diff --git "a/data/validation-forehead.jsonl" "b/data/validation-forehead.jsonl"
new file mode 100644--- /dev/null
+++ "b/data/validation-forehead.jsonl"
@@ -0,0 +1,924 @@
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Christopher","Timothy"],"index":13728,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998221457,"difficulty":0.001778543}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Inez's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] 0","hypothesis":"Crystal can now know that Inez can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Crystal","Inez"],"index":23982,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972608089,"difficulty":0.0027391911}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie does not know whether Marjorie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Carl can now know whether David can know whether Marjorie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marjorie","David","Carl"],"index":52927,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995366335,"difficulty":0.0004633665}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annie's forehead is not muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Annie can now know whether Sylvester can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sylvester","Patricia","Annie"],"index":26283,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9954330921,"difficulty":0.0045669079}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether or not everyone's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy. It is publicly announced that Maria knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ronald can now know whether Maria can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Ronald","Maria"],"index":59799,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.951094389,"difficulty":0.048905611}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis does not know whether Dennis's forehead is muddy. It is publicly announced that Louis's forehead is muddy. It is publicly announced that Rochelle knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Louis can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Louis","Rochelle","Lawrence","Dennis"],"index":26765,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica's forehead is not muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Donald can now know whether Monica can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Jennifer","Monica"],"index":36724,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiffany does not know whether Tiffany's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Tiffany can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ebony","Gregory","Tiffany","Terry"],"index":30831,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bart knows whether Randy's forehead is muddy. It is publicly announced that Randy knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Bart can now know whether Randy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randy","Bart"],"index":44377,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9770485759,"difficulty":0.0229514241}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanna knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Bradley can now know that Joanna can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Bradley","Joanna"],"index":31025,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997602105,"difficulty":0.0002397895}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcella's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Paul can now know that Jessica can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Jessica","Marcella","Paul"],"index":36098,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.819228828,"difficulty":1.819228828}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Philip does not know whether or not everyone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Dewayne can now know whether Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Heidi","Dewayne","Richard","Philip"],"index":45970,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991273284,"difficulty":0.0008726716}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Angela can now know whether Kenneth can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenneth","Angela"],"index":36914,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997592568,"difficulty":0.0002407432}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce does not know whether or not everyone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Joyce can now know whether Vicky can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Vicky","Joyce"],"index":35107,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996953011,"difficulty":0.0003046989}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janeth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Janet can now know that Jerry can know that Janeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arthur","Jerry","Janeth","Janet"],"index":42030,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6597003937,"difficulty":1.6597003937}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan does not know whether Joan's forehead is muddy. It is publicly announced that Charlotte's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Charlotte can now know that Joan can know whether Charlotte's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charlotte","Joan"],"index":12327,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994263649,"difficulty":0.0005736351}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris does not know whether or not everyone's forehead is muddy. It is publicly announced that Chris knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Chris can now know that Chris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gregory","Chris"],"index":36346,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8114206791,"difficulty":1.8114206791}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis's forehead is not muddy. It is publicly announced that Herbert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Dennis can now know that Herbert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Catherine","Dennis","Herbert"],"index":53390,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8422586322,"difficulty":0.1577413678}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene's forehead is muddy. It is publicly announced that Irene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"David can now know that Joseph can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Joseph","Irene","Jody"],"index":19967,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999168396,"difficulty":0.000831604}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cynthia can now know that Cheryl can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nathan","Cheryl","Cynthia"],"index":66100,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9930141568,"difficulty":0.0069858432}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melody knows whether someone's forehead is muddy. It is publicly announced that Austin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Janice can now know that Austin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Debra","Austin","Melody"],"index":43254,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9723722935,"difficulty":0.0276277065}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Paul can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dana","Paul","Roland"],"index":42713,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977637529,"difficulty":0.0022362471}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sally can now know whether Elsie can know that Elsie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elsie","Sally","Vera","Maggie"],"index":49408,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9847615957,"difficulty":0.0152384043}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela does not know whether Angela's forehead is muddy. It is publicly announced that Fernando's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Angela can now know that Fernando can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Angela","Richard","Fernando"],"index":26005,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985021353,"difficulty":0.0014978647}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"John can now know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sandra","John","Mark"],"index":11819,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999597609,"difficulty":0.000402391}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terri does not know whether Terri's forehead is muddy. It is publicly announced that Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agenta knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Mary can now know whether Cheryl can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Terri","Cheryl","Timothy"],"index":43798,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999207437,"difficulty":0.000792563}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Doreen's forehead is muddy. It is publicly announced that Earnest knows whether Doreen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Robert can now know whether Mark can know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Earnest","Mark","Doreen","Robert"],"index":38209,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.575820744,"difficulty":1.575820744}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy does not know whether Timothy's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy. It is publicly announced that Bobby knows whether Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Timothy can now know that Bobby's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Timothy","Charles","Bobby"],"index":2997,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9884310961,"difficulty":1.9884310961}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Martin can now know whether Martin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Martin","Guy","Jennifer"],"index":49468,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99646312,"difficulty":0.00353688}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sidney's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Sidney can now know whether Dorothy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Paul","Sidney"],"index":6847,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997865558,"difficulty":0.0002134442}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandie's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry does not know whether Harry's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Brandie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harry","Brandie"],"index":57162,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know that Maynard can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phyllis","Maynard","Jennifer"],"index":15078,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997600913,"difficulty":0.0002399087}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Devon does not know whether Devon's forehead is muddy. It is publicly announced that Brandi knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Shirley can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brandi","Devon","Charles","Shirley"],"index":45525,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997755885,"difficulty":0.0002244115}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane does not know whether Diane's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Travis can now know that Joseph can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Travis","Diane","Joseph"],"index":61209,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998498559,"difficulty":0.001501441}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna does not know whether Anna's forehead is muddy. It is publicly announced that Anna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bryan can now know that Reynaldo can know whether Reynaldo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bryan","Reynaldo","Anna"],"index":65448,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6611828804,"difficulty":1.6611828804}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Brian's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"William can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["William","Brian"],"index":39029,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.94575876,"difficulty":0.05424124}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"George can now know that Mike's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mike","William","George"],"index":51969,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6125044227,"difficulty":1.6125044227}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hallie does not know whether or not everyone's forehead is muddy. It is publicly announced that Norma knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Hallie can now know that Norma can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norma","Robert","Neil","Hallie"],"index":22614,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995077848,"difficulty":0.0004922152}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that Darla's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Darla can now know that William can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Darla"],"index":29767,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6372277141,"difficulty":0.3627722859}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Willie can now know whether Lucas can know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melissa","Willie","Lucas"],"index":498,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999540329,"difficulty":0.000459671}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dawn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know whether Nichole can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dawn","David","Brad","Nichole"],"index":34086,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9889290929,"difficulty":0.0110709071}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Sheryl can now know that Bill can know whether Brandon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kay","Brandon","Sheryl","Bill"],"index":31808,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994982481,"difficulty":0.0005017519}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Melissa can now know whether Tyrone can know whether Tyrone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melissa","Tyrone","Joseph"],"index":12378,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9834998846,"difficulty":0.0165001154}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Anthony can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Anthony","John"],"index":48174,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995728135,"difficulty":0.0004271865}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice does not know whether Alice's forehead is muddy. It is publicly announced that Joanna knows whether or not everyone's forehead is muddy. It is publicly announced that Alice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Joanna can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joanna","Ruby","Bill","Alice"],"index":42391,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ninfa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Ninfa can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ninfa","Julie"],"index":4428,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980146885,"difficulty":0.0019853115}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Alicia can now know that Sandra can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alicia","Sandra"],"index":18006,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9832450151,"difficulty":0.0167549849}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan does not know whether Juan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Jere can now know whether Marty can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marty","Jere","Mark","Juan"],"index":25604,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9090505242,"difficulty":0.0909494758}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Christopher can now know whether Ray can know that Ruby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Christopher","Ray"],"index":6662,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986159801,"difficulty":0.0013840199}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Christina can now know that Jan can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jan","Christina"],"index":45091,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944100976,"difficulty":0.0055899024}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathaniel does not know whether or not everyone's forehead is muddy. It is publicly announced that Nathaniel does not know whether Nathaniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nathaniel can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Jake","Nathaniel"],"index":41106,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991748929,"difficulty":0.0008251071}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know that Elizabeth can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Elizabeth"],"index":48781,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fay does not know whether Fay's forehead is muddy. It is publicly announced that Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Pamela can now know that Fay can know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Fay","Pamela","Sharon"],"index":37785,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9729511738,"difficulty":0.0270488262}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kevin can now know that John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","John"],"index":18207,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5133118629,"difficulty":1.5133118629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lloyd can now know that Raymond can know that Lester's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lester","Raymond","Richard","Lloyd"],"index":1459,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956976175,"difficulty":0.0043023825}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Mary can now know whether Stephen can know that Harrison's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cecile","Harrison","Stephen","Mary"],"index":29758,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9932096601,"difficulty":0.0067903399}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pedro can now know whether Jordan can know that Jordan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jordan","Pedro","Noel"],"index":56849,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9697989821,"difficulty":0.0302010179}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Kristen can now know that Kristen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kristen","Gary","George","Thomas"],"index":24839,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5689430833,"difficulty":0.4310569167}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest does not know whether Ernest's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Freddie can now know that Ernest can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Freddie","Ernest","David"],"index":12983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9891564846,"difficulty":0.0108435154}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Esther can now know that Amy can know that Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Esther","Amy"],"index":15117,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978860021,"difficulty":0.0021139979}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gerald can now know whether Derrick can know that Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Derrick","Jeffrey","Gerald"],"index":4416,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9873124957,"difficulty":0.0126875043}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raven knows whether someone's forehead is muddy. It is publicly announced that Dale does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jeffery can now know that Dale's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raven","Mary","Jeffery","Dale"],"index":37023,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6088863611,"difficulty":1.6088863611}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that Joyce does not know whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Joyce can now know whether Charles can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joyce","Charles"],"index":35963,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997822642,"difficulty":0.0002177358}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanette knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Vivian can now know whether Leslie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Myles","Jeanette","Leslie","Vivian"],"index":9434,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995989203,"difficulty":0.0004010797}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Linda can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Mary","Linda"],"index":13161,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9813010693,"difficulty":0.0186989307}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Vanessa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Vanessa","John"],"index":65166,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985497594,"difficulty":0.0014502406}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that April's forehead is not muddy. It is publicly announced that Sara does not know whether Sara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"April can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["April","Lydia","Sara"],"index":58878,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985260367,"difficulty":0.0014739633}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rocio does not know whether or not everyone's forehead is muddy. It is publicly announced that Kimberly knows whether or not nobody's forehead is muddy. It is publicly announced that Rocio does not know whether Rocio's forehead is muddy. It is publicly announced that Kimberly knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Rocio can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rocio","Kimberly"],"index":2014,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952782393,"difficulty":0.0047217607}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gina does not know whether Gina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Vicki can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vicki","Terrell","Gina","Crystal"],"index":46287,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996978045,"difficulty":0.0003021955}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Paul can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marie","Paul","Arianna"],"index":3467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice does not know whether Alice's forehead is muddy. It is publicly announced that Marilyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentb knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Alice can now know whether Marilyn can know that Marilyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Alice","Heidy","Marilyn"],"index":33967,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9054900408,"difficulty":0.0945099592}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco does not know whether Francisco's forehead is muddy. It is publicly announced that Kenneth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Kenneth can now know that Francisco's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eugene","Kenneth","Francisco","Julia"],"index":18912,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9690589309,"difficulty":0.0309410691}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adam's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Charlene can now know whether Charlene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charlene","Adam"],"index":44463,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9601352811,"difficulty":0.0398647189}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann does not know whether or not everyone's forehead is muddy. It is publicly announced that Francis knows whether or not everyone's forehead is muddy. It is publicly announced that Ann does not know whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentb knows that (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Francis can now know that Michael can know that Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Francis","Sandra","Ann"],"index":38488,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8863900304,"difficulty":1.8863900304}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernie knows whether Keith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Ernie can now know that Irene can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irene","Keith","Ernie","Rosemary"],"index":30907,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997032285,"difficulty":0.0002967715}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy. It is publicly announced that Angel knows whether Christopher's forehead is muddy. It is publicly announced that Christopher knows whether Angel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Angel can now know whether Christopher can know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angel","John","Christopher"],"index":64494,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9493365288,"difficulty":0.0506634712}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Stewart can now know that Melanie can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stewart","Kendra","John","Melanie"],"index":60764,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944264889,"difficulty":0.0055735111}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Edward can now know whether Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Edward"],"index":56192,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7015801072,"difficulty":1.7015801072}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether or not everyone's forehead is muddy. It is publicly announced that Dennis knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Dennis can now know whether Marguerite can know whether Marguerite's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marguerite","Dennis","Eduardo"],"index":44533,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8887568712,"difficulty":1.8887568712}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Blanche knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Joseph can now know whether Lawrence can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Callie","Joseph","Blanche"],"index":11546,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9955258965,"difficulty":0.0044741035}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stuart can now know whether Eugene can know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eugene","Stuart","Cynthia","Duncan"],"index":23583,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995054007,"difficulty":0.0004945993}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corina knows whether someone's forehead is muddy. It is publicly announced that Howard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Corina can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Fern","Howard","Corina"],"index":61854,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982414246,"difficulty":0.0017585754}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith does not know whether Keith's forehead is muddy. It is publicly announced that Carmela does not know whether Carmela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Irma can now know whether Keith can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Keith","Irma","Carmela"],"index":10955,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9962792993,"difficulty":0.0037207007}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jane can now know whether Anthony can know whether Jane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Jane","Terri"],"index":12428,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9965571165,"difficulty":0.0034428835}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neville does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Neville can now know that Eric can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eric","Neville","Glen"],"index":57397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976875782,"difficulty":0.0023124218}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know whether Lucille's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brian","Lucille","Bridgett","Keely"],"index":65375,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995377064,"difficulty":0.0004622936}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nina can now know that Jose can know that Grace's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kelly","Grace","Nina","Jose"],"index":9463,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6757603288,"difficulty":0.3242396712}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jesus can now know whether Donald can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesus","Mary","Donald"],"index":15769,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9719337821,"difficulty":1.9719337821}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Susan can now know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Susan","William"],"index":24895,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8423573971,"difficulty":0.1576426029}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nickie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Dianne can now know whether Anthony can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","David","Dianne","Nickie"],"index":408,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995177984,"difficulty":0.0004822016}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bud knows whether Curtis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Shawna can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bud","Curtis","Shawna","Julia"],"index":6332,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9880852699,"difficulty":0.0119147301}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith's forehead is not muddy. It is publicly announced that Kristopher's forehead is muddy. It is publicly announced that Edith knows whether Edith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kristopher can now know that Thuy can know whether Edith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edith","Kristopher","Thuy"],"index":25579,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995604157,"difficulty":0.0004395843}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Sheryl","Greg"],"index":67429,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936007857,"difficulty":0.0063992143}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether or not everyone's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Melissa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melissa","Freddie","Stephanie"],"index":33044,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9921340942,"difficulty":0.0078659058}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy does not know whether Jimmy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Erin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katherine","Jimmy","Jeanne","Erin"],"index":46923,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997475743,"difficulty":0.0002524257}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda's forehead is muddy. It is publicly announced that David knows whether Joseph's forehead is muddy. It is publicly announced that Joseph does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"David can now know whether Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brenda","Joseph","Edna","David"],"index":4600,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995070696,"difficulty":0.0004929304}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Megan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Austin can now know that Paula can know whether Paula's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paula","Austin","Megan"],"index":6285,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966689944,"difficulty":0.0033310056}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Jacquelyn can now know that Christine can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Charles","Jacquelyn","James"],"index":36917,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981284738,"difficulty":0.0018715262}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeannette's forehead is muddy. It is publicly announced that Gary does not know whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mike can now know whether Gary can know whether Mike's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mike","Jeannette","Gary"],"index":14305,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9978819489,"difficulty":0.0021180511}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randa knows whether or not everyone's forehead is muddy. It is publicly announced that Randa does not know whether Randa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Peggy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Randa","Jimmy","Peggy"],"index":12216,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981841445,"difficulty":0.0018158555}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence does not know whether Florence's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentb knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Florence can now know whether Robert can know that Freda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Freda","Florence","Vincent","Robert"],"index":41019,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9900333285,"difficulty":0.0099666715}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Glen can now know whether Meagan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Meagan","Wade","Glen"],"index":19091,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9964482784,"difficulty":0.0035517216}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Liane can now know whether Robert can know whether Liane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Maria","Liane"],"index":8548,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985557199,"difficulty":0.0014442801}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Keith can now know that Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francis","Matthew","Lori","Keith"],"index":33425,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939773083,"difficulty":0.0060226917}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Talia's forehead is muddy. It is publicly announced that Floyd does not know whether Floyd's forehead is muddy. It is publicly announced that Floyd knows whether Ralph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Floyd can now know whether Ralph can know whether Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Talia","Ralph","Jeffrey","Floyd"],"index":61564,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989338517,"difficulty":0.0010661483}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Pamela can now know that James can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Pamela","James"],"index":36234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983849525,"difficulty":0.0016150475}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexandra's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Alexandra knows whether Chae's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Chae can now know that Alice can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alexandra","Chae","Alice"],"index":36478,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy. It is publicly announced that Shawn does not know whether Shawn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Shawn can now know whether Eun can know that Shawn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eun","Linda","Shawn"],"index":50964,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5265455246,"difficulty":0.4734544754}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roland knows whether someone's forehead is muddy. It is publicly announced that Joseph knows whether Roland's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Doris can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doris","Joseph","Irene","Roland"],"index":59636,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984890223,"difficulty":0.0015109777}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rocky does not know whether Rocky's forehead is muddy. It is publicly announced that Bradley does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Bradley can now know that Wilma can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rocky","Bradley","Wilma"],"index":6031,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9490939975,"difficulty":0.0509060025}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Eric can now know that Amy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Teresa","Eric","Amy"],"index":16125,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983975291,"difficulty":0.0016024709}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether or not nobody's forehead is muddy. It is publicly announced that Darrell does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bruce can now know that Bruce's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bruce","Patrick","Darrell"],"index":46456,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5440402031,"difficulty":0.4559597969}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darell does not know whether Darell's forehead is muddy. It is publicly announced that Ollie knows whether Darell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Ollie can now know that Darell can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ollie","Elisa","Jose","Darell"],"index":61943,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997157454,"difficulty":0.0002842546}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jeffrey can now know whether Cassie can know whether Karen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Mary","Karen","Cassie"],"index":11617,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995340109,"difficulty":0.0004659891}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luther does not know whether Luther's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Brian can now know that Leo can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Luther","Leo"],"index":2183,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984735847,"difficulty":0.0015264153}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether someone's forehead is muddy. It is publicly announced that Dennis knows whether someone's forehead is muddy. It is publicly announced that Louis knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Louis can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Louis","Dennis"],"index":6914,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997361302,"difficulty":0.0002638698}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy's forehead is not muddy. It is publicly announced that Arthur does not know whether Arthur's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Helen can now know whether Arthur can know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Arthur","Timothy"],"index":23291,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990122318,"difficulty":0.0009877682}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rene does not know whether Rene's forehead is muddy. It is publicly announced that Diana knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"George can now know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rene","Linda","Diana","George"],"index":52211,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996106029,"difficulty":0.0003893971}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessie does not know whether Jessie's forehead is muddy. It is publicly announced that Frederick does not know whether Frederick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Randy can now know that Jessie can know whether Randy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frederick","Alicia","Randy","Jessie"],"index":60881,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992811084,"difficulty":0.0007188916}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know that Joseph can know whether Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Joseph","Julian"],"index":2948,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9725578427,"difficulty":0.0274421573}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Robert can now know that Joyce can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Joyce"],"index":35071,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995751977,"difficulty":0.0004248023}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathaniel knows whether someone's forehead is muddy. It is publicly announced that Nathaniel does not know whether or not everyone's forehead is muddy. It is publicly announced that Nathaniel does not know whether or not everyone's forehead is muddy. It is publicly announced that Kelly knows whether Kelly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Judson can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judson","Kelly","Nathaniel"],"index":37847,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.988483727,"difficulty":0.011516273}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arnold's forehead is muddy. It is publicly announced that Jo does not know whether or not everyone's forehead is muddy. It is publicly announced that Jo does not know whether Jo's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jo can now know whether Arnold can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arnold","Jo"],"index":38365,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Mary can now know that George can know that Joann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Judy","George","Joann","Mary"],"index":4633,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9925664663,"difficulty":0.0074335337}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"John can now know that Raymond can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raymond","Lucille","John"],"index":62991,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983154535,"difficulty":0.0016845465}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne knows whether Vicki's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Wayne can now know that Vicki can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stephen","Hugh","Wayne","Vicki"],"index":28481,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984048009,"difficulty":0.0015951991}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruben does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Freddie can now know that Amanda can know whether Freddie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Ruben","Freddie"],"index":27552,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992764592,"difficulty":0.0007235408}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley's forehead is not muddy. It is publicly announced that Mikki does not know whether Mikki's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know that Shirley can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shirley","Mikki","James"],"index":20706,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984691739,"difficulty":0.0015308261}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Loraine can now know that Patrick can know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Patrick","Loraine","Beverly"],"index":21056,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956634641,"difficulty":0.0043365359}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy does not know whether Jeremy's forehead is muddy. It is publicly announced that Terry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Terry can now know whether Jeremy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeremy","Terry"],"index":21285,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9722246528,"difficulty":0.0277753472}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barney","Christine","Mary","Jason"],"index":44052,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9809282422,"difficulty":0.0190717578}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cristal does not know whether Cristal's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Cristal can now know whether Mary can know that Cristal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eileen","Cristal","Mary"],"index":37460,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6429062486,"difficulty":0.3570937514}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Dora can now know whether Carolyn can know whether Becky's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Becky","Dora","Carolyn"],"index":64467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994137287,"difficulty":0.0005862713}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Penny knows whether Penny's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Penny can now know that Edith can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edith","James","Robert","Penny"],"index":63746,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984768033,"difficulty":0.0015231967}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara does not know whether Tamara's forehead is muddy. It is publicly announced that Tamara does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Tamara can now know that Charles can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tamara","Charles","Darla","Christine"],"index":52018,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9845522642,"difficulty":0.0154477358}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Elaine can now know that Joseph can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Joseph","Barbara","Elaine"],"index":16297,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9867905974,"difficulty":0.0132094026}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Corey can now know whether Corey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Corey","Gloria"],"index":30981,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9847390652,"difficulty":0.0152609348}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Sheila can now know whether Roxanne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Son","Sheila","Roxanne"],"index":9823,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994878769,"difficulty":0.0005121231}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Milton can now know whether Tiffany can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Milton","Tiffany","Laura"],"index":15422,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9836560488,"difficulty":0.0163439512}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Tracey can now know that Harold's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracey","Elizabeth","Harold"],"index":3344,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982489347,"difficulty":0.0017510653}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Anna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] 0","hypothesis":"Rocky can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Patricia","Anna","Rocky"],"index":63961,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983596206,"difficulty":0.0016403794}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cameron knows whether or not nobody's forehead is muddy. It is publicly announced that Cameron knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Cameron can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Kenneth","John","Cameron"],"index":31338,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981617332,"difficulty":0.0018382668}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annette does not know whether Annette's forehead is muddy. It is publicly announced that Wendy does not know whether Wendy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Wendy can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annette","Wendy","Patricia"],"index":5673,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9506411552,"difficulty":0.0493588448}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bradley","Robert","Linda","Claudia"],"index":52149,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952284098,"difficulty":0.0047715902}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebekah does not know whether or not everyone's forehead is muddy. It is publicly announced that Kiley knows whether someone's forehead is muddy. It is publicly announced that Rebekah does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kathleen can now know that Leona can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Rebekah","Kiley","Leona"],"index":44937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9599503875,"difficulty":0.0400496125}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emilio knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know whether Emilio can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emilio","Michael","Joseph"],"index":64816,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995773435,"difficulty":0.0004226565}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Susan can now know whether Howard can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Susan","Howard"],"index":62667,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9942193031,"difficulty":0.0057806969}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony knows whether or not everyone's forehead is muddy. It is publicly announced that Tony does not know whether Tony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Tony can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Tony","Vera","Steven"],"index":16045,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Linda can now know that Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Cynthia","Linda","Alma"],"index":57097,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977610111,"difficulty":0.0022389889}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that Crystal's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Crystal","Charles","Robert"],"index":63407,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9951686859,"difficulty":0.0048313141}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin does not know whether Justin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jennifer can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Justin","Latosha","Jennifer"],"index":2331,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997010827,"difficulty":0.0002989173}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mike knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Mike can now know whether Richard can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mike","Richard"],"index":59234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9923154116,"difficulty":0.0076845884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred's forehead is not muddy. It is publicly announced that Ismael does not know whether Ismael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Ismael can now know whether Fred can know that Ismael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ismael","Fred","William"],"index":22786,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5091009736,"difficulty":1.5091009736}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence's forehead is muddy. It is publicly announced that Ray's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Andrea can now know that Zachary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ray","Andrea","Zachary","Lawrence"],"index":25094,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9316990376,"difficulty":0.0683009624}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Roy can now know that Stephanie can know that Roy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Roy","Stephanie"],"index":12747,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937291145,"difficulty":0.0062708855}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Allen can now know that Junior can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Junior","Allen","Susan"],"index":3154,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy. It is publicly announced that Sue knows whether or not everyone's forehead is muddy. It is publicly announced that Duane knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"William can now know that Lucas can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sue","William","Duane","Lucas"],"index":29631,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996139586,"difficulty":0.003860414}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luann knows whether someone's forehead is muddy. It is publicly announced that Gary's forehead is muddy. It is publicly announced that Lori knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Luann can now know whether Gary can know that Luann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Luann","Lori","Gary"],"index":66584,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5647748113,"difficulty":0.4352251887}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elijah does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Elijah can now know whether Cherrie can know whether Vivian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elijah","Cherrie","Armando","Vivian"],"index":21138,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994450212,"difficulty":0.0005549788}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jamar can now know whether Jamar's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Jamar","Stephen"],"index":5401,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9680637121,"difficulty":0.0319362879}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica does not know whether Jessica's forehead is muddy. It is publicly announced that Dessie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Carlos can now know that Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dessie","Harry","Jessica","Carlos"],"index":13942,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6971794367,"difficulty":1.6971794367}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gary knows whether April's forehead is muddy. It is publicly announced that Jonathan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Gary can now know whether Jonathan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gary","Michelle","April","Jonathan"],"index":56034,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995006323,"difficulty":0.0004993677}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Natalie's forehead is not muddy. It is publicly announced that Amy knows whether Natalie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agentc knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Rita can now know whether Natalie can know that Natalie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Natalie","Amy","Rita"],"index":16346,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9865495563,"difficulty":0.0134504437}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Fernando can now know whether Francis can know that Fernando's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Francis","Fernando"],"index":50426,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9905208349,"difficulty":0.0094791651}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Devin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Devin can now know that Lianne can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lianne","Devin","Charles"],"index":58321,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.987788856,"difficulty":0.012211144}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carla's forehead is muddy. It is publicly announced that Charles's forehead is not muddy. It is publicly announced that Carla knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Carla can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carla","Joe","Charles"],"index":51164,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980040193,"difficulty":0.0019959807}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua does not know whether or not everyone's forehead is muddy. It is publicly announced that Cynthia knows whether Cynthia's forehead is muddy. It is publicly announced that Joshua knows whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Cynthia can now know whether Joshua can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joshua","Cynthia"],"index":52781,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9656608701,"difficulty":0.0343391299}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Patrick can now know whether Kimberly can know whether Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patrick","Kimberly","Sarah"],"index":6519,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989356399,"difficulty":0.0010643601}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"David can now know whether Jacqueline can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Jacqueline"],"index":59182,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997099042,"difficulty":0.0002900958}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Gilbert's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Judith can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Gilbert","Judith"],"index":6042,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997095466,"difficulty":0.0002904534}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether Charles's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Charles can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Gerald"],"index":22143,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7169127464,"difficulty":1.7169127464}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris knows whether Chris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Thomas can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Chris","Jerome","Thomas"],"index":66064,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982827902,"difficulty":0.0017172098}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether or not everyone's forehead is muddy. It is publicly announced that Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Gladys can now know whether Gerald can know that Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gladys","Gerald"],"index":32357,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9848662615,"difficulty":0.0151337385}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Marie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marie","Anthony"],"index":54477,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981586337,"difficulty":0.0018413663}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Leslie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cesar","Leslie","Samuel"],"index":37071,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981749058,"difficulty":0.0018250942}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tempie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Tempie can now know whether Robert can know that Tempie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Benjamin","Tempie"],"index":11832,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6458292007,"difficulty":1.6458292007}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis's forehead is not muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 1 ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Travis can now know that Barbara can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Travis","Krista"],"index":57154,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6964610219,"difficulty":1.6964610219}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gloria can now know that Lori can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lori","Rachel","Gloria","Mary"],"index":19458,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998357594,"difficulty":0.001642406}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Adam does not know whether Adam's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Yvonne can now know that Shawnta's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shawnta","Adam","Yvonne"],"index":63414,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940000772,"difficulty":0.0059999228}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy. It is publicly announced that Fannie knows whether or not everyone's forehead is muddy. It is publicly announced that Fannie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Scott can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Scott","Fannie"],"index":14467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997237325,"difficulty":0.0002762675}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy. It is publicly announced that Susan knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mark can now know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Susan","Kevin","Shaun"],"index":48019,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9113793373,"difficulty":0.0886206627}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeannette does not know whether Jeannette's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Doris can now know that Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Brenda","Jeannette","Doris"],"index":60357,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9908688068,"difficulty":0.0091311932}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Cole's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Cole can now know that Randall's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cole","Ricardo","Susan","Randall"],"index":43370,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981371164,"difficulty":0.0018628836}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas does not know whether Nicholas's forehead is muddy. It is publicly announced that Deanne knows whether or not nobody's forehead is muddy. It is publicly announced that Deanne knows whether Deanne's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Nicholas can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Nicholas","Deanne"],"index":29651,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998664856,"difficulty":0.001335144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phillip knows whether or not everyone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Joshua can now know whether Joshua's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Phillip","Jeff","Kenneth"],"index":49915,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8590909243,"difficulty":0.1409090757}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Olive can now know that Eileen can know that Olive's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marjorie","Eileen","Olive"],"index":7581,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9470750093,"difficulty":0.0529249907}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Katharine knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Katharine can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katharine","David","Louann"],"index":40674,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986611605,"difficulty":0.0013388395}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"David can now know that Danny can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Danny","James"],"index":1412,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997609258,"difficulty":0.0002390742}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joesph does not know whether Joesph's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gretchen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Gretchen can now know that Gretchen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joesph","Gretchen"],"index":58451,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9865352511,"difficulty":1.9865352511}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Callie does not know whether Callie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Callie can now know whether Jamie can know that Callie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Callie","Paul","Jamie"],"index":26321,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8529649377,"difficulty":0.1470350623}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samuel knows whether someone's forehead is muddy. It is publicly announced that Laura knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Laura can now know that Chad can know whether Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samuel","Laura","Chad","Kathy"],"index":35298,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990953207,"difficulty":0.0009046793}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy's forehead is not muddy. It is publicly announced that Jeremy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jeremy can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonathan","Jeremy","Sondra"],"index":44498,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997361302,"difficulty":0.0002638698}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester knows whether Roger's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Lester can now know that Roger can know that Roger's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Crystal","Latricia","Roger","Lester"],"index":13013,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974038005,"difficulty":0.0025961995}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Casey knows whether Adrian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Virginia can now know that Robert can know that Virginia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Casey","Virginia","Adrian"],"index":64344,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980924726,"difficulty":0.0019075274}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos does not know whether or not everyone's forehead is muddy. It is publicly announced that Carlos does not know whether Carlos's forehead is muddy. It is publicly announced that Joan's forehead is muddy. It is publicly announced that Joan knows whether Carlos's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Joan can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Carlos","Joan"],"index":8429,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.905769825,"difficulty":0.094230175}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Gerry can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Harold","Gerry"],"index":14058,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981903434,"difficulty":0.0018096566}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Claire can now know that Daniel can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Claire","Daniel","Linda","Janice"],"index":6933,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Rayna can now know whether Robert can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Paul","Rayna"],"index":32052,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Martha can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Martha","Diane"],"index":35378,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947021604,"difficulty":0.0052978396}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Graciela's forehead is not muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Eula can now know whether Mark can know that Graciela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Graciela","Eula"],"index":40794,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9972564578,"difficulty":0.0027435422}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether or not nobody's forehead is muddy. It is publicly announced that George knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"George can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Forrest","John","Thomas","George"],"index":6246,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972135425,"difficulty":0.0027864575}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emily's forehead is muddy. It is publicly announced that Emily's forehead is muddy. It is publicly announced that Emily's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Diane can now know that Kenneth can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emily","Kenneth","Vera","Diane"],"index":50167,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9892885685,"difficulty":0.0107114315}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leland's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Jennifer can now know that Leland can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harry","Shane","Leland","Jennifer"],"index":46289,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984825253,"difficulty":0.0015174747}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol does not know whether or not everyone's forehead is muddy. It is publicly announced that Nathan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Nathan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carol","Nathan"],"index":3004,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981706142,"difficulty":0.0018293858}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Marvin's forehead is muddy. It is publicly announced that George does not know whether George's forehead is muddy. It is publicly announced that Steven knows whether Marvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Steven can now know that Marvin can know whether Marvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","Steven","Mark","George"],"index":18932,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.933380425,"difficulty":0.066619575}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janie does not know whether Janie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Charles can now know that Janie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janie","Charles","John"],"index":18988,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949506521,"difficulty":0.0050493479}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonora does not know whether Leonora's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Sarah can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Sarah","Leonora"],"index":11820,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Charles can now know whether Michael can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Stephen","Charles","Ronald"],"index":18403,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9301029444,"difficulty":0.0698970556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Mary can now know that Angela can know whether Jill's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Angela","Jill","Mary"],"index":38772,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996197224,"difficulty":0.0003802776}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Natasha can now know whether James can know whether Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","James","Natasha"],"index":43763,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994937181,"difficulty":0.0005062819}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether Roy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Roy can now know whether Wanda can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carmen","Wanda","Roy","Mabel"],"index":8489,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997546077,"difficulty":0.0002453923}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Matthew can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hulda","Matthew","Richard"],"index":12932,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984970093,"difficulty":0.0015029907}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Garland does not know whether Garland's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Reuben can now know that Donna can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Priscilla","Reuben","Donna","Garland"],"index":61658,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9749309421,"difficulty":0.0250690579}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy. It is publicly announced that Barbara does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Barbara can now know whether Donna can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barbara","Donna"],"index":65444,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8764425516,"difficulty":1.8764425516}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Clara's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Clara can now know that Mary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Clara"],"index":48177,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.923597753,"difficulty":1.923597753}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie does not know whether Willie's forehead is muddy. It is publicly announced that Willie does not know whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Victoria can now know whether Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Willie","Gregory","Victoria"],"index":44282,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995214939,"difficulty":0.0004785061}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danny knows whether Logan's forehead is muddy. It is publicly announced that Julie knows whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Danny can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danny","Karen","Julie","Logan"],"index":16146,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985052347,"difficulty":0.0014947653}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Paula can now know that Manuel can know that Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Manuel","Doris","Paula"],"index":44572,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981671572,"difficulty":0.0018328428}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Linda can now know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Stephanie","Linda"],"index":65083,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9765768051,"difficulty":0.0234231949}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Sabrina knows whether Mary's forehead is muddy. It is publicly announced that Sabrina knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Renee can now know that Mary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sabrina","Renee","Mary","Linda"],"index":27461,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9485470653,"difficulty":1.9485470653}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos does not know whether Carlos's forehead is muddy. It is publicly announced that Carlos's forehead is muddy. It is publicly announced that Lorene's forehead is muddy. It is publicly announced that Annett's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agenta knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Carlos can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carlos","Annett","Lorene","Randolph"],"index":63925,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5842683911,"difficulty":0.4157316089}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Lenny can now know that Kenneth can know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lenny","Douglas","Edward","Kenneth"],"index":58700,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985154271,"difficulty":0.0014845729}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether someone's forehead is muddy. It is publicly announced that Ernesto's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] 0","hypothesis":"Ernesto can now know whether Susan can know whether Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Susan","Ernesto"],"index":64243,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5701498389,"difficulty":1.5701498389}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julian knows whether or not everyone's forehead is muddy. It is publicly announced that Reynaldo does not know whether Reynaldo's forehead is muddy. It is publicly announced that George knows whether Shirley's forehead is muddy. It is publicly announced that Reynaldo does not know whether Reynaldo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Julian can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","George","Julian","Reynaldo"],"index":58477,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8103806376,"difficulty":0.1896193624}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelita does not know whether Angelita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Angelita can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karla","Steven","Angelita","Jason"],"index":11840,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997612834,"difficulty":0.0002387166}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Beverly can now know that James can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","James","Beverly"],"index":21147,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997189641,"difficulty":0.0002810359}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guadalupe does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Dustin can now know that Dustin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kim","Dustin","Guadalupe","Mary"],"index":32463,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6206573844,"difficulty":0.3793426156}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myra does not know whether Myra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Mary can now know that Jacqueline can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacqueline","Mary","Christopher","Myra"],"index":27385,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983261228,"difficulty":0.0016738772}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronnie's forehead is muddy. It is publicly announced that Ronald does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ronnie can now know that Ronald can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ronald","Ronnie"],"index":4575,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9792891145,"difficulty":0.0207108855}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Walter's