diff --git "a/data/validation-forehead_mirror.jsonl" "b/data/validation-forehead_mirror.jsonl"
new file mode 100644--- /dev/null
+++ "b/data/validation-forehead_mirror.jsonl"
@@ -0,0 +1,983 @@
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Robert can now know that Wanda can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Walter","Wanda","Loralee","Robert"],"index":63331,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997463822,"difficulty":0.0002536178}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Matthew can now know that Bonnie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bonnie","Matthew","John","Lawrence"],"index":2950,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9942783117,"difficulty":0.0057216883}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester knows whether someone's forehead is muddy. It is publicly announced that Christopher knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Carmen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carmen","Charles","Christopher","Lester"],"index":48384,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998494029,"difficulty":0.001505971}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Susan","Gary","Don"],"index":8433,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982314706,"difficulty":0.0017685294}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold knows whether or not everyone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] Agentd knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Kenneth can now know that Sheldon can know that Sheldon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sheldon","Jennifer","Harold","Kenneth"],"index":24756,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9268339276,"difficulty":0.0731660724}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Paul knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Harley can now know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harley","Deborah","Paul","Everett"],"index":47363,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996805191,"difficulty":0.0003194809}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Helen can now know that Joyce can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Joyce","Helen"],"index":34668,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998423934,"difficulty":0.001576066}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Bobby can now know that Bobby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bobby","Catherine"],"index":63152,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975998998,"difficulty":0.0024001002}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether Roy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Roy can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Jesse","Roy","Mary"],"index":2457,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985148311,"difficulty":0.0014851689}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sidney knows whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sidney can now know whether Brenda can know that Brenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sidney","Brenda","Warren"],"index":59706,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996783733,"difficulty":0.0003216267}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvia knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Mary can now know whether Rita can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","James","Rita","Sylvia"],"index":6949,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997654557,"difficulty":0.0002345443}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Rachel knows whether Migdalia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Rachel can now know that Migdalia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Migdalia","Rachel","Melissa"],"index":33757,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9934878349,"difficulty":0.0065121651}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Steven can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Allison","Margaret","Steven","Stephen"],"index":6751,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997522235,"difficulty":0.0002477765}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"James can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Armando","Donald","James"],"index":67049,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984135628,"difficulty":0.0015864372}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Stacy knows whether Stacy's forehead is muddy. It is publicly announced that Salina knows whether Salina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jesus can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stacy","Salina","Jesus","Randy"],"index":26441,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9839292765,"difficulty":0.0160707235}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie knows whether Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Maria can now know that Corey can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stephanie","Maria","Corey","Jessica"],"index":25070,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983345866,"difficulty":0.0016654134}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not nobody's forehead is muddy. It is publicly announced that Myrtle's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] 0","hypothesis":"Myrtle can now know that Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorna","Betty","Raymond","Myrtle"],"index":38631,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9895688891,"difficulty":0.0104311109}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Stephany can now know whether Patricia can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Frank","Andrew","Stephany"],"index":48748,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997512698,"difficulty":0.0002487302}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alma knows whether Alma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ashley can now know that Alma can know whether Ashley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ashley","Alma","William","Michael"],"index":45425,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997430444,"difficulty":0.0002569556}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Joyce's forehead is muddy. It is publicly announced that Lori knows whether or not nobody's forehead is muddy. It is publicly announced that Joyce knows whether Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Thomas can now know whether Joyce's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Lori","Joyce"],"index":16992,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997000694,"difficulty":0.0002999306}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Amy can now know that Lance's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amy","Gwen","Lance"],"index":6423,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984067082,"difficulty":0.0015932918}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vicky knows whether Mark's forehead is muddy. It is publicly announced that Vicky's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Vanessa can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Vicky","Mark","Vanessa"],"index":55500,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"James can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","James","Dennis","Melanie"],"index":58168,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Michelle can now know whether Barbara can know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Barbara","Michelle","Wayne"],"index":43675,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996758699,"difficulty":0.0003241301}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Don's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Marlyn can now know whether Raymond can know that Don's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Don","Marlyn","Raymond","Theresa"],"index":36587,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997020364,"difficulty":0.0002979636}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Joseph can now know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Linda"],"index":52450,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997195601,"difficulty":0.0002804399}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Thomas can now know whether Bessie can know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Carol","Bessie","Thomas"],"index":9774,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996697903,"difficulty":0.0003302097}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Lyle can now know whether Thomas can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lyle","Reinaldo","Willie","Thomas"],"index":57470,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996731281,"difficulty":0.0003268719}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"James can now know that Lorraine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eva","Lorraine","Gail","James"],"index":38276,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984335303,"difficulty":0.0015664697}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Pamela can now know that Tracy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracy","Elizabeth","Pamela"],"index":27919,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983371496,"difficulty":0.0016628504}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donnell knows whether Donnell's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Donnell can now know that Joseph can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donnell","Joseph"],"index":29640,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997537732,"difficulty":0.0002462268}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffry knows whether Phyllis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jorge can now know whether Phyllis can know that Jeffry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jorge","Phyllis","Jeffry"],"index":43768,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996682405,"difficulty":0.0003317595}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jenny knows whether or not nobody's forehead is muddy. It is publicly announced that Tara's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Jenny can now know that