","Wanda","Sherry"],"index":8037,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8455911279,"difficulty":0.1544088721}
-{"premise":"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's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Deborah can now know that Richard can know whether Deborah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Deborah"],"index":180,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7858303189,"difficulty":0.2141696811}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Pablo. Pablo's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Pablo does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether 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":"Michael can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Pablo","Michael"],"index":5682,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5589279532,"difficulty":1.5589279532}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stella's card is shown to Josiah. Stella's card is shown to James. Josiah's card is shown to Stella. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Josiah can now know that James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Josiah","James","Stella"],"index":7157,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9777255058,"difficulty":0.0222744942}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pearl does not know whether Rick is thirsty. It is publicly announced that Rick does not know whether Timothy is thirsty. It is publicly announced that Pearl is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Timothy can now know whether Eugene can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Pearl","Eugene","Rick"],"index":6691,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9843459725,"difficulty":0.0156540275}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy does not know whether Bryon is thirsty. It is publicly announced that Amy does not know whether Bryon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Rosemary can now know whether William can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bryon","William","Rosemary","Amy"],"index":4955,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9090020061,"difficulty":0.0909979939}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valorie's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Donald can now know whether Valorie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Valorie","Donald"],"index":9490,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9715490341,"difficulty":0.0284509659}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Kathryn can now know that Richard can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Kathryn"],"index":9109,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.989038825,"difficulty":0.010961175}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Taren knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (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":"Heather can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Heather","Taren"],"index":4530,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9454013109,"difficulty":0.0545986891}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Lucille can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lucille","Joe","Patricia"],"index":9569,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9900639653,"difficulty":0.0099360347}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Leslie. James's card is shown to Andrew. James's card is shown to Brian. Brian's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Leslie can now know that Andrew can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leslie","Andrew","Brian","James"],"index":7394,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.617678225,"difficulty":0.382321775}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernard does not know whether or not everyone's forehead is muddy. It is publicly announced that Bernard does not know whether or not everyone's forehead is muddy. It is publicly announced that Steven knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (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) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Bernard can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Steven","Bernard"],"index":82,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9726301432,"difficulty":0.0273698568}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debora does not know whether Kimberly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Debora can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Debora","Alberto","Kimberly"],"index":499,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.865296483,"difficulty":0.134703517}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daryl does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Sara can now know that Daryl can know whether Gregory is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daryl","Gregory","Sara"],"index":6353,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8181777,"difficulty":0.1818223}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Mary can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","James"],"index":6866,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9806526899,"difficulty":0.0193473101}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alex is not thirsty. It is publicly announced that Kristopher does not know whether Sandra is thirsty. It is publicly announced that Mark does not know whether Sandra is thirsty. It is publicly announced that Kristopher is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] Agentd knows that (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] 0","hypothesis":"Mark can now know that Alex can know whether Sandra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alex","Kristopher","Sandra","Mark"],"index":1685,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.676597774,"difficulty":0.323402226}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"George can now know that Barbara can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barbara","George"],"index":4238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9789056778,"difficulty":0.0210943222}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Charles. Barbara's card is shown to Ann. Charles's card is shown to Barbara. Charles's card is shown to Virginia. Ann's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Virginia does not know whether Barbara picked a red card. It is publicly announced that Barbara does not know whether Barbara picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ann can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Ann","Barbara","Virginia"],"index":4636,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9875739217,"difficulty":0.0124260783}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby does not know whether or not everyone's forehead is muddy.","smcdel_problem":"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":"Mark can now know that Jeffrey can know that Bobby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bobby","Mark","Jeffrey"],"index":655,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9662032127,"difficulty":0.0337967873}
-{"premise":"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 John knows whether Steven's forehead is muddy. It is publicly announced that John knows whether Shanna's forehead is muddy.","smcdel_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) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Shanna can now know whether Shanna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shanna","John","Steven"],"index":5289,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9680244923,"difficulty":1.9680244923}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Catherine can now know that Antonio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Malcolm","Lindsay","Antonio","Catherine"],"index":6605,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9573541284,"difficulty":1.9573541284}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen is thirsty. It is publicly announced that Helen does not know whether Micheal is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Helen can now know whether Sylvia can know whether Micheal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvia","Micheal","Helen","Willie"],"index":1894,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9445813894,"difficulty":0.0554186106}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Glenn. Lucila's card is shown to Glenn. Glenn's card is shown to Christopher. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know that Glenn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glenn","Christopher","Lucila"],"index":8502,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9530413747,"difficulty":0.0469586253}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Rosalie. Cathy's card is shown to Rosalie. Rosalie's card is shown to Catherine. Rosalie's card is shown to Cathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rosalie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rosalie","Catherine","William","Cathy"],"index":9443,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9745804667,"difficulty":0.0254195333}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Darren can now know that Marty can know whether Marty is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darren","Marty","Brenda"],"index":5431,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8753007054,"difficulty":1.8753007054}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Agnes does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Agnes can now know that Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Agnes","Robert"],"index":5520,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.953635931,"difficulty":0.046364069}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is not thirsty. It is publicly announced that Brenda does not know whether Michele is thirsty. It is publicly announced that Joseph does not know whether Michele is thirsty. It is publicly announced that Brenda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! 2 ] 0","hypothesis":"Michele can now know whether James can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Brenda","Michele","Joseph"],"index":5920,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9829728603,"difficulty":0.0170271397}
-{"premise":"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 does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that 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":"Thelma can now know that Sandra can know that Katherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Katherine","Thelma","Stephen"],"index":1745,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9670274258,"difficulty":0.0329725742}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether William's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"William can now know that John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","John"],"index":2872,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9314047098,"difficulty":0.0685952902}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jeremy can now know whether Linda can know that Jeremy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeremy","Linda"],"index":9321,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.898167491,"difficulty":1.898167491}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilbur's card is shown to Virginia. Virginia's card is shown to Wilbur. Wilbur's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Virginia does not know whether Virginia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Barbara can now know whether Virginia can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Virginia","Wilbur","Barbara"],"index":3863,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9802645445,"difficulty":0.0197354555}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Brian. Kathryn's card is shown to Brian. David's card is shown to Ruth. David's card is shown to Kathryn. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that David picked a black card. It is publicly announced that David picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"David can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brian","David","Ruth","Kathryn"],"index":5109,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9742290378,"difficulty":0.0257709622}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eli does not know whether or not everyone is thirsty. It is publicly announced that Victor knows whether Victor is thirsty. It is publicly announced that Stephen does not know whether Victor is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Stephen can now know that Victor can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Eli","Victor","Donna"],"index":4950,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9645083547,"difficulty":0.0354916453}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Jenny. Eddie's card is shown to Jenny. Sandra's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Jenny does not know whether Eddie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jenny can now know whether Eddie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Jenny","Anna","Eddie"],"index":7785,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5317703485,"difficulty":0.4682296515}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Harvey knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Harvey can now know that Richard can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harvey","Norma","Richard"],"index":127,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9833161235,"difficulty":0.0166838765}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria does not know whether Maria's forehead is muddy. It is publicly announced that Chester knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Chester can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wilbur","Maria","Chester"],"index":826,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9677618146,"difficulty":0.0322381854}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Melinda can now know whether Ernest can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melinda","Ernest","Karen","Diana"],"index":5790,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9887505174,"difficulty":0.0112494826}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Marc is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Marc can now know that James can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Marc"],"index":8944,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8557110429,"difficulty":1.8557110429}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roberta's forehead is muddy. It is publicly announced that Roberta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Eric","Roberta"],"index":1378,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9751878977,"difficulty":0.0248121023}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmy's card is shown to Kimberly. Kimberly's card is shown to Jimmy. Shirley's card is shown to Jimmy. Jimmy's card is shown to Shirley. It is publicly announced that someone picked a red card. It is publicly announced that Kimberly knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jimmy can now know that Jimmy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kimberly","Jimmy","Shirley"],"index":4095,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9502711892,"difficulty":0.0497288108}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Carol knows whether Sara is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Carol can now know whether Sara can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sara","Carol"],"index":7654,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9872309566,"difficulty":0.0127690434}
-{"premise":"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's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Julia can now know that Martha can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Martha","Julia"],"index":6002,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9807053208,"difficulty":0.0192946792}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Carol can now know that Elaine can know that Carol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carol","Elaine"],"index":3531,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.972546339,"difficulty":0.027453661}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether someone's forehead is muddy. It is publicly announced that Gladys knows whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Greg can now know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Willie","Gladys","Greg"],"index":9534,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9268198013,"difficulty":0.0731801987}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alejandro can now know that Carl can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carl","Alejandro","Simonne","Courtney"],"index":4962,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9789296985,"difficulty":0.0210703015}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cherise's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Cherise can now know whether Brenda can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cherise","Brenda","Lizbeth"],"index":5325,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9847897887,"difficulty":0.0152102113}
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