forehead is muddy. It is publicly announced that Ursula does not know whether Ursula's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Walter can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ursula","Walter","Robert"],"index":58682,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960674047,"difficulty":0.0039325953}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyle knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Peggy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kyle","Joshua","Peggy","Chad"],"index":11422,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983129501,"difficulty":0.0016870499}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether Larry's forehead is muddy. It is publicly announced that Rachel's forehead is not muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] Agentc knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] 0","hypothesis":"Rachel can now know whether Larry can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Patricia","Rachel"],"index":65180,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9926813245,"difficulty":0.0073186755}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Bernice can now know whether Crystal can know whether Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Crystal","Mary","Bernice","Kelly"],"index":66990,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995275736,"difficulty":0.0004724264}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Christopher can now know whether Patricia can know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Alice","Corey","Patricia"],"index":65332,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7686004639,"difficulty":0.2313995361}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlotte does not know whether Charlotte's forehead is muddy. It is publicly announced that Riley does not know whether Riley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Trey can now know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlotte","Helen","Riley","Trey"],"index":35195,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928463101,"difficulty":0.0071536899}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean does not know whether Jean's forehead is muddy. It is publicly announced that Jean does not know whether Jean's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Alvin can now know whether Jean can know that Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alvin","Jean"],"index":26279,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9818912148,"difficulty":0.0181087852}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Cheryl can know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Richard","Thomas","Patricia"],"index":47468,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995802045,"difficulty":0.0004197955}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Clifton can now know whether Walter can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Walter","Clifton","David","Scott"],"index":10160,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997773767,"difficulty":0.0002226233}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gilbert's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gilbert knows whether Ray's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Nancy can now know that Ray can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gilbert","Ray","Nancy"],"index":30291,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Minnie does not know whether Minnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Warren can now know that Warren's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Minnie","John","Dennis","Warren"],"index":60878,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976613522,"difficulty":0.0023386478}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that June does not know whether June's forehead is muddy. It is publicly announced that June's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 0","hypothesis":"Laurence can now know that Larry can know that Laurence's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Larry","Laurence","June"],"index":21646,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7721371055,"difficulty":0.2278628945}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Nicholas can now know that Nicholas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Nicholas","Angela"],"index":62544,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6798789501,"difficulty":1.6798789501}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leroy does not know whether Leroy's forehead is muddy. It is publicly announced that Leroy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Leroy can now know that Rikki can know whether Rikki's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leroy","Rikki","James","Anna"],"index":18993,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9102736712,"difficulty":0.0897263288}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"David can now know whether Gretchen can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gretchen","Nancy","David","Jean"],"index":37191,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8500530124,"difficulty":0.1499469876}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Michael knows whether Peter's forehead is muddy. It is publicly announced that Peter knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Peter can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Peter"],"index":44899,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5929234028,"difficulty":1.5929234028}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kecia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Donald can now know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Kecia","Donald"],"index":11412,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994227886,"difficulty":0.0005772114}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"William can now know that Diana can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Diana","William"],"index":59267,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977948666,"difficulty":0.0022051334}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol does not know whether or not everyone's forehead is muddy. It is publicly announced that Carol does not know whether Carol's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Elvia can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elvia","John","Carol"],"index":35508,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Shelby's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Shelby can now know whether Joseph can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shelby","Joseph","Brandon"],"index":65936,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9965835214,"difficulty":0.0034164786}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esperanza knows whether Nicholas's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Nicholas can now know that Esperanza can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nicholas","Esperanza"],"index":16119,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984266758,"difficulty":0.0015733242}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffery does not know whether or not everyone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Jeffery does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Donald can now know that Charles can know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Jeffery","James","Charles"],"index":1486,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5183298588,"difficulty":0.4816701412}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Christina can now know whether Edward can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christina","Edward"],"index":49284,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9924875498,"difficulty":0.0075124502}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica's forehead is muddy. It is publicly announced that Jason does not know whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jessica can now know that Delores can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Delores","Jason","Doris"],"index":31764,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise knows whether someone's forehead is muddy. It is publicly announced that Rebecca's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Rebecca can now know that Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rebecca","Louise"],"index":43115,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9430866838,"difficulty":0.0569133162}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy. It is publicly announced that Edmund knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lila can now know that Edmund's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lila","Richard","Edmund","Eleanor"],"index":10450,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944201112,"difficulty":0.0055798888}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Jeri's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jeffery can now know whether Patricia can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeri","Jeffery","Patricia"],"index":24775,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9409270883,"difficulty":0.0590729117}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jean's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] 0","hypothesis":"Allen can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Allen","Jean","Victor"],"index":3610,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry knows whether someone's forehead is muddy. It is publicly announced that Brigette does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Sherry can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sherry","April","Diane","Brigette"],"index":49943,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937490225,"difficulty":0.0062509775}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Philip knows whether Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Ramiro can now know whether Philip can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Ramiro","Marie","Philip"],"index":47936,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995933175,"difficulty":0.0004066825}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl does not know whether Cheryl's forehead is muddy. It is publicly announced that Cheryl knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Mark can now know that Everett can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Robert","Mark","Everett"],"index":11532,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984897375,"difficulty":0.0015102625}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aimee's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Joseph can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aimee","Joseph","James","Mary"],"index":66130,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983641505,"difficulty":0.0016358495}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarice knows whether Lester's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentd knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Ricardo can now know whether Clarice can know that Lester's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Lester","Clarice","Ricardo"],"index":10181,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980683923,"difficulty":0.0019316077}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sadie does not know whether Sadie's forehead is muddy. It is publicly announced that Sadie does not know whether Sadie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sadie can now know whether Lon can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sadie","Lon"],"index":35707,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Mark can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alma","David","Mark"],"index":42501,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997383952,"difficulty":0.0002616048}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Todd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Todd","David","Sandra"],"index":53538,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996691942,"difficulty":0.0003308058}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susana does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Allen can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Susana","Allen","Lisa","Carol"],"index":51363,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly does not know whether Kimberly's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kimberly can now know that Mark can know that Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Kimberly","Marie"],"index":52453,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936430454,"difficulty":0.0063569546}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether or not everyone's forehead is muddy. It is publicly announced that Gary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Shawn can now know that Gary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Shawn","Gary"],"index":1957,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9776208997,"difficulty":1.9776208997}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean does not know whether Jean's forehead is muddy. It is publicly announced that Laura knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jean can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Junior","Jean","Laura"],"index":34066,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9075042605,"difficulty":0.0924957395}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know that Glenda can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Glenda","Carrie","Douglas"],"index":51003,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997603297,"difficulty":0.0002396703}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy. It is publicly announced that Shawn does not know whether Shawn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Shawn can now know that Melissa can know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shawn","Terrance","Melissa"],"index":29439,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9164907932,"difficulty":0.0835092068}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jarvis does not know whether Jarvis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jarvis can now know whether Diane can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jarvis","Pedro","Diane","Melvin"],"index":50050,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997623563,"difficulty":0.0002376437}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis does not know whether or not everyone's forehead is muddy. It is publicly announced that Dennis does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Thelma can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thelma","Dennis"],"index":1088,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9797036648,"difficulty":0.0202963352}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Catherine","Darren"],"index":18260,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973347783,"difficulty":0.0026652217}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carla's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Carla can now know that Kathleen can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Yasmin","Kathleen","Carla","Anthony"],"index":35069,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957940578,"difficulty":0.0042059422}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph does not know whether Joseph's forehead is muddy. It is publicly announced that Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] Agentc knows that (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 0","hypothesis":"Gertrude can now know that Joseph can know whether Sandy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandy","Benjamin","Gertrude","Joseph"],"index":4668,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994630218,"difficulty":0.0005369782}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alvin knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Edward can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alvin","Edward"],"index":2836,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997494817,"difficulty":0.0002505183}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Trenton does not know whether Trenton's forehead is muddy. It is publicly announced that Gina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Melody can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Selina","Trenton","Melody","Gina"],"index":58062,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986712933,"difficulty":0.0013287067}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Hilda can now know that Lisa can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Lisa","Hilda"],"index":43835,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999782145,"difficulty":0.000217855}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Melanie can now know whether Melanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jerry","Scott","Melanie"],"index":20760,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.596051991,"difficulty":0.403948009}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Brenda","Kevin","Sara"],"index":4322,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983286262,"difficulty":0.0016713738}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy does not know whether Jimmy's forehead is muddy. It is publicly announced that Kimberly does not know whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kimberly can now know that Pamela can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jimmy","Pamela","Kimberly"],"index":32167,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984253645,"difficulty":0.0015746355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph's forehead is muddy. It is publicly announced that Joshua knows whether Ralph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sharon can now know whether Amanda can know whether Joshua's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joshua","Ralph","Sharon","Amanda"],"index":49358,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999417305,"difficulty":0.000582695}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not nobody's forehead is muddy. It is publicly announced that Fred does not know whether Fred's forehead is muddy. It is publicly announced that Joseph does not know whether Joseph's forehead is muddy. It is publicly announced that Paul knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Paul can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Paul","Joseph","Fred"],"index":48618,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9498595595,"difficulty":1.9498595595}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eddie knows whether Katie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Richard can now know whether Katie can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eddie","Katie","Richard"],"index":6689,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9914331436,"difficulty":0.0085668564}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joshua can now know that Delaine can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pearl","Delaine","Joshua","Justin"],"index":702,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982863069,"difficulty":0.0017136931}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan knows whether Shane's forehead is muddy. It is publicly announced that Bryan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Shane can now know whether Bryan can know that Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Shane","Bryan"],"index":17326,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8313772678,"difficulty":0.1686227322}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Tina's forehead is muddy. It is publicly announced that Loretta does not know whether Loretta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Elizabeth can now know that Loretta can know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Loretta","Tina","Elizabeth"],"index":32670,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991061091,"difficulty":0.0008938909}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Noelle knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Beverley can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Beverley","Noelle","Maria"],"index":31355,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980990291,"difficulty":0.0019009709}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Domingo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Domingo can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Simon","Allison","Domingo"],"index":10609,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997282624,"difficulty":0.0002717376}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know that Daniel can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Daniel","Jeffrey"],"index":46905,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Enid's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Enid knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Enid can now know that Lucille can know whether Enid's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Enid","Scott","Lucille"],"index":16378,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995342493,"difficulty":0.0004657507}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dora","Thomas","Robert"],"index":35575,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996920824,"difficulty":0.0003079176}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"John can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","John","Jessica","Melisa"],"index":12152,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997437596,"difficulty":0.0002562404}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal does not know whether Crystal's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal knows whether Calandra's forehead is muddy. It is publicly announced that Crystal knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jack can now know that Calandra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Crystal","Jack","Calandra"],"index":55106,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9659466147,"difficulty":0.0340533853}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle does not know whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Thelma can now know that William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thelma","William","Michelle"],"index":29606,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980164766,"difficulty":0.0019835234}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether or not nobody's forehead is muddy. It is publicly announced that William's forehead is not muddy. It is publicly announced that Sarah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"William can now know whether Robert can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Robert","Brooke","Sarah"],"index":30483,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990593791,"difficulty":0.0009406209}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne does not know whether Anne's forehead is muddy. It is publicly announced that Anne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 0","hypothesis":"Orlando can now know that Roland can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Orlando","Sonia","Roland","Anne"],"index":9505,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963756204,"difficulty":0.0036243796}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know that Pamela can know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Kenneth","Pamela"],"index":31248,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994199276,"difficulty":0.0005800724}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Raymond's forehead is muddy. It is publicly announced that Raymond knows whether someone's forehead is muddy. It is publicly announced that Raymond's forehead is muddy. It is publicly announced that Nancy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Nancy can now know that Raymond can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raymond","Garrett","Nancy"],"index":35844,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976250529,"difficulty":0.0023749471}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia's forehead is muddy. It is publicly announced that Cynthia knows whether someone's forehead is muddy. It is publicly announced that Joyce knows whether Marie's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that Cynthia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Joyce","Robert","Cynthia"],"index":12648,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8655749559,"difficulty":1.8655749559}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michael can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Terry","Michael","Eddy"],"index":28672,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9871776104,"difficulty":0.0128223896}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Patricia can now know that Ernest's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Patricia","Ernest","Anna"],"index":32070,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7756222486,"difficulty":0.2243777514}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal's forehead is not muddy. It is publicly announced that Donald knows whether Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Crystal can now know that Donald can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Donald","Monica"],"index":48479,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen does not know whether Carmen's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Stefanie can now know that Carmen can know whether Carmen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stefanie","Carmen"],"index":5396,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9940028787,"difficulty":0.0059971213}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eddie does not know whether Eddie's forehead is muddy. It is publicly announced that Eddie does not know whether Eddie's forehead is muddy. It is publicly announced that Morgan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Eddie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eddie","Morgan"],"index":13507,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986537695,"difficulty":0.0013462305}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Diane can now know whether Jennifer can know whether Diane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Stacy","Jennifer"],"index":6378,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9968823195,"difficulty":0.0031176805}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Judy can now know whether Jennifer can know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stella","Judy","Jennifer"],"index":16968,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7881138325,"difficulty":0.2118861675}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley's forehead is not muddy. It is publicly announced that Stanley's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Stanley can now know that Stanley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Stanley"],"index":42225,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8239046931,"difficulty":1.8239046931}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Loretta can now know that Rose can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Loretta","Carmen","Rose","Burt"],"index":9513,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristin does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that Lucretia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucretia","Larry","Kristin"],"index":49069,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997809529,"difficulty":0.0002190471}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis knows whether or not nobody's forehead is muddy. It is publicly announced that Martin's forehead is not muddy. It is publicly announced that Phillip does not know whether Phillip's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Martin can now know whether Phillip can know that Phillip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phillip","Martin","Francis"],"index":20871,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6545600295,"difficulty":0.3454399705}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott's forehead is not muddy. It is publicly announced that Florence knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Scott can now know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michelle","Scott","Florence","Barbara"],"index":33773,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9929212928,"difficulty":0.0070787072}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Perry's forehead is not muddy. It is publicly announced that Jo knows whether Perry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Perry can now know that Alfred can know whether Perry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Perry","Jo","Alfred"],"index":2400,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999597609,"difficulty":0.000402391}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Lillian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] 0","hypothesis":"Joyce can now know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joyce","Robert","Lillian","John"],"index":30122,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999484539,"difficulty":0.000515461}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Evelyn can now know that Helen can know whether Kathleen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","Helen","Evelyn","Nicholas"],"index":24451,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996102452,"difficulty":0.0003897548}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Eric can now know that Bradley can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bradley","Robert","Eric","Betty"],"index":53514,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962922931,"difficulty":0.0037077069}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl does not know whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Carl can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carl","Adam","Frank","Gale"],"index":29077,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985696077,"difficulty":0.0014303923}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vanessa does not know whether Vanessa's forehead is muddy. It is publicly announced that Vanessa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ralph can now know that Vanessa can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vanessa","Douglas","Ralph","Dave"],"index":13394,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether someone's forehead is muddy. It is publicly announced that Joseph does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Christopher can now know that Derek can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Derek","Steven","Joseph"],"index":13712,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9899629951,"difficulty":0.0100370049}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Thomas can now know that David can know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","David","Kathy"],"index":54067,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993102551,"difficulty":0.0006897449}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Cherie can now know that Vicki can know whether Vicki's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Michele","Vicki","Cherie"],"index":1111,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958111048,"difficulty":0.0041888952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva does not know whether or not everyone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Catherine","Eva","James","Jermaine"],"index":33737,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979048967,"difficulty":0.0020951033}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Ruth's forehead is muddy. It is publicly announced that Ruth does not know whether Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Harold can now know whether Ruth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harold","Robert","Ruth"],"index":56537,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7792820334,"difficulty":0.2207179666}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Gregory can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debra","Richard","Gregory","Curt"],"index":46335,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984954596,"difficulty":0.0015045404}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is not muddy. It is publicly announced that William's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"William can now know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roxie","William","Stephanie"],"index":13606,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.785662353,"difficulty":0.214337647}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Robert can now know whether Cathy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janet","Cathy","Mary","Robert"],"index":57884,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994373918,"difficulty":0.0005626082}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise does not know whether Denise's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Denise can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Denise","Jeffery","Shirley"],"index":6632,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985647798,"difficulty":0.0014352202}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Cynthia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cynthia","Robert","Mary","Antonina"],"index":10831,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980159998,"difficulty":0.0019840002}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal knows whether Kathrine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Crystal can now know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathrine","Christopher","Crystal"],"index":15472,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981634021,"difficulty":0.0018365979}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Morris knows whether someone's forehead is muddy. It is publicly announced that Misty does not know whether Misty's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Morris knows whether Morris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Misty can now know whether Amanda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Misty","Morris","Amanda","Mary"],"index":26632,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991858602,"difficulty":0.0008141398}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jorge knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Diana can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edward","Jorge","Robert","Diana"],"index":45463,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9906045794,"difficulty":0.0093954206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana knows whether Diana's forehead is muddy. It is publicly announced that Eleanore knows whether Adam's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Diana can now know that Adam can know that Billy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Adam","Eleanore","Billy","Diana"],"index":6032,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981655478,"difficulty":0.0018344522}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Jacqueline can now know that Beverly can know that Beverly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacqueline","Beverly","Thomas","John"],"index":3281,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980015159,"difficulty":0.0019984841}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence knows whether someone's forehead is muddy. It is publicly announced that Clarence does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Felipe can now know that Clarence can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Clarence","Felipe"],"index":13453,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9757562876,"difficulty":0.0242437124}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dave can now know that Connie can know that Connie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dave","Connie","Dale","Carolyn"],"index":14241,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984972477,"difficulty":0.0015027523}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether or not everyone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Betty can now know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Corliss","Donald","Betty","Barbra"],"index":34880,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9129653573,"difficulty":0.0870346427}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether or not everyone's forehead is muddy. It is publicly announced that Lillian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Jesse can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lillian","Rebecca","Jesse"],"index":54607,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984682202,"difficulty":0.0015317798}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene does not know whether Irene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sandra can now know whether Dexter can know whether Irene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irene","Eugene","Sandra","Dexter"],"index":26759,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995361567,"difficulty":0.0004638433}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Dennis can now know that Dennis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darlene","Dennis","Heidy","Henry"],"index":673,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980928302,"difficulty":0.0019071698}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Melissa can now know that Albert can know whether Molly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Molly","Albert","Melissa"],"index":15391,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996254444,"difficulty":0.0003745556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane does not know whether Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Michael can now know that Eric can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","George","Michael","Jane"],"index":24530,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9718125463,"difficulty":0.0281874537}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill knows whether Susie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Deborah can now know whether Susie can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susie","Deborah","Bill","Craig"],"index":14368,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996820688,"difficulty":0.0003179312}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris does not know whether Doris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Ginny can now know that Rudolph can know whether Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","Rudolph","Ginny","Doris"],"index":66197,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996203184,"difficulty":0.0003796816}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shari