Tara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tara","Jenny"],"index":44407,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9828436375,"difficulty":0.0171563625}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Lilian","Stephen","Lisa"],"index":40079,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9964439273,"difficulty":0.0035560727}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Coral's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Alice can now know that Alice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Coral","Alice","Theron"],"index":61656,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9761471152,"difficulty":0.0238528848}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Fred knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Fred can now know whether Maria can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fred","Matthew","Maria","Doris"],"index":7691,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997487664,"difficulty":0.0002512336}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Donna can now know that Raymon can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Raymon","Donna"],"index":50824,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982896447,"difficulty":0.0017103553}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly's forehead is not muddy. It is publicly announced that Douglas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Douglas can now know whether Angla can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Kelly","Angla"],"index":59704,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997131228,"difficulty":0.0002868772}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Douglas can now know that Joseph can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Michael","Douglas"],"index":25495,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997790456,"difficulty":0.0002209544}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Donna can now know that Lisa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Albert","Mary","Lisa","Donna"],"index":64527,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984349608,"difficulty":0.0015650392}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Mark can now know whether Katerine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katerine","Candy","Mark","James"],"index":15492,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999725759,"difficulty":0.000274241}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"David can now know that Patricia can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Patricia","Angela","David"],"index":1663,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998252213,"difficulty":0.001747787}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that Leonard knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know whether Tyrone can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tyrone","Roy","David","Leonard"],"index":7941,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995989203,"difficulty":0.0004010797}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Stephanie can now know whether Dwayne can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Dwayne","Kenny","Stephanie"],"index":22883,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996396303,"difficulty":0.0003603697}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Kimberly knows whether Florence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Walter can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Florence","Kimberly","Charles"],"index":16691,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9940165281,"difficulty":0.0059834719}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Curt's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Curt can now know that Paul can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Curt","Paul"],"index":64229,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983882904,"difficulty":0.0016117096}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Helen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Allan","Angeline"],"index":13654,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986139536,"difficulty":0.0013860464}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether Taryn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jessica can now know whether Taryn can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Taryn","Ronald","Jessica"],"index":89,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997674823,"difficulty":0.0002325177}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rosie can now know that Raul can know that Raul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosie","Christopher","Raul"],"index":11143,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998555243,"difficulty":0.001444757}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mercedes knows whether or not nobody's forehead is muddy. It is publicly announced that Larry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Sandra can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mercedes","Sandra","Larry"],"index":20455,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984388947,"difficulty":0.0015611053}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Laura knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Glenda can now know whether Eric can know whether Glenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Glenda","Eric","Ron","Laura"],"index":16735,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996929169,"difficulty":0.0003070831}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether or not everyone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy. It is publicly announced that Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Gloria can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Gloria","Maria"],"index":60536,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Betty's forehead is muddy. It is publicly announced that Alfonso knows whether or not nobody's forehead is muddy. It is publicly announced that Betty knows whether Alfonso's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Alfonso can now know that Alfonso's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eric","Alfonso","Betty"],"index":60842,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9916743636,"difficulty":0.0083256364}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Steven's forehead is muddy. It is publicly announced that Magaret knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Frances can now know that Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Judith","Magaret","Frances"],"index":33825,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.832944572,"difficulty":0.167055428}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether Anthony's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] Agentd knows whether (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"George can now know whether Michael can know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Jeremy","Anthony","George"],"index":2162,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994075298,"difficulty":0.0005924702}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Rosella can now know that Julia can know that Herman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Herman","Julia","Rosella"],"index":24470,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9332294464,"difficulty":0.0667705536}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Thomas can now know whether Christopher can know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Christopher","Dorotha"],"index":6536,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996950626,"difficulty":0.0003049374}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Venita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Anna can now know that Venita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Venita","Anna"],"index":57870,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974250793,"difficulty":0.0025749207}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candice knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Candice can now know that Dan can know that Candice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dan","Candice"],"index":36325,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975981116,"difficulty":0.0024018884}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Julian can now know that Mario can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mario","Julian","Greg"],"index":31988,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983785152,"difficulty":0.0016214848}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Christopher can now know whether Miriam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Miriam","James","Christopher"],"index":31049,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997250438,"difficulty":0.0002749562}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Beverly can now know that Daniel can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Beverly","Daniel"],"index":47121,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997571111,"difficulty":0.0002428889}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy knows whether or not everyone's forehead is muddy. It is publicly announced that Jeremy knows whether Irma's forehead is muddy. It is publicly announced that Jeremy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jeremy can now know that Irma can know whether Jeremy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeremy","Irma"],"index":55185,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997096658,"difficulty":0.0002903342}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annette's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Annette can now know whether Laura can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clyde","Laura","Annette"],"index":14345,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997219443,"difficulty":0.0002780557}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia knows whether Herman's forehead is muddy. It is publicly announced that Melissa knows whether Herman's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Melissa can now know that Virginia can know whether Herman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Virginia","Herman","Melissa"],"index":57542,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997432828,"difficulty":0.0002567172}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgiann knows whether Georgiann's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Carrie can now know that Carrie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francis","Georgiann","Carrie"],"index":60467,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981473684,"difficulty":0.0018526316}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether Betty can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","John","Betty"],"index":56452,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99966681,"difficulty":0.00033319}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether Betsy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Betsy can now know that Betsy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dianne","Otto","Gerald","Betsy"],"index":57122,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973753691,"difficulty":0.0026246309}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Quentin knows whether Dan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Dan can now know that Quentin can know whether Dan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dan","Quentin"],"index":40780,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997444749,"difficulty":0.0002555251}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Lawrence can now know that George can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mandy","Lawrence","George"],"index":38368,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997848868,"difficulty":0.0002151132}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"James can now know that Melony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Melony","Edmund"],"index":3560,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9851629138,"difficulty":0.0148370862}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether someone's forehead is muddy. It is publicly announced that Jane knows whether or not nobody's forehead is muddy. It is publicly announced that Jane knows whether Linda's forehead is muddy. It is publicly announced that Farah knows whether Farah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Farah can now know that Jane can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Farah","Jane"],"index":21316,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969099164,"difficulty":0.0030900836}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nadine's forehead is muddy. It is publicly announced that Nadine knows whether Jerry's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ruben can now know that Jerry can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Ruben","Nadine"],"index":62295,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984186888,"difficulty":0.0015813112}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Blanca can now know whether Jim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kenneth","Blanca","Shawn","Jim"],"index":13971,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997373223,"difficulty":0.0002626777}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether Victoria's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Victoria can now know that Terry can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Victoria","Terry"],"index":35366,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997605681,"difficulty":0.0002394319}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Kimberly can know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Kimberly","Katherine","Benjamin"],"index":62003,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984419942,"difficulty":0.0015580058}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luisa knows whether someone's forehead is muddy. It is publicly announced that Luisa knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"James can now know whether Angela can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","James","Jeremy","Luisa"],"index":18146,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997059703,"difficulty":0.0002940297}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carole knows whether Steven's forehead is muddy. It is publicly announced that Carlos knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Carole can now know that Carlos can know whether Carole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carlos","Steven","Carole"],"index":7073,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997311234,"difficulty":0.0002688766}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samuel knows whether or not everyone's forehead is muddy. It is publicly announced that Elmira knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Harry can now know that Samuel can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harry","Samuel","Colleen","Elmira"],"index":15032,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cedric knows whether Cedric's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sean can now know that Cedric can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sean","Cedric"],"index":14973,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999545753,"difficulty":0.000454247}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Amy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Mary can now know that Elizabeth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eduardo","Amy","Elizabeth","Mary"],"index":64768,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983974099,"difficulty":0.0016025901}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Luanne can now know that Diana can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Luanne","Diana"],"index":26255,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996279478,"difficulty":0.0003720522}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole's forehead is muddy. It is publicly announced that Maria knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Sarah can now know that Lisa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","Maria","Lisa","Nicole"],"index":4496,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984804988,"difficulty":0.0015195012}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Nancy can now know that Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Estella","Nancy"],"index":58635,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9939134717,"difficulty":0.0060865283}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether Lance's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lance can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeanette","Scott","Lance"],"index":27106,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985018969,"difficulty":0.0014981031}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacy knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Stacy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Stacy","Nancy","Anthony"],"index":60811,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982460737,"difficulty":0.0017539263}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lydia knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Ronald can now know whether Staci can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Staci","Lydia","Ronald"],"index":35514,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995769858,"difficulty":0.0004230142}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wallace can now know whether Michael can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geneva","Wallace","Michael","Theresa"],"index":50380,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jared knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jared can now know that Jeffrey can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Henry","Jared","Jeffrey"],"index":7748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983170033,"difficulty":0.0016829967}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Kimberly's forehead is muddy. It is publicly announced that Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Ralph can now know whether Kimberly can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kimberly","Ralph"],"index":47052,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997857213,"difficulty":0.0002142787}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorthey knows whether Jacqueline's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jacqueline can now know that James can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorthey","Jacqueline","James"],"index":20864,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995955825,"difficulty":0.0004044175}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Clara can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Norma","April","Clara"],"index":35978,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984278679,"difficulty":0.0015721321}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton knows whether Milton's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Milton can now know that Shana can know that Milton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julio","Shana","Milton"],"index":4692,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974611998,"difficulty":0.0025388002}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Myrtice can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alvin","David","Myrtice"],"index":14469,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997550845,"difficulty":0.0002449155}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest knows whether or not nobody's forehead is muddy. It is publicly announced that Michael's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] 0","hypothesis":"Ernest can now know that Ernest's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brittney","Bethany","Ernest","Michael"],"index":57658,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937018156,"difficulty":0.0062981844}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know that Norma can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Norma","Jesse"],"index":55409,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984179735,"difficulty":0.0015820265}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Bennett can now know that William can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bennett","William","Dennis"],"index":45860,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9841819406,"difficulty":0.0158180594}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Tony can now know that Tony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marlene","Tony","Scott"],"index":20874,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9647946954,"difficulty":0.0352053046}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosalie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Mabel