knows whether someone's forehead is muddy. It is publicly announced that Steven does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Shari can now know that Steven can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Steven","Shari"],"index":15380,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9498566985,"difficulty":1.9498566985}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Frederick can now know that Randy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frederick","Barbara","Randy","Linda"],"index":51162,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5939893126,"difficulty":0.4060106874}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Ashley can now know whether Alexa can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ashley","Alexa"],"index":18663,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Glenn can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Glenn","Brian"],"index":26143,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983316064,"difficulty":0.0016683936}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sam does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marlene can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sam","Francis","Barry","Marlene"],"index":2674,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979096055,"difficulty":0.0020903945}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis does not know whether or not everyone's forehead is muddy. It is publicly announced that Harlan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Harlan can now know whether Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Louis","Harlan","Doris"],"index":21618,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993761182,"difficulty":0.0006238818}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Ruth can now know whether Joey can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joey","Lea","Ruth","Lyn"],"index":16088,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997562766,"difficulty":0.0002437234}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jessie can now know whether Thomas can know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Dale","Jessie"],"index":7052,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7663590908,"difficulty":0.2336409092}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cody can now know that Curt can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nathanial","Curt","Michael","Cody"],"index":10561,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985615611,"difficulty":0.0014384389}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Raymond can now know whether Kimberly can know that Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Willie","Kimberly","Raymond"],"index":2743,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9041911364,"difficulty":0.0958088636}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dorothy can now know that Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Annette","Dorothy","Carmelita"],"index":65622,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9532199502,"difficulty":0.0467800498}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ana does not know whether Ana's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Humberto can now know whether Ana can know whether Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raeann","Dorothy","Ana","Humberto"],"index":42227,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991814494,"difficulty":0.0008185506}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ted's forehead is not muddy. It is publicly announced that Ted knows whether Ted's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Richard can now know whether George can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Richard","Ted"],"index":58640,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996265173,"difficulty":0.0003734827}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Evelyn can know whether Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Marian","Evelyn"],"index":32175,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964680672,"difficulty":0.0035319328}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Caitlin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Caitlin can now know whether Lois can know that Caitlin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Caitlin","Theodore","Lois"],"index":41893,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5979687572,"difficulty":0.4020312428}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Gilda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Gilda","Randal","Kelly"],"index":50168,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5825780034,"difficulty":0.4174219966}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether someone's forehead is muddy. It is publicly announced that Ollie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"Janice can now know that Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Ollie","Gerald","Mike"],"index":15279,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99189502,"difficulty":0.00810498}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa does not know whether Rosa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Elizabeth can now know whether Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Nancy","Rosa","Sarah"],"index":18357,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995949864,"difficulty":0.0004050136}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jessica can now know whether Michelle can know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Anthony","Jessica","Alicia"],"index":30079,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993261099,"difficulty":0.0006738901}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myron does not know whether or not everyone's forehead is muddy. It is publicly announced that Myron does not know whether Myron's forehead is muddy. It is publicly announced that Brad's forehead is muddy. It is publicly announced that Brad knows whether Myron's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brad can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Myron","Brad"],"index":44765,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975484014,"difficulty":0.0024515986}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edgar knows whether Edgar's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Clifton can now know whether Joe can know whether Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Joe","Clifton","Edgar"],"index":53393,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9461075664,"difficulty":1.9461075664}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Sara can now know whether Mario can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sara","Mario"],"index":65376,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9528006911,"difficulty":0.0471993089}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa does not know whether Teresa's forehead is muddy. It is publicly announced that Jonathan does not know whether Jonathan's forehead is muddy. It is publicly announced that George knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"George can now know whether Jonathan can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jonathan","George","Teresa"],"index":42179,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7795401812,"difficulty":1.7795401812}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosalinda does not know whether Rosalinda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Peter can now know whether Rosalinda can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Michael","Dorothy","Rosalinda"],"index":65844,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997668862,"difficulty":0.0002331138}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Rita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Gertrude can now know that Gertrude's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Rita","Matthew","Gertrude"],"index":4570,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980331063,"difficulty":0.0019668937}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Earl knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Robert can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earl","Mary","Robert","Emma"],"index":46574,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5322064161,"difficulty":0.4677935839}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Dorothy can now know whether Dean can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Francine","Dean","Erin","Dorothy"],"index":57556,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9968597889,"difficulty":1.9968597889}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred knows whether or not nobody's forehead is muddy. It is publicly announced that Fred knows whether Christina's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Christina can now know whether Fred can know whether Fred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Christina","Fred"],"index":52520,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5210182071,"difficulty":1.5210182071}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Paul can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kendall","Jeffrey","Paul"],"index":39958,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984662533,"difficulty":0.0015337467}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Deborah can now know whether Iris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vivian","Hubert","Deborah","Iris"],"index":54765,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999586165,"difficulty":0.000413835}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"James can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Naomi","James"],"index":38419,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997258782,"difficulty":0.0002741218}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joey can now know that Justin can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Justin","Joey","Elizabeth"],"index":41298,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sara does not know whether Sara's forehead is muddy. It is publicly announced that Jason knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sara","Jennifer","Jason","James"],"index":19702,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986559153,"difficulty":0.0013440847}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Mark can know that Tamara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tamara","Mark","William"],"index":46088,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9972651005,"difficulty":0.0027348995}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy. It is publicly announced that Ray does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"James can now know whether Ray can know that Ray's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ray","James"],"index":56411,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7287795544,"difficulty":0.2712204456}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sara does not know whether Sara's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Sara knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Sara can now know whether James can know that Shayla's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","James","Sara","Shayla"],"index":24211,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9800772667,"difficulty":0.0199227333}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know whether Patty can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Patty","Helen","Belinda"],"index":65450,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9974527955,"difficulty":0.0025472045}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shauna does not know whether Shauna's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jacob can now know that Jacob's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Linda","Jacob","Shauna"],"index":18050,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9924227595,"difficulty":0.0075772405}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monique knows whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Monique can now know that Cynthia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Monique","Misti","Dale"],"index":48278,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983281493,"difficulty":0.0016718507}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stella knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Calvin can now know whether James can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Stella","Calvin"],"index":46779,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9766814113,"difficulty":0.0233185887}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Mindi's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mindi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Dolly can now know that Mindi's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christopher","Terrance","Dolly","Mindi"],"index":45520,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9325314164,"difficulty":0.0674685836}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Doyle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Michael can now know whether Doyle can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Doyle","Michael"],"index":26814,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997562766,"difficulty":0.0002437234}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Joe can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Mark","Joe","Heather"],"index":42766,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928213954,"difficulty":0.0071786046}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina does not know whether Tina's forehead is muddy. It is publicly announced that Annette knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Tina can now know whether Annette can know whether Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Annette","Tina"],"index":41465,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991426468,"difficulty":0.0008573532}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether someone's forehead is muddy. It is publicly announced that Arlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] 0","hypothesis":"Pauline can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Travis","Christopher","Arlene","Pauline"],"index":14665,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Vera can now know that Raymond can know whether Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vera","Raymond","Tonie","James"],"index":61764,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9935888052,"difficulty":0.0064111948}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] 0","hypothesis":"Kathy can now know that Edward can know whether Kathy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edward","Kathy"],"index":25840,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995151758,"difficulty":0.0004848242}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ida's forehead is muddy. It is publicly announced that Helen does not know whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Sylvia can now know whether Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ida","Sylvia","Doris","Helen"],"index":12650,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995747209,"difficulty":0.0004252791}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Marie knows whether Harry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Harry can now know that Leana can know whether Leana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marie","Harry","Leana"],"index":37368,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7550287247,"difficulty":1.7550287247}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jillian knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Anthony can now know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Jillian","Christopher","Stephen"],"index":26033,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9620984793,"difficulty":0.0379015207}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Edith can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dale","Sue","Edith"],"index":42969,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9847962856,"difficulty":0.0152037144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy does not know whether Timothy's forehead is muddy. It is publicly announced that Dorthy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agenta knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] 0","hypothesis":"Eddie can now know whether Dorthy can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eddie","Timothy","John","Dorthy"],"index":65962,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980042577,"difficulty":0.0019957423}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Steven can now know whether Frank can know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","Steven","Ruth"],"index":46943,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991167188,"difficulty":0.0008832812}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Grace knows whether John's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Constance can now know whether Grace can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","John","Constance","Grace"],"index":38096,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.984310627,"difficulty":0.015689373}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Beverly can now know that Mary can know whether Beverly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Beverly"],"index":49796,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999194324,"difficulty":0.000805676}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Petronila does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Petronila","Richard","James","Melissa"],"index":5819,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997288585,"difficulty":0.0002711415}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Betty can now know that Ruby can know whether Ruby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruby","Betty","Patricia"],"index":58363,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9542159438,"difficulty":0.0457840562}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Xavier does not know whether Xavier's forehead is muddy. It is publicly announced that Barbera does not know whether Barbera's forehead is muddy. It is publicly announced that Xavier knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Barbara can now know that James can know that Xavier's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbera","Barbara","Xavier","James"],"index":41201,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9844685197,"difficulty":0.0155314803}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aurelia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Lillian can now know whether Aurelia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lillian","Aurelia"],"index":66730,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995322227,"difficulty":0.0004677773}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Fallon can now know whether Charles can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Charles","Fallon"],"index":35183,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999712646,"difficulty":0.000287354}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall knows whether Randall's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lisa can now know whether Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Jason","Randall","Carolyn"],"index":66,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9915906191,"difficulty":1.9915906191}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela does not know whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Angela can now know whether Teodoro can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sandra","Teodoro","Angela"],"index":3782,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9182172418,"difficulty":0.0817827582}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether Alejandro's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Helen can now know whether Leo can know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stanley","Helen","Leo","Alejandro"],"index":42509,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.972982347,"difficulty":0.027017653}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is not muddy. It is publicly announced that Aaron does not know whether Aaron's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Aaron can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Matthew","Douglas","Aaron"],"index":11673,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9546611905,"difficulty":1.9546611905}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita does not know whether Rita's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Daniel can now know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julian","Rita","Daniel"],"index":31028,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9853459597,"difficulty":0.0146540403}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy does not know whether Randy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know that Randy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Randy","Steven","Kenneth"],"index":40364,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998341918,"difficulty":0.001658082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucinda does not know whether Lucinda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Michael can now know whether Gloria can know whether Gloria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Kenneth","Lucinda","Michael"],"index":3080,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9072183371,"difficulty":0.0927816629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Carmen can now know whether Latoya's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carmen","Lewis","Jeffery","Latoya"],"index":27500,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994018078,"difficulty":0.0005981922}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not everyone's forehead is muddy. It is publicly announced that Raymond does not know whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Giuseppe can now know whether Sam's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Raymond","Sam","Giuseppe"],"index":53245,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994444251,"difficulty":0.0005555749}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gustavo knows whether or not nobody's forehead is muddy. It is publicly announced that Judith does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Judith can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gustavo","Lucille","Judith"],"index":40833,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979858398,"difficulty":0.0020141602}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances's forehead is muddy. It is publicly announced that Tiffany knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Frances can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tiffany","Art","Frances","Nora"],"index":31787,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997196794,"difficulty":0.0002803206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Aaron can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aaron","Devon","Leslie","Eva"],"index":11935,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978786707,"difficulty":0.0021213293}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"David can now know whether Steven can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Steven","David"],"index":10170,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6253997087,"difficulty":1.6253997087}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ross's forehead is not muddy. It is publicly announced that Bob knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Bob can now know whether Ross's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bob","Ross","Roland"],"index":29887,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995997548,"difficulty":0.0004002452}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether someone's forehead is muddy. It is publicly announced that Jacqueline knows whether Bradley's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Leesa can now know whether Jacqueline can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Leesa","Bradley","Jacqueline"],"index":48043,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99975878,"difficulty":0.00024122}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Jennifer","Keenan","Joseph"],"index":48001,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978715181,"difficulty":0.0021284819}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Paul can now know whether Theresa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Frank","Paul","Theresa","Sheba"],"index":33840,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995660186,"difficulty":0.0004339814}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Naomi knows whether Ronnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ronnie can now know that Ramona can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronnie","Dana","Naomi","Ramona"],"index":8509,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9893364906,"difficulty":0.0106635094}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jennifer can now know that Latoya can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Shirley","Latoya","David"],"index":21006,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984117746,"difficulty":0.0015882254}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kent does not know whether or not everyone's forehead is muddy. It is publicly announced that Minnie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Minnie can now know that Kent can know whether Kent's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Minnie","Bradley","Carla","Kent"],"index":51342,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5991976857,"difficulty":0.4008023143}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandi knows whether Iva's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Iva does not know whether Iva's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Iva can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brandi","Ethel","Iva"],"index":47181,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983462095,"difficulty":0.0016537905}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Thomas knows whether Rebecca's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rebecca can now know that Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Thomas","David","Rebecca"],"index":44779,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997788072,"difficulty":0.0002211928}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Joann can now know whether Peter can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Peter","Joann"],"index":776,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.985491693,"difficulty":0.014508307}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlton knows whether or not nobody's forehead is muddy. It is publicly announced that Joshua's forehead is not muddy. It is publicly announced that Alisha does not know whether Alisha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Carlton can now know whether Joshua can know whether Alisha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alisha","Joshua","Carlton"],"index":15651,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998739779,"difficulty":0.001260221}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laveta knows whether Miguel's forehead is muddy. It is publicly announced that Laveta knows whether or not everyone's forehead is muddy. It is publicly announced that Miguel knows whether Laveta's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Miguel can now know that Laveta can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Laveta","Miguel"],"index":2905,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981360435,"difficulty":0.0018639565}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Mark can now know whether Nancy can know whether Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Henry","Mark","Tina"],"index":28182,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995253086,"difficulty":0.0004746914}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Clifford can now know whether Nellie can know that Clifford's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clifford","Daniel","Rose","Nellie"],"index":60470,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9353080988,"difficulty":0.0646919012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felice does not know whether Felice's forehead is muddy. It is publicly announced that Marlin knows whether Marlin's forehead is muddy. It is publicly announced that Marlin knows whether Marlin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Felice can now know that Mona can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mona","Felice","Marlin"],"index":28700,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984069467,"difficulty":0.0015930533}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne knows whether Tara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Yvonne can now know whether Tara can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Yvonne","Tara","Heather"],"index":40857,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99975878,"difficulty":0.00024122}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know whether Kim can know that Kim's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","Mary","Mathew"],"index":11609,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5876282454,"difficulty":1.5876282454}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth's forehead is muddy. It is publicly announced that James knows whether Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Ruth can now know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Evelyn","Ruth","Jennifer","James"],"index":24200,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6400895715,"difficulty":0.3599104285}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Charlotte can now know whether Dana can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Dana","Charlotte"],"index":13881,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9959841967,"difficulty":0.0040158033}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether Brenda's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brenda","Mary","Helen"],"index":5497,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997506738,"difficulty":0.0002493262}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Jesse's forehead is muddy. It is publicly announced that Frances does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jesse can now know that Jerry can know whether Jesse's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Jerry","Jesse","Frances"],"index":62657,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991500378,"difficulty":0.0008499622}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack does not know whether Jack's forehead is muddy. It is publicly announced that Fredrick knows whether or not nobody's forehead is muddy. It is publicly announced that Fredrick knows whether Fredrick's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Fredrick can now know whether Jack's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jack","Fredrick"],"index":61127,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994928837,"difficulty":0.0005071163}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paula knows whether someone's forehead is muddy. It is publicly announced that Lesia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Paula can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lesia","Paula"],"index":39005,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985281229,"difficulty":0.0014718771}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Agnes does not know whether Agnes's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Claude can now know that Josie can know whether Josie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Josie","Agnes","Claude"],"index":57676,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9883092642,"difficulty":0.0116907358}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether or not nobody's forehead is muddy. It is publicly announced that Ryan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ryan can now know whether Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ryan","Laura"],"index":14355,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994526505,"difficulty":0.0005473495}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cory does not know whether or not everyone's forehead is muddy. It is publicly announced that Andrew knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Cory can now know that Andrew can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cory","Andrew"],"index":49653,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9683306813,"difficulty":0.0316693187}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose knows whether Eugenia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Rose can now know that Jana can know whether Jana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eugenia","Rose","Violet","Jana"],"index":35663,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.991230011,"difficulty":0.008769989}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Chris can now know that Mildred's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mildred","Dorothy","Chris"],"index":20511,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976503253,"difficulty":0.0023496747}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ron knows whether someone's forehead is muddy. It is publicly announced that Ron knows whether Janet's forehead is muddy. It is publicly announced that Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"Janet can now know whether Ron can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janet","Robert","Ron"],"index":49786,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7653000355,"difficulty":0.2346999645}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reuben does not know whether Reuben's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Anthony knows whether or not everyone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] Agenta knows that (Agentd knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Everett can now know that Irene can know that Reuben's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Everett","Anthony","Reuben","Irene"],"index":41312,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7786930799,"difficulty":0.2213069201}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether Diane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Alexandria can now know whether Brian can know whether Diane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Alexandria","Brian"],"index":17541,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999545753,"difficulty":0.000454247}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether Robert's forehead is muddy. It is publicly announced that Henry does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Henry can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Henry","Robert"],"index":42880,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.943652451,"difficulty":1.943652451}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wade knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Guillermo can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donald","Guillermo","Wade","Polly"],"index":13090,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997261167,"difficulty":0.0002738833}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Franklyn does not know whether Franklyn's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3&4) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jacob can now know that Franklyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacob","Franklyn","Maureen","Mary"],"index":28824,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9978314042,"difficulty":0.0021685958}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emma's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Emma can now know that Roberta can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roberta","Emma","Mark"],"index":16558,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984155893,"difficulty":0.0015844107}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne knows whether someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Joanne can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joanne","James","Rickey","Patrick"],"index":63319,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.649230659,"difficulty":0.350769341}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela does not know whether Pamela's forehead is muddy. It is publicly announced that Pamela does not know whether Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Pamela can now know whether Kathleen can know whether Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathleen","Pamela"],"index":5252,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991668463,"difficulty":0.0008331537}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mike can now know that James can know that Mike's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mike","James"],"index":4366,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981702566,"difficulty":0.0018297434}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick does not know whether or not everyone's forehead is muddy. It is publicly announced that Iris knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Iris can now know that Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","Veronica","Iris","Tracy"],"index":25191,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5688973069,"difficulty":0.4311026931}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Gerald can now know that Carmen can know whether Cortney's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cortney","Carmen","Janice","Gerald"],"index":21903,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995391369,"difficulty":0.0004608631}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy. It is publicly announced that Carl does not know whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lillian can now know whether Dorothy can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Carl","Lillian"],"index":2115,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Ramon can now know that Christine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Aline","Ramon","Christine"],"index":23848,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982428551,"difficulty":0.0017571449}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Justin can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Charles","Justin","Annie"],"index":42152,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995948672,"difficulty":0.0004051328}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Virginia