can now know that Jennie can know that Mabel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennie","Michael","Mabel","Rosalie"],"index":19995,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9784299135,"difficulty":0.0215700865}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Sandra knows whether Sandra's forehead is muddy. It is publicly announced that Kyle knows whether Kyle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kyle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Kyle","James","Laura"],"index":18696,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9910384417,"difficulty":0.0089615583}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Krista knows whether Krista's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Krista can now know that Sarah can know that Krista's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sarah","Stanley","Krista"],"index":13007,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976298809,"difficulty":0.0023701191}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Patricia can now know whether Stephanie can know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Stephanie","Patricia"],"index":57844,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997113347,"difficulty":0.0002886653}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marlo's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Marlo can now know that Julie can know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marlo","Julie","Scott"],"index":7491,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957060218,"difficulty":0.0042939782}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Magda knows whether Magda's forehead is muddy. It is publicly announced that Roxanne knows whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Magda can now know that Larry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Magda","Adam","Roxanne"],"index":65670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977667332,"difficulty":0.0022332668}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gabriel knows whether Dannielle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Dannielle can now know that Gabriel can know that Dannielle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gabriel","Timothy","Janet","Dannielle"],"index":36508,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973996878,"difficulty":0.0026003122}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramon knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mark can now know that Ramon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Ramon","Mark","Melinda"],"index":44509,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983677268,"difficulty":0.0016322732}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maddie's forehead is not muddy. It is publicly announced that Maddie knows whether Nancy's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Nancy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Nancy can now know that Maddie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nancy","Maddie"],"index":27085,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984916449,"difficulty":0.0015083551}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfredo knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rhonda can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Alfredo","Jeremy","Rhonda"],"index":22027,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9427281618,"difficulty":0.0572718382}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Joyce can now know that David can know that Jan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joyce","David","Jan"],"index":20756,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984745383,"difficulty":0.0015254617}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glen knows whether Glen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Terry can now know that Glen can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Glen","Elijah","Leora","Terry"],"index":34490,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983652234,"difficulty":0.0016347766}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Matthew's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Gregory can now know that Matthew can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gregory","Matthew","Martha"],"index":41133,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996908903,"difficulty":0.0003091097}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Margie knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Margie can now know that Frank can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margie","Frank","David"],"index":64787,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997611642,"difficulty":0.0002388358}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Stewart's forehead is muddy. It is publicly announced that Jimmie's forehead is not muddy. It is publicly announced that Jimmie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Jimmie","Stewart"],"index":42320,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Tammy can now know that Steve can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tammy","Steve"],"index":63601,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996311665,"difficulty":0.0003688335}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"Stewart can now know that Christopher can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Lourdes","Jeremy","Stewart"],"index":10456,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9964630008,"difficulty":0.0035369992}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Elizabeth can now know that Eleanor's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charlie","Elizabeth","Eleanor"],"index":65737,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8399729133,"difficulty":0.1600270867}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lenora knows whether Katie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Lenora can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","Mary","Lenora","Katie"],"index":44477,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998172164,"difficulty":0.001827836}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Lester can now know that Lester's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kathy","Lester"],"index":39484,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.955119133,"difficulty":0.044880867}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Linda can now know that Suzanne can know that Julio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julio","Linda","Judith","Suzanne"],"index":9851,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9362828135,"difficulty":0.0637171865}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Chelsey can now know that Elida can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jamie","Chelsey","Elida"],"index":26580,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982631803,"difficulty":0.0017368197}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gordon can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justine","Gordon","Christopher","Carolina"],"index":25610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982891679,"difficulty":0.0017108321}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Andrea knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Christopher can now know that Klara can know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrea","Klara","Christopher","Samantha"],"index":55462,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965535402,"difficulty":0.0034464598}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lisa can now know that Kisha can know that Julia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Lisa","Julia","Kisha"],"index":35492,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9822385311,"difficulty":0.0177614689}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Marjorie can know that Lourdes's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lourdes","William","Willie","Marjorie"],"index":545,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986203909,"difficulty":0.0013796091}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Natividad can now know that Cathleen can know that Natividad's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Natividad","Kay","Cathleen"],"index":34998,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9776135683,"difficulty":0.0223864317}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell knows whether someone's forehead is muddy. It is publicly announced that Russell knows whether someone's forehead is muddy. It is publicly announced that Russell knows whether someone's forehead is muddy. It is publicly announced that Russell knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Russell can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Russell","Timothy","Jasmine"],"index":10012,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996802807,"difficulty":0.0003197193}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica's forehead is muddy. It is publicly announced that Monica knows whether Monica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Karla can now know that Monica can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jonas","Karla","Monica"],"index":23319,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982963204,"difficulty":0.0017036796}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chelsey knows whether Chelsey's forehead is muddy. It is publicly announced that Arthur knows whether Anita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Nicole can now know whether Nicole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anita","Nicole","Chelsey","Arthur"],"index":34494,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989537001,"difficulty":0.0010462999}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether Otto's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Matthew can now know whether Jason can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Otto","Matthew","Jason"],"index":26947,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995954633,"difficulty":0.0004045367}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Joseph can now know that Thomas