can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tami","Virginia","Eunice","Mary"],"index":57974,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979069233,"difficulty":0.0020930767}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"William can now know that Barbara can know whether Kris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Kris","Barbara"],"index":31759,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995835423,"difficulty":0.0004164577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Rose can now know whether David can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Chung","Lawrence","David"],"index":38737,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Shirley can now know that Francis can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Francis","Patricia","Laurie","Shirley"],"index":53966,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984667897,"difficulty":0.0015332103}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Martha can now know whether Zachary can know that Aaron's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barton","Martha","Aaron","Zachary"],"index":49027,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9905303121,"difficulty":0.0094696879}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Julia does not know whether Julia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Helen can now know that Melanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Julia","Melanie"],"index":55047,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936019778,"difficulty":0.0063980222}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norene does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Christopher can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rosa","Norene","Alonzo","Christopher"],"index":4282,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987570047,"difficulty":0.0012429953}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward does not know whether Edward's forehead is muddy. It is publicly announced that Edward's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agentb knows that (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Evelyn can now know that Amber can know whether Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Evelyn","Edward","Amber"],"index":13869,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987498522,"difficulty":0.0012501478}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Max does not know whether Max's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Mary can now know that Rebecca can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Bianca","Mary","Max"],"index":58369,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985105395,"difficulty":0.0014894605}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shayla does not know whether or not everyone's forehead is muddy. It is publicly announced that Shayla knows whether Sharon's forehead is muddy. It is publicly announced that Shayla does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Garry can now know whether Shayla's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sharon","Robert","Shayla","Garry"],"index":6484,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991618395,"difficulty":0.0008381605}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather does not know whether Heather's forehead is muddy. It is publicly announced that Cecil knows whether Heather's forehead is muddy. It is publicly announced that Cecil does not know whether Cecil's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Heather can now know that Cecil can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Lula","Cecil","Heather"],"index":39504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960898161,"difficulty":0.0039101839}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Stephen can now know whether Joseph can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","William","Stephen"],"index":27479,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8855143189,"difficulty":0.1144856811}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrea does not know whether Andrea's forehead is muddy. It is publicly announced that Andrea does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Carol can now know that Andrea can know that Andrea's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Andrea","Carol"],"index":27297,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7957153916,"difficulty":1.7957153916}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Leona can now know that Johnny's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leona","Casey","Johnny"],"index":1122,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9908549786,"difficulty":0.0091450214}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Virgil can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virgil","Leonard","Mark"],"index":61966,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988723397,"difficulty":0.0011276603}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Holly knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lisa can now know that Holly can know whether Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katelyn","Holly","Lisa","Donald"],"index":33646,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.996437788,"difficulty":0.003562212}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Kathleen can now know that Rita can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathleen","Rita"],"index":46868,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993658662,"difficulty":0.0006341338}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Theresa can now know whether Judy can know whether Judy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Raymond","Theresa","Laurence","Judy"],"index":55147,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9899004102,"difficulty":0.0100995898}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Thomas can now know that Patricia can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Glen","Thomas","Patricia"],"index":45710,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994543195,"difficulty":0.0005456805}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Andrew can now know that Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Andrew","Gregory"],"index":44413,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9935798645,"difficulty":0.0064201355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ned does not know whether or not everyone's forehead is muddy. It is publicly announced that Lakesha knows whether or not everyone's forehead is muddy. It is publicly announced that Ned does not know whether Ned's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Bonita can now know that Ned can know that Bonita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Lakesha","Bonita","Ned"],"index":21080,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.954092443,"difficulty":1.954092443}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy. It is publicly announced that Brian knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Theresa can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Theresa","Brian"],"index":44523,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994521737,"difficulty":0.0005478263}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Denise can now know that Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amanda","Nicole","Denise","Bryan"],"index":14628,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.637182653,"difficulty":0.362817347}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Luis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"David can now know that Luis can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gregorio","Donald","David","Luis"],"index":21653,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9724668264,"difficulty":0.0275331736}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether or not nobody's forehead is muddy. It is publicly announced that Amanda does not know whether Amanda's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Amanda can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Elizabeth","Amanda"],"index":62398,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8599433303,"difficulty":0.1400566697}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether someone's forehead is muddy. It is publicly announced that Gregory knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Catherine can now know whether Gregory can know whether Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Gregory"],"index":16938,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9667216539,"difficulty":0.0332783461}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Charles can now know that Alfred can know that Alfred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","James","Alfred","Bridgett"],"index":16136,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962182641,"difficulty":0.0037817359}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Judy can now know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Adeline","Patricia","Thelma","Judy"],"index":27664,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993793964,"difficulty":0.0006206036}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria does not know whether Gloria's forehead is muddy. It is publicly announced that Gloria's forehead is muddy. It is publicly announced that Andrew's forehead is muddy. It is publicly announced that Victor's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agentc knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Andrew can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gloria","Victor","Andrew","Chelsea"],"index":33483,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994686246,"difficulty":0.0005313754}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether Samuel's forehead is muddy. It is publicly announced that Debra does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Samuel can now know that Debra can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Debra","Samuel"],"index":12172,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988902211,"difficulty":0.0011097789}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tasha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Lee can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tasha","Roberto","Lee","Jordan"],"index":43937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969688058,"difficulty":0.0030311942}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christian does not know whether Christian's forehead is muddy. It is publicly announced that Christian's forehead is not muddy. It is publicly announced that Christian knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Joan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christian","Joan"],"index":41199,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990255833,"difficulty":0.0009744167}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Lee can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lee","Russell","Marcelino","Lillie"],"index":33767,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994413257,"difficulty":0.0005586743}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether or not nobody's forehead is muddy. It is publicly announced that Joseph does not know whether or not everyone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Joseph can now know that Jane can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jane","Joseph"],"index":35615,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994743466,"difficulty":0.0005256534}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy. It is publicly announced that Sylvia does not know whether Sylvia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jodi can now know that Sylvia can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvia","Jodi","Angela","Charles"],"index":51803,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999442637,"difficulty":0.000557363}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gina does not know whether or not everyone's forehead is muddy. It is publicly announced that Gina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Gwendolyn can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gwendolyn","Gina"],"index":27837,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979179502,"difficulty":0.0020820498}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Howard can now know that Claudia can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Howard","Claudia"],"index":5079,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9965342283,"difficulty":0.0034657717}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edie's forehead is muddy. It is publicly announced that Kristen does not know whether Kristen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kristen can now know whether James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Edie","Kristen"],"index":49900,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9569419622,"difficulty":1.9569419622}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Dennis can now know that Grace can know that Grace's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Grace","Deborah"],"index":23909,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975827932,"difficulty":0.0024172068}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Camille's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Angela can now know whether Angela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Greg","Angela","Camille","Liza"],"index":26937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9921646118,"difficulty":0.0078353882}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Damian does not know whether Damian's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Phyllis can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Damian","Phyllis"],"index":25991,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994899035,"difficulty":0.0005100965}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nancy can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peggie","Nancy","Raymond"],"index":5289,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9919658899,"difficulty":0.0080341101}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Donald","Christa"],"index":45260,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.993101716,"difficulty":0.006898284}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jacqueline can now know whether Jacqueline's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Jennifer","Jacqueline"],"index":38532,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952594638,"difficulty":0.0047405362}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Annette can now know that Luis can know whether Annette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annette","Luis","James","Peter"],"index":65802,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987558126,"difficulty":0.0012441874}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Christine can now know that Sandra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Randall","Christine","Lee","Sandra"],"index":36399,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8639273047,"difficulty":1.8639273047}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cristina does not know whether Cristina's forehead is muddy. It is publicly announced that Steven knows whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"James can now know whether Steven can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Harry","Steven","Cristina"],"index":15299,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993168116,"difficulty":0.0006831884}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kim can now know whether Steven can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Kim","Steven","Laura"],"index":24648,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991835952,"difficulty":0.0008164048}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dave can now know that Mark can know whether Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Joseph","Dave"],"index":15249,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993745685,"difficulty":0.0006254315}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kayla does not know whether or not everyone's forehead is muddy. It is publicly announced that Kayla does not know whether Kayla's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kayla can now know that Melody can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kayla","Melody"],"index":20293,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994831085,"difficulty":0.0005168915}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jillian knows whether Jacob's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Noah can now know that Jacob can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Jillian","Noah","Jacob"],"index":8789,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9793463945,"difficulty":0.0206536055}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Elisa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Elisa","James","Martha"],"index":1639,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974695444,"difficulty":0.0025304556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale does not know whether Dale's forehead is muddy. It is publicly announced that Dale does not know whether Dale's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Dale","Kurt","Laura"],"index":29784,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989639521,"difficulty":0.0010360479}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wonda can now know whether Victor can know that Sean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Victor","Kay","Sean","Wonda"],"index":11657,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9777367711,"difficulty":0.0222632289}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Chu can now know whether Sandra can know whether Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Denise","Aaron","Chu"],"index":4036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9910079837,"difficulty":0.0089920163}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy. It is publicly announced that Loretta knows whether Loretta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Loretta can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Jeremy","Loretta","Mike"],"index":64206,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994511008,"difficulty":0.0005488992}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agentd knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Michael can now know that Brian can know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Brian","Diane","Michael"],"index":59713,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9073625803,"difficulty":0.0926374197}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leo knows whether or not nobody's forehead is muddy. It is publicly announced that Leo knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marie","Mary","John","Leo"],"index":66784,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993274212,"difficulty":0.0006725788}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether Gerald's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Gerald can now know whether Roger can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Gerald","Roger"],"index":40145,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993740916,"difficulty":0.0006259084}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that Mathew can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Mathew"],"index":43972,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994872808,"difficulty":0.0005127192}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa does not know whether Rosa's forehead is muddy. It is publicly announced that Gilbert knows whether Rosa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Rosa can now know that Kim can know whether Rosa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gilbert","Kim","Nicholas","Rosa"],"index":7800,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998771131,"difficulty":0.001228869}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew does not know whether Matthew's forehead is muddy. It is publicly announced that Josie knows whether or not everyone's forehead is muddy. It is publicly announced that Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Josie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josie","Jose","Gary","Matthew"],"index":44707,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994594455,"difficulty":0.0005405545}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Rhonda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Doris can now know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rhonda","Timothy","Doris"],"index":23089,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990792274,"difficulty":0.0009207726}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"James can now know whether Larry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chester","James","Larry"],"index":4801,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993721843,"difficulty":0.0006278157}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clare knows whether Clare's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Clare can now know that Monica can know whether Monica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monica","Cheryl","Edward","Clare"],"index":45442,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9912911654,"difficulty":1.9912911654}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Caroline can now know that Sheila can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irene","Dorothy","Sheila","Caroline"],"index":23970,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988268018,"difficulty":0.0011731982}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Steven can now know that Lorna can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lorna","Blythe","Steven"],"index":45586,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9130086899,"difficulty":0.0869913101}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Ramona knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"April can now know that Ramona can know that April's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ramona","Nancy","April","John"],"index":50940,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972443581,"difficulty":0.0027556419}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas's forehead is muddy. It is publicly announced that Sidney knows whether Jimmy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jimmy can now know whether Thomas can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmy","Thomas","Sidney"],"index":47560,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9108695984,"difficulty":0.0891304016}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Roger can now know whether Randall can know that Beau's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beau","Randall","John","Roger"],"index":19013,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9949059486,"difficulty":0.0050940514}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwayne knows whether or not everyone's forehead is muddy. It is publicly announced that Dwayne does not know whether Dwayne's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Dwayne can now know that Edward can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dwayne","Joseph","Edward"],"index":52428,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994668365,"difficulty":0.0005331635}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether Ernie's forehead is muddy. It is publicly announced that Joe does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Joe can now know whether Ernie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joe","Ernie"],"index":50519,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994619489,"difficulty":0.0005380511}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Gerald's forehead is muddy. It is publicly announced that Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Joseph can now know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gerald","Joseph"],"index":32486,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6843591332,"difficulty":1.6843591332}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilfred knows whether Wilfred's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Miguel can now know that Wilfred can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Miguel","Wilfred"],"index":52561,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989053011,"difficulty":0.0010946989}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Michael"],"index":44676,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990488887,"difficulty":0.0009511113}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy. It is publicly announced that Barbara knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Mary can now know that Virginia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Mary","Virginia","David"],"index":47908,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989796281,"difficulty":0.0010203719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie knows whether or not everyone's forehead is muddy. It is publicly announced that Grant does not know whether Grant's forehead is muddy. It is publicly announced that Marie does not know whether Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Laura can now know that Pedro can know whether Pedro's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laura","Grant","Pedro","Marie"],"index":26925,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.954102993,"difficulty":1.954102993}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracey does not know whether Tracey's forehead is muddy. It is publicly announced that Lori knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Lori can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tracey","Lori"],"index":45738,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993844032,"difficulty":0.0006155968}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debbie does not know whether Debbie's forehead is muddy. It is publicly announced that Debbie's forehead is not muddy. It is publicly announced that Debbie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Debbie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debbie","Danny"],"index":61802,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994871616,"difficulty":0.0005128384}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether someone's forehead is muddy. It is publicly announced that Gerald knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Gerald can now know that Leanne can know whether Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leanne","Gerald"],"index":26514,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9887728095,"difficulty":0.0112271905}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annie's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Barbara can now know that Annie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ramona","Annie","Barbara"],"index":10636,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988364577,"difficulty":0.0011635423}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry does not know whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Amanda can now know that Bruce can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Georgia","Bruce","Henry","Amanda"],"index":9827,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9878419042,"difficulty":0.0121580958}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ray can now know that Ray's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ray","Eric","Mary"],"index":161,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953373671,"difficulty":0.0046626329}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Trisha's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Veronica can now know whether Trisha can know that Veronica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Veronica","Trisha","Linda"],"index":51192,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8251340389,"difficulty":1.8251340389}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Windy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Johnny can now know whether Johnny's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darrell","Marvin","Windy","Johnny"],"index":46486,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955875874,"difficulty":0.0044124126}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maggie does not know whether Maggie's forehead is muddy. It is publicly announced that Omar knows whether Omar's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Omar can now know that Maggie can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Carlos","Omar","Maggie"],"index":63707,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994270802,"difficulty":0.0005729198}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Duane knows whether Andrew's forehead is muddy. It is publicly announced that Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] 0","hypothesis":"Juanita can now know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Andrew","Cecilia","Duane"],"index":65572,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8164285421,"difficulty":0.1835714579}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maryellen does not know whether Maryellen's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether Maryellen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Maryellen","Rosemary"],"index":8863,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992415905,"difficulty":0.0007584095}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Jeannie can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Richard","Mary","Jeannie"],"index":34327,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9912125468,"difficulty":0.0087874532}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether Markus's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Brenda can now know whether Markus can know whether Markus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brenda","Markus"],"index":17353,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.986253202,"difficulty":1.986253202}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gerald can now know whether Thomas can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Kelly","Sharon","Gerald"],"index":64248,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.968875587,"difficulty":0.031124413}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Octavio's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Anna can now know whether Ebony can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Anna","Octavio","Ebony"],"index":25172,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993000031,"difficulty":0.0006999969}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margie knows whether or not everyone's forehead is muddy. It is publicly announced that Sybil's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Sybil can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sybil","Margie","Betty"],"index":8252,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.999037385,"difficulty":0.000962615}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila does not know whether Sheila's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Leroy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Sheila can now know whether Leroy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sheila","Leroy"],"index":16099,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9832487106,"difficulty":0.0167512894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know that Edward can know that Francis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Francis","Edward","Thomas"],"index":63630,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949413538,"difficulty":0.0050586462}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Edward can now know that Craig can know whether Alan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alan","Marshall","Edward","Craig"],"index":53948,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993514419,"difficulty":0.0006485581}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rene can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rene","Gary","Kyle","Angelina"],"index":57684,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994564652,"difficulty":0.0005435348}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Marie can now know that Alejandro's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alejandro","Todd","Marie","Nicole"],"index":58385,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976565838,"difficulty":0.0023434162}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Kenneth can now know that Walter's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Kim","Kenneth","Ann"],"index":21179,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977300763,"difficulty":0.0022699237}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Tracy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Tracy can now know whether Mandi can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mandi","Tracy"],"index":22132,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993848801,"difficulty":0.0006151199}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Nicholas can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicholas","Jennifer","James"],"index":24559,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994689822,"difficulty":0.0005310178}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Priscilla can know that Priscilla's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susanne","James","Priscilla"],"index":29972,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9032694101,"difficulty":0.0967305899}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loretta does not know whether Loretta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Loretta can now know whether Loretta's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Loretta","Eric","Virginia"],"index":41786,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.993293047,"difficulty":0.006706953}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Donald can now know whether Christopher can know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Elizabeth","Christopher"],"index":65557,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9765360951,"difficulty":0.0234639049}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Everett knows whether Sheila's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Everett can now know whether Everett's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Everett","Aaron","Sheila"],"index":34121,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9935541153,"difficulty":0.0064458847}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Hal can now know whether Jonathan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hal","Jonathan","Gladys"],"index":27260,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993675351,"difficulty":0.0006324649}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal does not know whether Crystal's forehead is muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Hazel can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Crystal","Jennifer","Hazel"],"index":5580,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990112782,"difficulty":0.0009887218}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Debra's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Lucila can now know whether Debra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lucila","Debra"],"index":11122,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9968807697,"difficulty":0.0031192303}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Doug can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Jesus","Doug","Ernie"],"index":45318,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972398281,"difficulty":0.0027601719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonita's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Mabel can now know whether Leslie can know whether Bonita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Mabel","Bonita","Leslie"],"index":16292,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992311001,"difficulty":0.0007688999}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce does not know whether Joyce's forehead is muddy. It is publicly announced that Karma's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Karma can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rolando","Karma","Joyce","Shirley"],"index":26492,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994495511,"difficulty":0.0005504489}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Laura knows whether Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Laura can now know that Matthew can know whether Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Laura","Matthew","Carrie"],"index":61595,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9381406903,"difficulty":1.9381406903}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton does not know whether Milton's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Al can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Milton","Al","Sadie"],"index":11012,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988926053,"difficulty":0.0011073947}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Lilian does not know whether Lilian's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lilian can now know that Merle can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Merle","Lilian"],"index":9184,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993054867,"difficulty":0.0006945133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Brad can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Brad","Jennifer","Joseph"],"index":21214,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9777145386,"difficulty":0.0222854614}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Dianne can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Dianne","Christopher"],"index":59928,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9543781877,"difficulty":0.0456218123}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Gabriel can now know whether Cindy can know that Cindy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cindy","Beverly","John","Gabriel"],"index":12793,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994245708,"difficulty":0.005754292}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know whether Leroy can know that Barry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barry","Leroy","David","Brian"],"index":271,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9847352505,"difficulty":0.0152647495}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Gerald can now know that Patricia can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Patricia","Gerald"],"index":12262,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8778366446,"difficulty":0.1221633554}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Stephanie