can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joseph","Thomas"],"index":47978,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984285235,"difficulty":0.0015714765}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Fredrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Fredrick can now know whether Pauline can know whether Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pauline","Gary","Fredrick","Ruby"],"index":22674,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997195601,"difficulty":0.0002804399}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"George can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","George","John"],"index":3872,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997820258,"difficulty":0.0002179742}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether Amy's forehead is muddy. It is publicly announced that Joseph knows whether Carroll's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Ronnie can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carroll","Ronnie","Amy","Joseph"],"index":27103,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998013854,"difficulty":0.001986146}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Henry can now know that Albert can know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Henry","Albert","Ruth"],"index":24553,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963536263,"difficulty":0.0036463737}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ben knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Danny can now know whether Ben can know whether Danny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michele","Ben","Danny","Harley"],"index":28806,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996886253,"difficulty":0.0003113747}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harriet's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Laureen can now know that Frank can know that Harriet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Laureen","Harriet","Frank"],"index":4412,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9824192524,"difficulty":0.0175807476}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ricardo knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Margery can now know that Ricardo can know that Margery's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margery","Ricardo","Charles","Keith"],"index":6584,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8987367153,"difficulty":0.1012632847}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alejandro knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Alejandro can now know whether Doris can know whether Doris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alejandro","Doris","Pat"],"index":5390,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996345043,"difficulty":0.0003654957}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcos knows whether Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Marcos can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Janet","Marcos"],"index":17302,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998273015,"difficulty":0.001726985}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know whether Jordan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Jordan","Timothy"],"index":57622,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997202754,"difficulty":0.0002797246}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Joseph can now know that Donald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Deborah","Donald"],"index":20554,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985126853,"difficulty":0.0014873147}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenny's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Kenny can now know whether Kirk can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenny","Kirk"],"index":25951,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995478988,"difficulty":0.0004521012}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Leroy can now know that Richard can know that Leroy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Stacey","Leroy"],"index":43661,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9420685768,"difficulty":0.0579314232}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Karen can now know whether John can know whether Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","John","Kenneth"],"index":36036,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997060895,"difficulty":0.0002939105}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramon knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Elizabeth can now know that Ramon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ramon","Elizabeth"],"index":26962,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984360337,"difficulty":0.0015639663}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Howard can now know whether Howard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Michael","Howard"],"index":34532,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993106127,"difficulty":0.0006893873}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"James can now know whether John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","John"],"index":9807,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996689558,"difficulty":0.0003310442}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Shannon can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","James","Jean","Shannon"],"index":26309,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997403026,"difficulty":0.0002596974}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether Brice's forehead is muddy. It is publicly announced that Brice knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Brice can now know that Maria can know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brice","Maria"],"index":62716,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99581182,"difficulty":0.00418818}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Kathryn knows whether Stanley's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Stanley can now know that Kathryn can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathryn","Anthony","Stanley"],"index":52801,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997575879,"difficulty":0.0002424121}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melody's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Melody can now know that Paula can know that Paula's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paula","James","Melody","Mary"],"index":49687,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9945645332,"difficulty":0.0054354668}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis knows whether Emmanuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Carmen can now know whether Francis can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Carmen","Mildred","Emmanuel"],"index":36549,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995815158,"difficulty":0.0004184842}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lidia knows whether Lidia's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Lidia can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lidia","Nina","James","Betty"],"index":17303,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9422448277,"difficulty":0.0577551723}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Joshua can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Justin","James","Joshua","Annette"],"index":11593,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983022213,"difficulty":0.0016977787}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynne knows whether someone's forehead is muddy. It is publicly announced that Lynne knows whether Ingrid's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentd knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Lynne can now know that Ingrid can know that Ingrid's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darius","Ingrid","Jennifer","Lynne"],"index":41466,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971254468,"difficulty":0.0028745532}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Sarah can now know that Jeffrey can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Norma","Sarah","Carolyn","Jeffrey"],"index":63639,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984458089,"difficulty":0.0015541911}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Todd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Refugio can now know that Duane can know whether Duane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Todd","Virgie","Refugio","Duane"],"index":54203,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996305704,"difficulty":0.0003694296}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Herbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Jennifer can now know whether Lewis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jennifer","Mario","Herbert","Lewis"],"index":65314,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997329116,"difficulty":0.0002670884}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know whether Diane can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnny","Barbara","Sandra","Diane"],"index":46152,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997672439,"difficulty":0.0002327561}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kathleen can now know whether Manuel can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Manuel","Donald"],"index":43163,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996591806,"difficulty":0.0003408194}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd knows whether or not nobody's forehead is muddy. It is publicly announced that Anne knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Anne can now know whether Lloyd can know that Anne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anne","Lloyd"],"index":27804,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999102354,"difficulty":0.000897646}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lavada can now know that William can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lavada","William","Alex"],"index":45625,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997708201,"difficulty":0.0002291799}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Tomas can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janice","Tomas","Peggy"],"index":49575,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997422099,"difficulty":0.0002577901}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne knows whether or not everyone's forehead is muddy. It is publicly announced that Maria knows whether Suzanne's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Maria can now know whether Suzanne can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Suzanne","Maria"],"index":20547,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Raymond can now know that Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Todd","Karen","Raymond","Patricia"],"index":47248,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9120535254,"difficulty":0.0879464746}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Kim knows whether Clarice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Ashley can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Clarice","Kim","Ashley"],"index":51100,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9974675179,"difficulty":0.0025324821}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 1 ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 1 ] 0","hypothesis":"Geneva can now know that Albert can know whether Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Albert","Geneva","Charlotte"],"index":35427,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996782541,"difficulty":0.0003217459}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Cortney can now know that Dustin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Travis","Cortney","Dustin"],"index":18839,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984742999,"difficulty":0.0015257001}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tom knows whether Tom's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Melanie can now know that Tom can know that Tom's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Garret","Melanie","Tom"],"index":36963,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972168207,"difficulty":0.0027831793}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nicholas can now know that Ruben can know that Nicholas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicholas","Ruben","Adam"],"index":7784,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961905479,"difficulty":0.0038094521}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether or not everyone's forehead is muddy. It is publicly announced that Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Steven can now know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Margaret","Steven","Thomas"],"index":25500,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8845721483,"difficulty":0.1154278517}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathryn knows whether someone's forehead is muddy. It is publicly announced that Regina knows whether someone's forehead is muddy. It is publicly announced that Debbie knows whether Regina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Regina can now know that Regina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debbie","Tom","Kathryn","Regina"],"index":40433,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959890246,"difficulty":0.0040109754}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Daniel can now know that Harry can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Harry","William"],"index":55944,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99978441,"difficulty":0.00021559}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Georgia can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","Jason","Georgia"],"index":63344,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994446635,"difficulty":0.0005553365}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Darrell can now know that Reginald can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darrell","Reginald","Priscilla"],"index":43539,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997541308,"difficulty":0.0002458692}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Marcos can now know that John can know that Marcos's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shane","James","John","Marcos"],"index":47846,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9572719932,"difficulty":0.0427280068}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether or not everyone's forehead is muddy. It is publicly announced that Mark knows whether Bonnie's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Bonnie can now know that Mark can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Mark","Raymond"],"index":4090,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997535348,"difficulty":0.0002464652}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leland knows whether Curtis's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether Curtis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Eugene can now know that Dennis can know whether Leland's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Curtis","Leland","Eugene","Dennis"],"index":50497,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997256398,"difficulty":0.0002743602}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lisa can now know whether Dustin can know whether Antonio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dustin","Gerald","Lisa","Antonio"],"index":10943,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997258782,"difficulty":0.0002741218}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether Kevin's forehead is muddy. It is publicly announced that Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentc knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Kevin can now know whether Darin can know that Arthur's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darin","Arthur","Kevin"],"index":12772,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996337891,"difficulty":0.0003662109}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Carmen can now know that Nancy can know that Joshua's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Carmen","Nancy"],"index":48024,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9275840521,"difficulty":0.0724159479}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phyllis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Juan can now know that Cody can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cody","Phyllis","Juan"],"index":65892,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982789755,"difficulty":0.0017210245}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edna knows whether or not everyone's forehead is muddy. It is publicly announced that Edna knows whether Brian's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Joy can now know that Brian can know that Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Edna","Joy"],"index":33344,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.6072207093,"difficulty":0.3927792907}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Benjamin can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Elizabeth","Benjamin","Alexandria"],"index":17323,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983854294,"difficulty":0.0016145706}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Judith can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Norma","Judith","John"],"index":11311,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982094765,"difficulty":0.0017905235}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elsie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Elsie can now know that Frances can know that Elsie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Elsie","Frances"],"index":64998,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981866479,"difficulty":0.0018133521}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sue knows whether Sue's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kimberly can now know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vanessa","Ronald","Sue","Kimberly"],"index":56568,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982333183,"difficulty":0.0017666817}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia knows whether Michell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Vernon can now know whether Dana can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michell","Dana","Virginia","Vernon"],"index":6196,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996250868,"difficulty":0.0003749132}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Dwayne can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edna","Dwayne"],"index":64718,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997600913,"difficulty":0.0002399087}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Whitney knows whether Jo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Jo can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Jo","Arthur","Whitney"],"index":42714,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983003736,"difficulty":0.0016996264}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Kathryn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Elsie can now know whether Kathryn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kathryn","Elsie"],"index":4349,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997139573,"difficulty":0.0002860427}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Jennifer can now know that Cindy can know that Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cindy","Jennifer"],"index":30305,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9572074413,"difficulty":0.0427925587}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Landon can now know that Rachael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rachael","Flor","Landon","Raymond"],"index":59372,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9982574582,"difficulty":0.0017425418}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that Darius's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Shirley can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","Regina","Darius","Charles"],"index":64388,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99850595,"difficulty":0.00149405}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andre knows whether Christine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Margaret can now know that Christine can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olive","Andre","Margaret","Christine"],"index":1099,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997418523,"difficulty":0.0002581477}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know that Joe can know whether Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Myriam","Anthony","Robert"],"index":12392,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994240999,"difficulty":0.0005759001}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Kathleen can now know that Eric can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathleen","Eric","Lorretta"],"index":33943,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984213114,"difficulty":0.0015786886}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alissa knows whether Sol's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Alissa can now know that Frances can know whether Sol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sol","Frances","Alissa"],"index":45323,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997467399,"difficulty":0.0002532601}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernie knows whether Bernie's forehead is muddy. It is publicly announced that Ellen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] Agentd knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Jeanne can now know that George can know that Bernie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bernie","George","Ellen","Jeanne"],"index":2279,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9756733179,"difficulty":0.0243266821}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherri's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Sherri can now know that Stewart can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dawn","Patricia","Stewart","Sherri"],"index":8527,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984018207,"difficulty":0.0015981793}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Timothy can now know that James can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Timothy"],"index":50749,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997497201,"difficulty":0.0002502799}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bertha can now know that Aaron can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brandon","Aaron","Bertha"],"index":34084,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984629154,"difficulty":0.0015370846}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Wanda can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debra","Wanda","Shawn"],"index":752,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983018637,"difficulty":0.0016981363}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheri knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Sheri can now know that David can know that Stacy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sheri","Stacy","David"],"index":12374,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983351827,"difficulty":0.0016648173}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hubert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Hubert can now know whether Phillip's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hubert","Emil","Phillip"],"index":27234,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997393489,"difficulty":0.0002606511}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bret knows whether Michelle's forehead is muddy. It is publicly announced that Timothy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Bret can now know whether Timothy can know whether Bret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Michelle","Bret"],"index":39281,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997039437,"difficulty":0.0002960563}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sue's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"David can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Sue","Connie","Crystal"],"index":2944,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998354733,"difficulty":0.001645267}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Alysia can now know that Phyllis can know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Phyllis","John","Alysia"],"index":64904,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985232949,"difficulty":0.0014767051}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle knows whether Harold's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Daniel can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Daniel","Danielle","Harold"],"index":62231,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997511506,"difficulty":0.0002488494}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clara can now know that Vernie can know whether Clara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Vernie","Clara","Tyler"],"index":28653,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997453094,"difficulty":0.0002546906}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Melissa can now know that Jamie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Jamie","Mark","Katie"],"index":22583,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9266421795,"difficulty":0.0733578205}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarissa knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Johnny can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janice","Clarissa","Johnny"],"index":1749,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9981592298,"difficulty":0.0018407702}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy. It is publicly announced that Chae knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Chae can now know that Diane can know that Chae's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Chae","Diane"],"index":24723,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975507855,"difficulty":0.0024492145}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Claude can now know that Therese can know that Claude's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bridget","Claude","Daryl","Therese"],"index":66810,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957838058,"difficulty":0.0042161942}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Celia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Joe","Celia","Beatrice"],"index":14964,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982111454,"difficulty":0.0017888546}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy. It is publicly announced that Christopher knows whether Donald's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Donald knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Christopher can now know that Donald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donald","Christopher"],"index":54272,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983156919,"difficulty":0.0016843081}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know that Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","David","Latasha","Karen"],"index":20642,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984135628,"difficulty":0.0015864372}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Ingrid can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Mary","Billy","Ingrid"],"index":10899,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983534813,"difficulty":0.0016465187}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Virginia can now know whether Carl can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Virginia","Carl"],"index":49921,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996585846,"difficulty":0.0003414154}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Joshua can now know that Jean can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jean","Joshua","Jessica"],"index":14270,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984026551,"difficulty":0.0015973449}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Dawn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Dawn can now know that Cheryl can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Galen","Dawn","Robert","Cheryl"],"index":34965,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977167845,"difficulty":0.0022832155}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Harold can now know that Edna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sheila","Edna","Kathy","Harold"],"index":55551,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969839454,"difficulty":0.0030160546}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Brittany can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christopher","Brittany"],"index":12774,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997608066,"difficulty":0.0002391934}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felicia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Felicia can now know whether Bonnie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Benita","Felicia","Bonnie","Johanna"],"index":52087,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Guadalupe's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Frank can now know that Preston can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","Preston","Guadalupe"],"index":2313,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997629523,"difficulty":0.0002370477}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesse knows whether Jesse's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"Amy can now know that Macy can know that Macy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesse","Macy","Amy","Mary"],"index":3751,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9932724237,"difficulty":0.0067275763}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Ursula can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melinda","Ursula","William","Robert"],"index":3229,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983007312,"difficulty":0.0016992688}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Nina can now know that Debra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nina","Debra","Victor"],"index":55710,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9982606769,"difficulty":0.0017393231}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marion can now know that Marion's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marion","Betty","Molly","Hong"],"index":45869,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984922409,"difficulty":0.0015077591}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corrin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Rosa can now know whether Elmer can know that