does not know whether Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"John can now know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","John","Stephanie"],"index":43941,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996720612,"difficulty":0.003279388}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tara knows whether Tara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Tracy can now know that Tara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tracy","Tara","William","Frederick"],"index":58909,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9610216618,"difficulty":1.9610216618}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether or not nobody's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Dorsey can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dorsey","Sharon"],"index":24615,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989411235,"difficulty":0.0010588765}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know whether Helen can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Helen","Daniel","Paul"],"index":7460,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999414444,"difficulty":0.000585556}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"William can now know that Damon can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Damon","William"],"index":29527,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9928255081,"difficulty":0.0071744919}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen knows whether or not everyone's forehead is muddy. It is publicly announced that Ellen does not know whether Ellen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Irene can now know that Crystal can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellen","Crystal","Irene"],"index":43193,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994414449,"difficulty":0.0005585551}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vera knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Micheal can now know that Vera can know that Leigh's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Micheal","Leigh","Brian","Vera"],"index":59438,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970165491,"difficulty":0.0029834509}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sean knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Lamar can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lamar","Sean","Mollie"],"index":53227,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994060993,"difficulty":0.0005939007}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandy knows whether someone's forehead is muddy. It is publicly announced that Brandy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Brandy can now know whether Marie can know that Brandy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brandy","Marie"],"index":28997,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.821416378,"difficulty":0.178583622}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vaughn does not know whether Vaughn's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Patsy can now know that Vaughn can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patsy","Sandy","James","Vaughn"],"index":3926,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994115829,"difficulty":0.0005884171}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Annalee's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Annalee can now know whether John can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Annalee","Sharon","John","Melissa"],"index":36394,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9207553864,"difficulty":0.0792446136}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Melissa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Melissa can now know whether Mary can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Melissa","Laverne"],"index":26809,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994786382,"difficulty":0.0005213618}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Larry can now know whether James can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ettie","Ricardo","Larry","James"],"index":52133,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993678927,"difficulty":0.0006321073}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosalie does not know whether Rosalie's forehead is muddy. It is publicly announced that Johnny does not know whether Johnny's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rosalie can now know that Johnny can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnny","Vinita","Rosalie"],"index":10079,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994338155,"difficulty":0.0005661845}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Linda's forehead is muddy. It is publicly announced that Kelly does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Steven can now know whether Linda can know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Steven","Kelly"],"index":28812,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9785232544,"difficulty":0.0214767456}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Melissa can now know that Imogene can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Imogene","Melissa"],"index":62535,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994302392,"difficulty":0.0005697608}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley does not know whether Stanley's forehead is muddy. It is publicly announced that Micheal's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Janice can now know whether Janice's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Micheal","Stanley","Anna"],"index":18983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9788726568,"difficulty":0.0211273432}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Heather can now know that Sheryl can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Heather","Sheryl","Delia"],"index":2229,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998837173,"difficulty":0.001162827}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alicia can now know that William can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Alicia","Caridad","Jose"],"index":18791,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9961367249,"difficulty":0.0038632751}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorene knows whether someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Lorene can now know that Michael can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Lorene"],"index":46628,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7131379843,"difficulty":1.7131379843}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Joe can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Laura","Robert","Frank"],"index":42709,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9659634233,"difficulty":0.0340365767}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rey does not know whether Rey's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Alvin can now know whether Rey can know that Rey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rey","Alvin"],"index":1061,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5063548684,"difficulty":0.4936451316}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether someone's forehead is muddy. It is publicly announced that Stanley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] 0","hypothesis":"Stanley can now know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rita","Patricia","Stanley","Charles"],"index":39922,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9769226313,"difficulty":0.0230773687}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecilia does not know whether Cecilia's forehead is muddy. It is publicly announced that Cecilia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Cecilia can now know that Dave can know that Cecilia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Dave","Cecilia","Morris"],"index":47241,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9946680069,"difficulty":0.0053319931}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know that Jesse can know that Jesse's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edward","Jesse","Daniel"],"index":56650,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9682372212,"difficulty":0.0317627788}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha does not know whether Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Rebecca can now know that Martha can know whether Jeff's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeff","Willie","Rebecca","Martha"],"index":42838,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990854263,"difficulty":0.0009145737}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether or not nobody's forehead is muddy. It is publicly announced that Laura knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Clarissa can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Clarissa","Laura"],"index":12083,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983381033,"difficulty":0.0016618967}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Donald can now know that Michael can know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lynda","Reba","Donald","Michael"],"index":51428,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9720478654,"difficulty":0.0279521346}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Danny can now know that Anthony can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rodney","Anthony","Danny","June"],"index":17854,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988926053,"difficulty":0.0011073947}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Randi can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Robert","Mary","Randi"],"index":45433,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7305128574,"difficulty":0.2694871426}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Everett can now know that Janice can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janice","Bradford","Everett","Carolyn"],"index":49266,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984355569,"difficulty":0.0015644431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Francis can now know that Zachary can know that Zachary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juanita","Francis","Justin","Zachary"],"index":39612,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9912159443,"difficulty":0.0087840557}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Joshua can now know whether Jennifer can know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Helen","Joshua"],"index":57355,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9916252494,"difficulty":0.0083747506}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Everette's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Maria can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Maria","Everette"],"index":59708,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9954427481,"difficulty":0.0045572519}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy does not know whether Randy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that Robert can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Randy","Robert","John"],"index":56126,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993470311,"difficulty":0.0006529689}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stuart knows whether Stuart's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Stuart can now know that Stuart's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stuart","Jeffery","Debra","Belinda"],"index":33321,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9576666355,"difficulty":1.9576666355}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Viola does not know whether Viola's forehead is muddy. It is publicly announced that Viola knows whether or not nobody's forehead is muddy. It is publicly announced that Viola does not know whether Viola's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Viola can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Viola","Julian"],"index":51022,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994431138,"difficulty":0.0005568862}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason does not know whether or not everyone's forehead is muddy. It is publicly announced that Isabella knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kathryn can now know that Isabella can know that Isabella's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Isabella","Kathryn"],"index":51105,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6452077031,"difficulty":1.6452077031}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michael can now know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Yang","John","William"],"index":40098,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9909676909,"difficulty":0.0090323091}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander does not know whether or not everyone's forehead is muddy. It is publicly announced that Earlie knows whether Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Earlie can now know whether Alexander can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alexander","Earlie","Mary"],"index":62330,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993625283,"difficulty":0.0006374717}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luke knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Regina knows whether Luke's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Matthew can now know that Luke's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Luke","Matthew","Regina"],"index":520,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958309531,"difficulty":0.0041690469}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Noel's forehead is muddy. It is publicly announced that Noel knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Noel can now know whether Leslie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sherry","Mary","Noel","Leslie"],"index":9451,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9613759518,"difficulty":0.0386240482}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dena's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Harry can now know whether Dena can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dena","John","Raymond","Harry"],"index":51721,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994906187,"difficulty":0.0005093813}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie knows whether or not nobody's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know that Connie can know whether Connie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Robert","Connie"],"index":66302,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9915804267,"difficulty":1.9915804267}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether someone's forehead is muddy. It is publicly announced that Joyce knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Donald can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Joyce","Donald"],"index":5843,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994250536,"difficulty":0.0005749464}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gussie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rosemarie can now know that Gussie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Gussie","Rosemarie","Johnny"],"index":16154,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981770515,"difficulty":0.0018229485}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine does not know whether Geraldine's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jewel can now know that Frank can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geraldine","Jewel","Frank"],"index":32126,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994223118,"difficulty":0.0005776882}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann's forehead is muddy. It is publicly announced that Gregory knows whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Gregory can now know that Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shirley","Ann","Nicole","Gregory"],"index":52966,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6167799234,"difficulty":0.3832200766}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Brenda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cynthia","Brenda"],"index":38050,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979789853,"difficulty":0.0020210147}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether or not nobody's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy. It is publicly announced that Charles's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Kathy can now know whether Charles can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathy","Charles"],"index":37783,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994677901,"difficulty":0.0005322099}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Ashley knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ashley can now know that Mark can know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Ashley","Mark"],"index":13715,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9852390289,"difficulty":0.0147609711}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether Jaime's forehead is muddy. It is publicly announced that Brittany knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jaime can now know that Jaime's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","John","Brittany","Jaime"],"index":63983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9933179617,"difficulty":0.0066820383}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know that Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Melissa","Richard","Alan"],"index":45679,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8719962835,"difficulty":0.1280037165}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Jessica's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christina","Jessica","John"],"index":33848,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7277472019,"difficulty":1.7277472019}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Griselda does not know whether or not everyone's forehead is muddy. It is publicly announced that Marjorie knows whether Griselda's forehead is muddy. It is publicly announced that Griselda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Griselda can now know whether Marjorie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Griselda","Marjorie"],"index":35111,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8895205855,"difficulty":0.1104794145}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether James's forehead is muddy. It is publicly announced that James's forehead is muddy. It is publicly announced that Kay does not know whether Kay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kay can now know whether James can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kay","Paul","Ashley","James"],"index":2535,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9585688114,"difficulty":0.0414311886}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether Horace's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Horace can now know that Jessica can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Rachel","Horace","Jessica"],"index":7504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988868833,"difficulty":0.0011131167}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa's forehead is not muddy. It is publicly announced that Lisa knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lisa can now know that Hortencia can know that Hortencia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tara","Hortencia","Lisa"],"index":17241,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960526228,"difficulty":0.0039473772}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know whether Angela can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Angela","Jill"],"index":30321,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993294477,"difficulty":0.0006705523}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debby does not know whether Debby's forehead is muddy. It is publicly announced that Stephanie knows whether Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Debby can now know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Stephanie","Debby"],"index":57745,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.947312355,"difficulty":1.947312355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Marilyn can now know that Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marilyn","Terry","Angela","Lisa"],"index":65397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973394275,"difficulty":0.0026605725}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristin's forehead is not muddy. It is publicly announced that Cynthia does not know whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lauren can now know whether Lauren's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kristin","Lauren","Cynthia"],"index":11466,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9955501556,"difficulty":1.9955501556}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randolph does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Randolph can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Randolph","Theo"],"index":30042,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975929856,"difficulty":0.0024070144}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Lisa's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Lisa can now know that Brandy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brandy","Lisa"],"index":23379,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988613129,"difficulty":0.0011386871}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris does not know whether Doris's forehead is muddy. It is publicly announced that Doris does not know whether Doris's forehead is muddy. It is publicly announced that Doris's forehead is not muddy. It is publicly announced that Darlene does not know whether Darlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Darlene can now know that Brenda can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brenda","Doris","Darlene"],"index":27841,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990482926,"difficulty":0.0009517074}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Gladys can now know whether Jana can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gladys","Dennis","Jana","Bobby"],"index":47729,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9890079498,"difficulty":0.0109920502}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tonya knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tonya can now know whether Mary can know whether Heather's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","Lynne","Mary","Tonya"],"index":67120,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991244674,"difficulty":0.0008755326}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Shirley can now know that Jay can know that Jay's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jay","Shirley","William"],"index":35279,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9715803266,"difficulty":0.0284196734}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Mary can now know whether Otis can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Otis","Thomas","Mary"],"index":35468,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994320273,"difficulty":0.0005679727}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nancy can now know whether Mary can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eldon","Mary","Nancy"],"index":63887,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993299246,"difficulty":0.0006700754}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith knows whether Claude's forehead is muddy. It is publicly announced that Lynne does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Claude can now know that Judith can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Claude","Judith","Lynne"],"index":43845,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994718432,"difficulty":0.0005281568}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiffany knows whether Eugene's forehead is muddy. It is publicly announced that Gretchen knows whether Eugene's forehead is muddy. It is publicly announced that Eugene does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Gretchen can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eugene","Gretchen","Tiffany"],"index":53298,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980599284,"difficulty":0.0019400716}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maureen knows whether Rachel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agenta knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Nadine can now know whether Maureen can know that Maureen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nadine","Andrew","Rachel","Maureen"],"index":30938,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.976439476,"difficulty":0.023560524}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether or not nobody's forehead is muddy. It is publicly announced that Dorothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Ira can now know whether Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ira","Dorothy"],"index":25325,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9933350086,"difficulty":0.0066649914}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jim's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Margaret can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Robert","Jim","Shane"],"index":15655,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9903964996,"difficulty":0.0096035004}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hazel's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Hazel can now know that Joseph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hazel","Joseph"],"index":56198,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999473989,"difficulty":0.000526011}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is muddy. It is publicly announced that Jimmy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Jimmy can now know whether Kathleen can know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","Patricia","Jimmy","James"],"index":50429,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991756082,"difficulty":0.0008243918}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maggie knows whether or not everyone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that Stephanie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Alfredo","Robert","Maggie"],"index":63378,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994878769,"difficulty":0.0005121231}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gerald can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathryn","Gerald","John"],"index":57521,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989227653,"difficulty":0.0010772347}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy. It is publicly announced that Katrina's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Barbara can now know whether Gary can know whether Katrina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Katrina","Barbara"],"index":10343,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999147892,"difficulty":0.000852108}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"James can now know whether John can know whether Frank's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","James","John"],"index":37188,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998052597,"difficulty":0.001947403}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Adrian can now know whether Jared's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christine","Jared","Anita","Adrian"],"index":1237,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992967844,"difficulty":0.0007032156}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] Agenta knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Hubert can now know that Jean can know whether Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hubert","Carol","Matthew","Jean"],"index":54312,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8714450002,"difficulty":0.1285549998}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy. It is publicly announced that Madeline knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Dewayne can now know whether Dewayne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Madeline","Diane","James","Dewayne"],"index":9542,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8220277429,"difficulty":0.1779722571}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sergio does not know whether Sergio's forehead is muddy. It is publicly announced that Frances does not know whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Frances can now know whether Donald can know that Frances's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sergio","Frances","Donald"],"index":57475,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9859579206,"difficulty":0.0140420794}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Valarie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Russell","Jan","Valarie"],"index":47635,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988105297,"difficulty":0.0011894703}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Martin can now know whether Lucille can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucille","Clark","Martin"],"index":8244,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994107485,"difficulty":0.0005892515}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samuel does not know whether or not everyone's forehead is muddy. It is publicly announced that Samuel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Samuel can now know whether William can know that Samuel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Samuel"],"index":14420,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9713799357,"difficulty":0.0286200643}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Susan can now know that Leticia can know that Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leticia","Christine","Susan"],"index":56442,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9904530048,"difficulty":0.0095469952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Joseph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","John","Joseph","Mark"],"index":48925,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999381423,"difficulty":0.000618577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know whether Jacquelyn can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Jacquelyn","William","Charles"],"index":19018,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9880135059,"difficulty":0.0119864941}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Cassandra can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cassandra","Larry","Donald"],"index":13658,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994302392,"difficulty":0.0005697608}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Latosha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brandon can now know whether Jeanette can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Latosha","Brandon","Jeanette"],"index":65784,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8771925569,"difficulty":0.1228074431}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Edith can now know whether Brian can know that Edith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Edith","Brian"],"index":15214,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968488812,"difficulty":0.0031511188}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Susan can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janice","Daniel","Susan"],"index":58194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995126724,"difficulty":0.0004873276}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Edward can now know that Bessie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Bessie","Edward"],"index":22216,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928200841,"difficulty":0.0071799159}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Chester","Brandy","Valeria"],"index":36264,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994594455,"difficulty":0.0005405545}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nellie can now know whether Erma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nellie","Sharon","Erma"],"index":2602,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986225367,"difficulty":0.0013774633}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Ira can now know that Kimberly can know that Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kimberly","Ira"],"index":1247,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996080339,"difficulty":0.003919661}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earl does not know whether or not everyone's forehead is muddy. It is publicly announced that Earl knows whether Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Nancy can now know whether Raymond can know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earl","Raymond","Willie","Nancy"],"index":45035,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9857031703,"difficulty":0.0142968297}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Muriel can now know whether Nancy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Muriel","Nancy","Paul","Betty"],"index":52446,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990972281,"difficulty":0.0009027719}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Alison's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Alison can now know whether Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Sylvester","Alison"],"index":28052,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9745853543,"difficulty":0.0254146457}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Mark can now know that Carl can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Willie","Carl"],"index":26807,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989705086,"difficulty":0.0010294914}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Consuelo knows whether Consuelo's forehead is muddy. It is publicly announced that Consuelo knows whether Consuelo's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know whether Consuelo can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Khalilah","Christopher","Consuelo","Karen"],"index":4504,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994545579,"difficulty":0.0005454421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] 0","hypothesis":"Laurie can now know that Franklin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Franklin","William","Laurie"],"index":53426,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9957244396,"difficulty":0.0042755604}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Ronnie can now know that Joan can know that Joan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maribel","Joan","Ronnie","Steven"],"index":3778,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996096909,"difficulty":0.003903091}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know that John can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","John","Jose"],"index":12192,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9859461188,"difficulty":0.0140538812}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle does not know whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that George can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","George","John","Richard"],"index":5342,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989106655,"difficulty":0.0010893345}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edgar can now know that Elizabeth can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Debby","Edgar","Elizabeth"],"index":8390,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993770719,"difficulty":0.0006229281}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edgar's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Anderson can now know that Edgar can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lupe","Edgar","Mark","Anderson"],"index":54472,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994667172,"difficulty":0.0005332828}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Glenda can now know that Paul can know that Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paul","Glenda","Debra"],"index":67141,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997744441,"difficulty":0.002255559}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"George can now know whether Jeremy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeremy","Sandra","George","Thomas"],"index":17574,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993801117,"difficulty":0.0006198883}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sharon can now know whether Janice can know whether Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janice","Sharon"],"index":40552,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9875692725,"difficulty":0.0124307275}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy. It is publicly announced that Gregory's forehead is muddy. It is publicly announced that Sandra knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Gregory can now know that Sandra can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Doris","Sandra","Gregory"],"index":29090,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990463853,"difficulty":0.0009536147}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Velma knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Velma can now know that Karen can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Karen","Velma"],"index":26113,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989244342,"difficulty":0.0010755658}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patsy does not know whether Patsy's forehead is muddy. It is publicly announced that Frank knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kirk can now know whether Patsy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patsy","Kirk","Frank","Julius"],"index":65913,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990727901,"difficulty":0.0009272099}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose does not know whether or not everyone's forehead is muddy. It is publicly announced that Tina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tina can now know that Cassandra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Aaron","Tina","Cassandra"],"index":66194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.811308682,"difficulty":0.188691318}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ray can now know that Ray's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ray","Michael","John"],"index":12147,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9517096877,"difficulty":0.0482903123}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jose can now know whether Jennifer can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jose","John","Jennifer"],"index":26935,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9738767147,"difficulty":0.0261232853}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether or not nobody's forehead is muddy. It is publicly announced that Louise does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Robert","Louise"],"index":7731,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974628687,"difficulty":0.0025371313}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon's forehead is muddy. It is publicly announced that Gordon knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Gordon can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gordon","George"],"index":40848,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7976820469,"difficulty":0.2023179531}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herbert knows whether Cindy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Cindy can now know that Adrian can know whether Cindy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herbert","Cindy","Adrian"],"index":6676,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998581171,"difficulty":0.001418829}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessie can now know that Myrna can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessie","Paul","Myrna","Timothy"],"index":11720,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988403916,"difficulty":0.0011596084}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dallas does not know whether Dallas's forehead is muddy. It is publicly announced that Donald knows whether Dallas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Douglas can now know whether Dallas can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Douglas","Kyle","Dallas"],"index":3553,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.970345974,"difficulty":0.029654026}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Richard can know whether Everett's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dan","Richard","Everett","Robert"],"index":37683,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988480806,"difficulty":0.0011519194}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Damien knows whether someone's forehead is muddy. It is publicly announced that Eva knows whether Damien's forehead is muddy. It is publicly announced that Maryjane does not know whether Maryjane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Damien can now know that Maryjane can know whether Eva's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eva","Maryjane","Damien"],"index":5038,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992216825,"difficulty":0.0007783175}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Marjorie knows whether or not nobody's forehead is muddy. It is publicly announced that Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! 2 ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! 2 ] 0","hypothesis":"Richard can now know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marjorie","Christopher","Richard"],"index":40066,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9881928563,"difficulty":0.0118071437}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maureen does not know whether Maureen's forehead is muddy. It is publicly announced that Maureen does not know whether Maureen's forehead is muddy. It is publicly announced that Philip knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Philip can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maureen","Philip"],"index":33616,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990051389,"difficulty":0.0009948611}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia does not know whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Rosa can now know that Cynthia can know that Loretta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rosa","Loretta","Cynthia","Arlene"],"index":9908,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976249337,"difficulty":0.0023750663}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Robert can now know whether Gerry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ryan","Gerry","Pamela","Robert"],"index":65366,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990538955,"difficulty":0.0009461045}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Jose can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Bobby","Michael","Julia"],"index":51098,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994583726,"difficulty":0.0005416274}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Barbara can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Stephanie","Nicholas"],"index":44471,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992419481,"difficulty":0.0007580519}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Frankie can now know whether Brenda can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frankie","Brenda"],"index":27038,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999153614,"difficulty":0.000846386}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Larry can now know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Larry","Jaime","James"],"index":67471,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991931319,"difficulty":0.0008068681}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie does not know whether Leslie's forehead is muddy. It is publicly announced that Leslie does not know whether Leslie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Leslie can now know whether Rodney can know whether Rodney's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rodney","Leslie"],"index":12276,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9878424406,"difficulty":1.9878424406}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha does not know whether Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Denise can now know whether Denise's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Reed","Martha","Denise"],"index":13317,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9930463433,"difficulty":0.0069536567}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether Sandra's forehead is muddy. It is publicly announced that Brian knows whether or not everyone's forehead is muddy. It is publicly announced that Duane does not know whether Duane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Duane can now know whether Sandra can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Duane","Brian"],"index":15906,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993243217,"difficulty":0.0006756783}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether Francisco's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Brandy can now know that Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francisco","Brandy","Brenda"],"index":9079,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976274371,"difficulty":0.0023725629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene knows whether Irene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Irene can now know that Ester can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ester","Irene","Natalie","Thomas"],"index":14147,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990237951,"difficulty":0.0009762049}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jada does not know whether Jada's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jada can now know whether Morris can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andy","Jada","Morris"],"index":58199,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9562150836,"difficulty":0.0437849164}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"James can now know whether Judith can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Judith","James"],"index":5966,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993788004,"difficulty":0.0006211996}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leon does not know whether Leon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jennifer can now know that Shannon can know whether Leon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leon","Shannon","Patricia","Jennifer"],"index":44186,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988431931,"difficulty":0.0011568069}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Bernadette's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Charles can now know that Allene can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Bernadette","Allene"],"index":36745,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993633628,"difficulty":0.0006366372}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Christina can now know that Patricia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shannon","Mary","Patricia","Christina"],"index":24999,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.58872962,"difficulty":0.41127038}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Kimberly can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","James","Julie","Carol"],"index":33456,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9732993245,"difficulty":0.0267006755}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Christopher can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Christopher","John"],"index":49009,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988836646,"difficulty":0.0011163354}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine does not know whether Geraldine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Danny can now know whether Geraldine can know whether Geraldine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Danny","Danielle","Geraldine"],"index":24125,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8782573342,"difficulty":1.8782573342}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Thelma's forehead is muddy. It is publicly announced that Gail does not know whether Gail's forehead is muddy. It is publicly announced that John knows whether Thelma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Gail can now know whether John can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thelma","John","Robert","Gail"],"index":10226,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994320273,"difficulty":0.0005679727}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vincent knows whether someone's forehead is muddy. It is publicly announced that Josef does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Vincent can now know that Josef can know whether Josef's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Josef","Vincent"],"index":42661,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5455007553,"difficulty":0.4544992447}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Lorena can now know whether Dennis can know whether Lorena's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dennis","Lorena"],"index":51400,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9941189289,"difficulty":0.0058810711}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy. It is publicly announced that Francis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Jennifer can now know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francis","Jennifer","Wilma"],"index":37158,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7682616115,"difficulty":0.2317383885}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Anthony can now know whether Timothy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cecil","Anthony","Timothy"],"index":46592,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992505908,"difficulty":0.0007494092}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Anthony can now know whether Vicente can know that Vicente's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janet","Anthony","Vicente"],"index":57270,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5714560747,"difficulty":0.4285439253}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy. It is publicly announced that Roosevelt's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] 0","hypothesis":"Yajaira can now know whether Chad can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Yajaira","Richard","Chad","Roosevelt"],"index":19163,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.841930151,"difficulty":0.158069849}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marc does not know whether Marc's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lloyd can now know that Lloyd's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicole","Marc","Lloyd","Don"],"index":9340,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9920592308,"difficulty":0.0079407692}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Bennett can now know whether Grace can know that Bennett's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Grace","Donna","Bennett"],"index":21384,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9217781425,"difficulty":0.0782218575}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edna's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Walter can now know that Edna can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Walter","Edna"],"index":67059,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9180483222,"difficulty":0.0819516778}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether or not nobody's forehead is muddy. It is publicly announced that Ruth knows whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ruth can now know that Joyce can know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joyce","Ruth"],"index":25496,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.867560029,"difficulty":0.132439971}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Therese's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agentb knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Leslie can now know whether Tracy can know that Leslie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tracy","Leslie","Frederic","Therese"],"index":25843,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9234944582,"difficulty":0.0765055418}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy does not know whether Roy's forehead is muddy. It is publicly announced that Katie does not know whether Katie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Katie can now know whether Roy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katie","Tanya","Roy"],"index":34003,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9741597176,"difficulty":0.0258402824}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Bruce's forehead is muddy. It is publicly announced that Charles's forehead is not muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Beatrice can now know whether Charles can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Bruce","Beatrice","Charles"],"index":65435,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9787034392,"difficulty":0.0212965608}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Verna knows whether someone's forehead is muddy. It is publicly announced that Verna knows whether Elaine's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Elaine can now know that Sharon can know that Odette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sharon","Odette","Elaine","Verna"],"index":20504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965867996,"difficulty":0.0034132004}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether Maxwell's forehead is muddy. It is publicly announced that Andrew does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Maxwell can now know whether Andrew can know whether Maxwell's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrew","Maxwell"],"index":52304,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983726144,"difficulty":0.0016273856}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miriam knows whether or not nobody's forehead is muddy. It is publicly announced that Miriam knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Doris can now know whether Christopher can know whether Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Doris","Miriam"],"index":63156,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9403145313,"difficulty":0.0596854687}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy. It is publicly announced that Wayne knows whether Wayne's forehead is muddy. It is publicly announced that Wayne knows whether Wayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kevin can now know whether Gene can know that Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gene","Kevin","Wayne"],"index":7262,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9818284512,"difficulty":0.0181715488}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Barbara can now know that Judith can know whether Judith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Judith","Christopher"],"index":27186,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9914643168,"difficulty":0.0085356832}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathan knows whether Winnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Leslie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Winnie","Nathan","Leslie"],"index":63926,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994581342,"difficulty":0.0005418658}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick does not know whether Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know that Patrick can know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eddie","James","Patrick","John"],"index":18470,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.974103272,"difficulty":0.025896728}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Julio can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marjorie","Julio","Paul","Wesley"],"index":44919,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.968619287,"difficulty":0.031380713}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bud knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Annette can now know that Kenneth can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Patricia","Annette","Bud"],"index":32776,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954282045,"difficulty":0.0045717955}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"George can now know whether Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Donna","Marie"],"index":17059,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994156361,"difficulty":0.0005843639}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerry knows whether Roseanna's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roseanna does not know whether Roseanna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Roseanna can now know whether Roseanna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kerry","Bobby","Roseanna"],"index":32074,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9853823185,"difficulty":1.9853823185}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ella's forehead is not muddy. It is publicly announced that Francis knows whether Ella's forehead is muddy. It is publicly announced that Ella knows whether Francis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Amy can now know whether Ella can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Francis","Amy","Ella"],"index":24964,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9936743975,"difficulty":0.0063256025}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Susan can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","William","Susan","James"],"index":30238,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993537068,"difficulty":0.0006462932}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharleen does not know whether Sharleen's forehead is muddy. It is publicly announced that Lashonda does not know whether Lashonda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sharleen can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lashonda","Elizabeth","Sharleen"],"index":5482,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9753379822,"difficulty":0.0246620178}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Tracey can now know that James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tracey","James","Natasha"],"index":7926,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970393181,"difficulty":0.0029606819}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Christine can now know whether Jo can know whether Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Christine","Jo"],"index":57674,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988502264,"difficulty":0.0011497736}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean does not know whether Jean's forehead is muddy. It is publicly announced that Deborah does not know whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Paul can now know whether Deborah can know whether Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deborah","Paul","Jean"],"index":23260,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992815852,"difficulty":0.0007184148}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Kristin"],"index":20212,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987517595,"difficulty":0.0012482405}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jorge's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Charles can now know that Gilbert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gilbert","Charles","Jorge"],"index":46960,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989709854,"difficulty":0.0010290146}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeff knows whether or not everyone's forehead is muddy. It is publicly announced that Jeff does not know whether Jeff's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patsy can now know whether Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patsy","Jeff","Patricia","Jose"],"index":50467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993023872,"difficulty":0.0006976128}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether or not nobody's forehead is muddy. It is publicly announced that Dorothy knows whether Valerie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Valerie can now know whether Dorothy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Valerie","Dorothy"],"index":17005,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7813405395,"difficulty":0.2186594605}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Julie knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mary can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julie","David","Mary"],"index":6594,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9944506884,"difficulty":0.0055493116}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wesley does not know whether Wesley's forehead is muddy. It is publicly announced that Wesley does not know whether Wesley's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Wesley can now know that Norma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Norma","Wesley"],"index":45272,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9899677038,"difficulty":1.9899677038}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan does not know whether Bryan's forehead is muddy. It is publicly announced that Bryan does not know whether Bryan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jesse can now know that Mariano's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bryan","Mariano","Jesse","Norma"],"index":57640,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947992563,"difficulty":0.0052007437}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know whether David can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosa","Richard","David"],"index":3478,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9744918346,"difficulty":0.0255081654}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Ronnie can now know whether Lloyd can know that Lloyd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["April","Ronnie","Lloyd"],"index":41449,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939180613,"difficulty":0.0060819387}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rolland does not know whether Rolland's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Rolland can now know whether Rolland's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rolland","Mary"],"index":27744,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6821377277,"difficulty":1.6821377277}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony does not know whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Milton can now know that Anthony can know that Milton's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vern","Sarah","Milton","Anthony"],"index":35973,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965079427,"difficulty":0.0034920573}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ismael can now know whether Ken's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","James","Ismael","Ken"],"index":63057,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993185997,"difficulty":0.0006814003}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Destiny does not know whether Destiny's forehead is muddy. It is publicly announced that Mark knows whether or not nobody's forehead is muddy. It is publicly announced that Mark knows whether Mark's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Destiny can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Destiny","Mark"],"index":8552,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993376136,"difficulty":0.0006623864}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd's forehead is muddy. It is publicly announced that Todd knows whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Todd can now know whether Frances can know whether Priscilla's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Todd","Frances","Priscilla"],"index":17108,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993568063,"difficulty":0.0006431937}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"William can now know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Dennis","Martha"],"index":53932,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956265688,"difficulty":0.0043734312}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel's forehead is muddy. It is publicly announced that Rachel knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Henry can now know whether Rachel can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rachel","Henry"],"index":44464,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9652942419,"difficulty":0.0347057581}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Edith can now know that Edward can know that Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melissa","Edward","Edith","Margaret"],"index":47249,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974198341,"difficulty":0.0025801659}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Troy can now know whether Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Joseph","Gerald","Troy"],"index":44578,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993104935,"difficulty":0.0006895065}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley does not know whether Bradley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Steve can now know whether Debra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Delbert","Bradley","Steve","Debra"],"index":6077,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9660412073,"difficulty":0.0339587927}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether or not everyone's forehead is muddy. It is publicly announced that Howard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Gerald can now know whether Howard can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Howard","Gerald"],"index":16067,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994524121,"difficulty":0.0005475879}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allen's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Allen can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allen","Sandra","Christina","Robert"],"index":2035,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9940142035,"difficulty":0.0059857965}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Teresa's forehead is muddy. It is publicly announced that Christopher knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Teresa can now know that Christopher can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Teresa","Christopher"],"index":48830,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994391799,"difficulty":0.0005608201}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether June's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Jose can now know whether Michelle can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","Michelle","Evelyn","June"],"index":46594,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993316531,"difficulty":0.0006683469}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that Louise's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Louise can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Louise","David"],"index":47236,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994847775,"difficulty":0.0005152225}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessie does not know whether Jessie's forehead is muddy. It is publicly announced that Joannie knows whether or not everyone's forehead is muddy. It is publicly announced that Joannie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Joannie can now know whether Joannie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jessie","Joannie"],"index":60733,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6893233657,"difficulty":1.6893233657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy. It is publicly announced that Iluminada's forehead is muddy. It is publicly announced that Betty does not know whether or not everyone's forehead is muddy. It is publicly announced that Betty's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Iluminada can now know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Michael","Iluminada","Joe"],"index":40744,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7684305906,"difficulty":0.2315694094}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Virginia can now know that Verda can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Virginia","John","Verda"],"index":64468,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996147275,"difficulty":0.003852725}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen knows whether Fernando's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Fernando can now know whether Carmen can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Fernando","Carmen"],"index":45043,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9235044122,"difficulty":0.0764955878}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon does not know whether Shannon's forehead is muddy. It is publicly announced that Peter's forehead is muddy. It is publicly announced that Gene knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gene can now know whether Gene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peter","Gene","Julie","Shannon"],"index":60694,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.665229857,"difficulty":0.334770143}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Adam can now know whether Christopher can know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Frances","Adam"],"index":51298,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939661622,"difficulty":0.0060338378}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kim can now know that Michael can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kim","Josephine","Michael"],"index":9921,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9950358272,"difficulty":0.0049641728}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence does not know whether Florence's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Florence can now know that William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","William","Terry"],"index":8254,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948319197,"difficulty":0.0051680803}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Morgan does not know whether Morgan's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Morgan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Morgan can now know whether Mary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Robert","Morgan","Stephanie"],"index":8075,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8325880766,"difficulty":0.1674119234}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Frances knows whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Michael can now know whether Frances can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Frances","Steven"],"index":25453,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9974722266,"difficulty":0.0025277734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phoebe knows whether Phoebe's forehead is muddy. It is publicly announced that Phoebe knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Corina can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Phoebe","Francisco","Corina","David"],"index":47972,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990518689,"difficulty":0.0009481311}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Jeffrey can now know that William can know that Victoria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","George","William","Victoria"],"index":45746,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8837310076,"difficulty":0.1162689924}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne knows whether someone's forehead is muddy. It is publicly announced that Joanne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] 0","hypothesis":"Mary can now know whether Frank can know whether Joanne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joanne","Frank","Mary"],"index":67380,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992098808,"difficulty":0.0007901192}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Gina can now know whether Ariel can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rose","Gina","Ariel"],"index":57752,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994683862,"difficulty":0.0005316138}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janet can now know whether Carl can know whether Carl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Romaine","Carl","Janet"],"index":4447,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9945928454,"difficulty":0.0054071546}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Julius knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Mary can now know whether Julius can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julius","Harold","William","Mary"],"index":55970,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994633794,"difficulty":0.0005366206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Willie knows whether Dan's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Willie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willie","Eunice","Dan","Betty"],"index":3216,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966650605,"difficulty":0.0033349395}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jay can now know that Harold can know whether Roy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roy","Jay","Donna","Harold"],"index":31754,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992895126,"difficulty":0.0007104874}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Warren does not know whether Warren's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sandy can now know whether Jina can know whether Jina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Warren","Jina","Janice","Sandy"],"index":5424,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8240503669,"difficulty":0.1759496331}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jessica can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christina","Stephanie","Michael","Jessica"],"index":47506,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994083643,"difficulty":0.0005916357}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know that William can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Andrew","Timothy"],"index":51345,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990235567,"difficulty":0.0009764433}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur does not know whether Arthur's forehead is muddy. It is publicly announced that Ethel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Willie can now know that Ethel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ethel","Arthur","Willie"],"index":39812,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6739034653,"difficulty":0.3260965347}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa does not know whether Lisa's forehead is muddy. It is publicly announced that Danielle knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Saundra can now know that Saundra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Saundra","Lisa","William","Danielle"],"index":47086,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958635569,"difficulty":0.0041364431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Nell knows whether Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Sarah can now know whether Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dale","Sarah","Steven","Nell"],"index":31329,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9936109185,"difficulty":0.0063890815}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"John can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","William","Lori","Krystal"],"index":63934,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999507308,"difficulty":0.000492692}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen's forehead is not muddy. It is publicly announced that Evelyn knows whether Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Evelyn can now know whether Stephen can know that Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephen","Evelyn","Clair"],"index":16807,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7370009422,"difficulty":0.2629990578}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce does not know whether Joyce's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Matthew can now know whether Joyce can know whether Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Matthew","Joyce"],"index":56308,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990573525,"difficulty":0.0009426475}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Barry can now know whether Linda can know that Barry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barry","Linda","Mildred"],"index":56073,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943014383,"difficulty":0.0056985617}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marion can now know whether Paul can know whether Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Nellie","Marion","Bryan"],"index":19805,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992440939,"difficulty":0.0007559061}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luis knows whether Luis's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Darin can now know that Luis can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Darin","Luis"],"index":37375,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990371466,"difficulty":0.0009628534}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vanessa knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Alma can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vanessa","Alma"],"index":225,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994850159,"difficulty":0.0005149841}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether someone's forehead is muddy. It is publicly announced that Richard knows whether Natalie's forehead is muddy. It is publicly announced that Natalie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Christopher can now know that Richard can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Richard","John","Natalie"],"index":40765,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977629185,"difficulty":0.0022370815}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy's forehead is muddy. It is publicly announced that Amy's forehead is not muddy. It is publicly announced that Roy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Amy can now know that Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roy","Martha","Amy"],"index":62092,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8620136976,"difficulty":0.1379863024}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lea's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Lea can now know that William can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lea","William"],"index":42851,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986460805,"difficulty":0.0013539195}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Arthur can now know that Arthur's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arthur","Ruth","James"],"index":31176,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963750243,"difficulty":0.0036249757}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ray does not know whether Ray's forehead is muddy. It is publicly announced that Ray does not know whether Ray's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Mamie can now know whether Natalie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Natalie","Ray","Mamie","William"],"index":27128,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992637038,"difficulty":0.0007362962}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Debra can now know whether Gary can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Connie","Debra"],"index":48930,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958623648,"difficulty":0.0041376352}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"George can now know that Richard can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["George","Richard"],"index":56183,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998960495,"difficulty":0.001039505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Beatrice can now know whether Edwin can know that Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beatrice","Tina","Edwin","Jean"],"index":58940,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9709118009,"difficulty":0.0290881991}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dominic knows whether someone's forehead is muddy. It is publicly announced that Frances does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Carolyn can now know that Frances can know whether Frances's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dominic","Carolyn","Frances"],"index":18133,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5649847984,"difficulty":0.4350152016}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Brandon can now know that Jenna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","Brandon","Robert","Jenna"],"index":48913,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997516036,"difficulty":0.002483964}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa does not know whether or not everyone's forehead is muddy. It is publicly announced that Geraldine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Lavern can now know that Geraldine can know that Lavern's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Lavern","Ike","Geraldine"],"index":11279,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8784355521,"difficulty":0.1215644479}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Nancy can now know that Alexander can know that Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alexander","Brian","Nancy"],"index":57731,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99597013,"difficulty":0.00402987}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jane can now know whether Nelson can know whether Nelson's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jane","Nelson","Thomas"],"index":22706,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5195842385,"difficulty":0.4804157615}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacey knows whether or not everyone's forehead is muddy. It is publicly announced that Paul knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Paul can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Becky","Paul","Stacey"],"index":63845,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990472198,"difficulty":0.0009527802}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur does not know whether Arthur's forehead is muddy. It is publicly announced that Roseanne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Dennis can now know whether Roseanne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dennis","Arthur","Roseanne"],"index":54980,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9976952672,"difficulty":0.0023047328}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Timothy's forehead is muddy. It is publicly announced that Timothy knows whether Timothy's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Leah can know whether Leah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Jessica","Timothy","Leah"],"index":39655,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9933011532,"difficulty":1.9933011532}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Natalie can now know that Mary can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Natalie","Richard","Virginia","Mary"],"index":35234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956620336,"difficulty":0.0043379664}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sari can now know that Robert can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sari","David","Robert","Patricia"],"index":59036,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991782308,"difficulty":0.0008217692}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Susie can now know whether David can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Susie","David"],"index":29573,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993946552,"difficulty":0.0006053448}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Dawn can now know that David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dawn","Dierdre","Jennifer","David"],"index":27880,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9845087528,"difficulty":0.0154912472}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pauline knows whether Delores's forehead is muddy. It is publicly announced that Pauline's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Pauline can now know that Delores can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Deborah","Pauline","Delores"],"index":8511,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984824061,"difficulty":0.0015175939}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jay knows whether Jay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Carol can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Catherine","Jay","Carol","Michelle"],"index":44987,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989424348,"difficulty":0.0010575652}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether Carolyn's forehead is muddy. It is publicly announced that Carolyn knows whether Willie's forehead is muddy. It is publicly announced that Carolyn knows whether or not everyone's forehead is muddy. It is publicly announced that Willie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Willie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carolyn","Barry","Willie"],"index":27721,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979997277,"difficulty":0.0020002723}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luke knows whether or not nobody's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Luke can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Luke"],"index":26240,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972561002,"difficulty":0.0027438998}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman knows whether someone's forehead is muddy. It is publicly announced that Norman knows whether Ann's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Norman can now know that Jennifer can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Kathy","Ann","Norman"],"index":39083,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990085959,"difficulty":0.0009914041}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Cynthia knows whether Kenneth's forehead is muddy. It is publicly announced that Phyllis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Kenneth can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cynthia","Margaret","Kenneth","Phyllis"],"index":63462,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996250689,"difficulty":0.003749311}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that Muoi knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Elizabeth can now know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Elizabeth","Muoi"],"index":17515,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9755656719,"difficulty":0.0244343281}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Opal's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Opal can now know that Mary can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vincent","Mary","Opal","John"],"index":18803,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9909015894,"difficulty":0.0090984106}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adam does not know whether Adam's forehead is muddy. It is publicly announced that Adam's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 0","hypothesis":"Angela can now know that Sherri can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sherri","Angela","Amber","Adam"],"index":12343,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984273911,"difficulty":0.0015726089}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maureen does not know whether Maureen's forehead is muddy. It is publicly announced that Alan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Alan can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tracy","Maureen","Alan"],"index":26727,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995076656,"difficulty":0.0004923344}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Aaron can now know that Hyacinth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Aaron","Hyacinth"],"index":48227,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9586543441,"difficulty":0.0413456559}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Celina does not know whether Celina's forehead is muddy. It is publicly announced that Elaine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Celina can now know that Elaine can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Elaine","Celina"],"index":28275,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986798167,"difficulty":0.0013201833}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy does not know whether Jeremy's forehead is muddy. It is publicly announced that Kathleen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Tonya can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tonya","Jeremy","Kathleen","Dennis"],"index":41321,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994811416,"difficulty":0.0005188584}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy. It is publicly announced that Donna knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Linda can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Donna","Linda"],"index":26643,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9725339413,"difficulty":0.0274660587}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Lois can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Josie","Shirley","Michael","Lois"],"index":37503,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988535643,"difficulty":0.0011464357}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether someone's forehead is muddy. It is publicly announced that Paul knows whether or not everyone's forehead is muddy. It is publicly announced that Nicole's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nicole can now know that Annette can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nicole","Annette","Paul","Walter"],"index":64202,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9942094088,"difficulty":0.0057905912}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Margaret can now know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Margaret","Stephanie"],"index":28809,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979222417,"difficulty":0.0020777583}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Agnes does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Agnes can now know that Jamie can know that Agnes's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Agnes","Jamie"],"index":51200,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.60395962,"difficulty":1.60395962}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel does not know whether Manuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Helen can now know that Manuel can know whether Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Manuel","Helen","Sharon"],"index":42032,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9937449098,"difficulty":0.0062550902}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corey knows whether Albert's forehead is muddy. It is publicly announced that Corey's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Corey can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Albert","Corey"],"index":46221,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9249738455,"difficulty":0.0750261545}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jim does not know whether Jim's forehead is muddy. It is publicly announced that Joleen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Joleen can now know that Robert can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jim","Joleen","Robert"],"index":38751,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994712472,"difficulty":0.0005287528}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy. It is publicly announced that Doris's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] 0","hypothesis":"Luther can now know that Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Doris","Gregory","Luther"],"index":66956,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6279829144,"difficulty":0.3720170856}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce does not know whether Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Daniel can now know whether Bruce can know that Wm's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Bruce","Wm"],"index":52039,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.966147542,"difficulty":0.033852458}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alison can now know that Rex can know that Alison's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rex","Alison","Alberto","Lenard"],"index":22823,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977799058,"difficulty":0.0022200942}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elsa knows whether Antoinette's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Antoinette can now know whether Elsa can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Elsa","Antoinette"],"index":41735,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.912442565,"difficulty":0.087557435}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alvin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Diana can now know that Alvin can know whether Alvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Diana","Alvin"],"index":59159,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6452065706,"difficulty":0.3547934294}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria does not know whether Gloria's forehead is muddy. It is publicly announced that Donna knows whether Gloria's forehead is muddy. It is publicly announced that Evelyn knows whether Evelyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Donna can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Evelyn","Gloria","Donna"],"index":42435,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8981098533,"difficulty":1.8981098533}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Leticia can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leticia","Angelica","Matthew"],"index":64328,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994879961,"difficulty":0.0005120039}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria's forehead is not muddy. It is publicly announced that Louis knows whether Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Maria can now know whether Richard can know that Janice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Janice","Maria","Richard"],"index":8108,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.979985714,"difficulty":0.020014286}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris does not know whether Chris's forehead is muddy. It is publicly announced that Chris knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Chris can now know whether Martha can know that Chris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Milford","Martha","Chris"],"index":64541,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7640830278,"difficulty":0.2359169722}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramon's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Ramon can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ramon","Mary","Henry","George"],"index":65137,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989970326,"difficulty":0.0010029674}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mitchell can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Thomas","Mitchell","Robert"],"index":41137,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953106046,"difficulty":0.0046893954}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Barbara's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Barbara can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Barbara","John"],"index":37051,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987888932,"difficulty":0.0012111068}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emily knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Elizabeth can now know whether Emily can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emily","Elizabeth","Denise"],"index":48054,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994377494,"difficulty":0.0005622506}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dane knows whether or not nobody's forehead is muddy. It is publicly announced that Dane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] 0","hypothesis":"Gregory can now know that Dane's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dane","Gregory","Carmen"],"index":61494,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9423854351,"difficulty":0.0576145649}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is not muddy. It is publicly announced that Joan does not know whether Joan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Joan can now know whether Casey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Larry","Casey","Joan"],"index":50268,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993603826,"difficulty":0.0006396174}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrice knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"George can now know whether Patrice can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","George","Patrice"],"index":47196,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9295451641,"difficulty":0.0704548359}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra does not know whether Debra's forehead is muddy. It is publicly announced that Debra knows whether Carlos's forehead is muddy. It is publicly announced that Carlos knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Debra can now know whether Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Debra","Carlos"],"index":20563,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6934528947,"difficulty":0.3065471053}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Vernon can now know that Henry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vernon","Ryan","Ronald","Henry"],"index":1579,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989458919,"difficulty":0.0010541081}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa does not know whether Rosa's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Brittany can now know whether Rosa can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brittany","Rosa"],"index":4465,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992726445,"difficulty":0.0007273555}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Valencia can now know whether Jessica can know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Valencia","Mark","Lena"],"index":63789,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6547693014,"difficulty":0.3452306986}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lula knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Lula can now know whether Cristina can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sheri","Cristina","Jason","Lula"],"index":62113,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989762306,"difficulty":0.0010237694}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgia knows whether or not everyone's forehead is muddy. It is publicly announced that Georgia does not know whether Georgia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Georgia can now know that Georgia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Georgia","Lori","Patricia"],"index":14402,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9605391026,"difficulty":0.0394608974}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie does not know whether Carrie's forehead is muddy. It is publicly announced that Martha knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Martha can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ignacio","Carrie","Martha"],"index":198,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.962931633,"difficulty":0.037068367}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Christopher can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Karmen","Christopher"],"index":34916,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994276166,"difficulty":0.0005723834}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether someone's forehead is muddy. It is publicly announced that Linda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Melissa can now know whether Linda can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Melissa"],"index":33270,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994643331,"difficulty":0.0005356669}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kenneth can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Priscilla","Charles","Ruth","Kenneth"],"index":47917,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7280811071,"difficulty":0.2719188929}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annemarie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Annemarie","William"],"index":17831,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6241753697,"difficulty":0.3758246303}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"William can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Lynette"],"index":46521,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9911651015,"difficulty":0.0088348985}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is muddy. It is publicly announced that Rose knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know that Rose can know that Jesus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Edward","Jesus","Margaret"],"index":46722,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9942352176,"difficulty":0.0057647824}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kirsten knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Nancy can now know that Kirsten can know whether Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Kirsten"],"index":67518,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9267517328,"difficulty":0.0732482672}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Roy does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Carlos can now know that Roy can know that Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roy","Carlos","James"],"index":42316,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9260514975,"difficulty":0.0739485025}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl does not know whether Cheryl's forehead is muddy. It is publicly announced that Randall does not know whether Randall's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Cheryl can now know that Lauren can know that Cheryl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cheryl","Lauren","Randall"],"index":51300,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937397242,"difficulty":0.0062602758}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Barbara's forehead is muddy. It is publicly announced that Barbara knows whether Lawrence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Steven can now know that Lawrence can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Lawrence","Barbara","Greg"],"index":46359,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990493655,"difficulty":0.0009506345}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Beth can now know whether David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Beth","John"],"index":52767,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9977972507,"difficulty":0.0022027493}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarice knows whether Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Clarice can now know whether Bobby's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bobby","Clarice"],"index":4565,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992514253,"difficulty":0.0007485747}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether Megan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Megan can now know that Megan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alexis","Diane","Gale","Megan"],"index":2935,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9798380136,"difficulty":0.0201619864}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agenta knows whether (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"David can now know whether Melissa can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Matthew","William","Melissa"],"index":11706,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.97945261,"difficulty":0.02054739}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Oscar's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Oscar","Tamara","Charlotte","William"],"index":48832,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9863311052,"difficulty":0.0136688948}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodger knows whether Trenton's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Trenton","Rodger","Michael"],"index":9646,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993698001,"difficulty":0.0006301999}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Alfred can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","Benjamin","Robert","Alfred"],"index":4775,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987990856,"difficulty":0.0012009144}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlota knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Ralph can now know whether Ralph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carlota","Ralph"],"index":56722,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9932649136,"difficulty":0.0067350864}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roxie knows whether someone's forehead is muddy. It is publicly announced that Roxie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] 0","hypothesis":"Roxie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roxie","John","Randy"],"index":41601,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994927645,"difficulty":0.0005072355}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy. It is publicly announced that Charles knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Catherine can now know that Charles can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Charles"],"index":47626,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994776845,"difficulty":0.0005223155}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Clarence can now know whether Cynthia can know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clarence","Cynthia","Ruth"],"index":21542,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.95106107,"difficulty":0.04893893}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd does not know whether Todd's forehead is muddy. It is publicly announced that Todd knows whether George's forehead is muddy. It is publicly announced that George knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"George can now know whether Todd's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Todd","George"],"index":13198,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983709455,"difficulty":0.0016290545}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys knows whether Gladys's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gladys can now know whether Herman can know that Herman's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herman","Jennifer","Gladys"],"index":38384,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9889166355,"difficulty":1.9889166355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether someone's forehead is muddy. It is publicly announced that Russell does not know whether Russell's forehead is muddy. It is publicly announced that Dixie does not know whether or not everyone's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agentd knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dixie can now know whether Russell's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Russell","Elizabeth","David","Dixie"],"index":28544,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989278913,"difficulty":0.0010721087}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan does not know whether or not everyone's forehead is muddy. It is publicly announced that Juan knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Ronald can now know that Juan can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juan","Darlene","Millicent","Ronald"],"index":33273,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990296364,"difficulty":0.0009703636}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nolan knows whether Rochelle's forehead is muddy. It is publicly announced that Rochelle does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Rochelle can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rochelle","Nolan"],"index":46155,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994531274,"difficulty":0.0005468726}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kelly can now know whether Norman can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norman","Nancy","Florine","Kelly"],"index":38420,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999260366,"difficulty":0.000739634}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Coleen does not know whether Coleen's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy. It is publicly announced that Diane does not know whether Diane's forehead is muddy. It is publicly announced that Amanda knows whether Coleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Coleen can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Coleen","Diane","Amanda"],"index":452,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8667322993,"difficulty":0.1332677007}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elaine can now know whether Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Elaine","Kenneth"],"index":11260,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994268417,"difficulty":0.0005731583}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Patricia can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Patricia","Robert","Carl"],"index":31190,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7141662836,"difficulty":0.2858337164}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Misty's forehead is muddy. It is publicly announced that Gregory knows whether Misty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Bertha can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bertha","Misty","Pete","Gregory"],"index":64075,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994949102,"difficulty":0.0005050898}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tyler does not know whether Tyler's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Marion can now know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronald","Tyler","Patrick","Marion"],"index":32830,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992398024,"difficulty":0.0007601976}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Britney does not know whether or not everyone's forehead is muddy. It is publicly announced that Sanford's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Sanford can now know that Britney's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Britney","Sanford"],"index":7964,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.705057621,"difficulty":1.705057621}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime knows whether someone's forehead is muddy. It is publicly announced that Erin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Erin can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erin","Jaime"],"index":4551,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9875178933,"difficulty":0.0124821067}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lyle can now know that Nona can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nona","Lyle","Richard","Rodney"],"index":19578,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9862282276,"difficulty":0.0137717724}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Geneva can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Geneva","James","Robert"],"index":3390,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9222339988,"difficulty":0.0777660012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy. It is publicly announced that Pamela does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"John can now know that Pamela can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Allan","John"],"index":40811,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9884323478,"difficulty":0.0115676522}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laverne knows whether Billy's forehead is muddy. It is publicly announced that Laverne does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Billy can now know whether Dale's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dale","Billy","Laverne"],"index":4381,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992241859,"difficulty":0.0007758141}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Karen can now know that Michael can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Michael","Adam"],"index":28368,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988976717,"difficulty":0.0011023283}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not nobody's forehead is muddy. It is publicly announced that Joseph does not know whether Joseph's forehead is muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Frankie can now know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Abel","Joseph","Frankie"],"index":45894,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9427005053,"difficulty":0.0572994947}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether Leo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kimberly can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leo","Gloria","Kimberly"],"index":61835,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994434714,"difficulty":0.0005565286}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reginald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Ruby can now know that Reginald can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ruby","Reginald"],"index":62626,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989832044,"difficulty":0.0010167956}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether or not everyone's forehead is muddy. It is publicly announced that Lawrence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Lawrence can now know that Lawrence's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lawrence","Teresa","Lucia"],"index":4288,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9807016253,"difficulty":0.0192983747}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ginger","Jennifer","Steven"],"index":23814,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983512163,"difficulty":0.0016487837}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Erin can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Erin","Harold"],"index":28518,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990215302,"difficulty":0.0009784698}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Anthony can now know that Pamela can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anthony","Pamela"],"index":27328,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989575148,"difficulty":0.0010424852}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Monica can now know that Vanessa can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vanessa","Gabriela","Monica","Bonnie"],"index":49513,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994744658,"difficulty":0.0005255342}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jason can now know that Richard can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jason","Richard","Ashley","Maria"],"index":5435,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996137917,"difficulty":0.003862083}