Corrin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Corrin","Rosa","Elmer"],"index":63063,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996984005,"difficulty":0.0003015995}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon knows whether Marlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Pearline can now know that Brandon can know that Marlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pearline","Brandon","Marlene","Jimmie"],"index":11426,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981820583,"difficulty":0.0018179417}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Annette can now know whether Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Denise","Annette","Bryan"],"index":12883,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997381568,"difficulty":0.0002618432}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lydia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Lydia can now know that Samantha can know that Alice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Samantha","Alice","Lydia","Grace"],"index":61040,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9506228566,"difficulty":0.0493771434}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Brian can now know that Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Timothy","Nancy","Wanda"],"index":63583,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983003736,"difficulty":0.0016996264}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marva knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Marva can now know that Stephanie can know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stephanie","Marva"],"index":9085,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978233576,"difficulty":0.0021766424}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dianna knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Victoria knows whether Victoria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jess can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Victoria","Theresa","Dianna","Jess"],"index":14286,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9957184196,"difficulty":0.0042815804}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmie knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Carol can now know that Jimmie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Carol","Jimmie"],"index":2023,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997550845,"difficulty":0.0002449155}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Karen can now know that Sarah can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Heather","Karen","Sarah"],"index":59170,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997157454,"difficulty":0.0002842546}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irma's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Ronald can now know whether Joseph can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Ronald","Irma","Joseph"],"index":39703,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996730089,"difficulty":0.0003269911}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy. It is publicly announced that Wilma's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Linda can now know whether Wayne can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lesley","Linda","Wayne","Wilma"],"index":17032,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995222092,"difficulty":0.0004777908}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christopher","Rose","Timothy"],"index":26325,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997380376,"difficulty":0.0002619624}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice knows whether or not everyone's forehead is muddy. It is publicly announced that Dave's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Dave can now know whether Alice can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alice","Dave"],"index":35680,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997773767,"difficulty":0.0002226233}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Nancy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Ellen","Terry"],"index":26427,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985111356,"difficulty":0.0014888644}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvia knows whether Sylvia's forehead is muddy. It is publicly announced that Ruth knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Ruth can now know whether Shawn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Sylvia","Shawn","Ruth"],"index":34132,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997385144,"difficulty":0.0002614856}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy. It is publicly announced that Joseph's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Germaine can now know whether Karl can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Germaine","Joseph","Diane","Karl"],"index":39782,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996184111,"difficulty":0.0003815889}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tom knows whether Wendy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Juanita can now know that Wendy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wendy","Barbara","Juanita","Tom"],"index":63292,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984158278,"difficulty":0.0015841722}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that Pearl knows whether Lupita's forehead is muddy. It is publicly announced that Ivey knows whether Pearl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agentd knows whether (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lupita can now know whether David can know that Lupita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Ivey","Pearl","Lupita"],"index":13044,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995740056,"difficulty":0.0004259944}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether Norma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Norma can now know whether Jose can know that Charlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charlene","Gladys","Jose","Norma"],"index":43545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996622801,"difficulty":0.0003377199}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alexis can now know that Brian can know that Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cindy","Alexis","Shane","Brian"],"index":24887,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985411167,"difficulty":0.0014588833}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Dwayne can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Dwayne","Armando","John"],"index":38059,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999717176,"difficulty":0.000282824}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Leona can now know that Annette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leona","Lawrence","Annette"],"index":18168,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967167974,"difficulty":0.0032832026}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Joshua can now know whether Sean can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bradley","Sean","Joshua","Rita"],"index":23171,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996811152,"difficulty":0.0003188848}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyle's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Danielle can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danielle","Kyle","John"],"index":1971,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986515641,"difficulty":0.0013484359}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Roy can now know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roy","Patrick","Charles"],"index":31748,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999745667,"difficulty":0.000254333}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Shirley knows whether Shirley's forehead is muddy. It is publicly announced that Lottie knows whether Lottie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Herman can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shirley","Lottie","Herman","Veronica"],"index":44807,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996765852,"difficulty":0.0003234148}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Joseph can now know whether Raymond can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Joseph"],"index":36139,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995877147,"difficulty":0.0004122853}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Noel knows whether Sook's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Donna can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sook","Sammie","Donna","Noel"],"index":46957,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997591376,"difficulty":0.0002408624}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Carolyn can now know whether Douglas can know whether Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vicky","Jesus","Douglas","Carolyn"],"index":56424,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996007085,"difficulty":0.0003992915}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"William can now know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rosa","William","Antoine","Sabrina"],"index":1326,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.998311758,"difficulty":0.001688242}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myra knows whether Myra's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Myra can now know whether Amy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Myra","Amy"],"index":415,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997327924,"difficulty":0.0002672076}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether Deborah's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Elizabeth can now know that Melissa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Kathy","Melissa","Elizabeth"],"index":25238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983618855,"difficulty":0.0016381145}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Arthur can now know that Sharon can know that Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Arthur","Christina"],"index":10492,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984976053,"difficulty":0.0015023947}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jennifer knows whether or not nobody's forehead is muddy. It is publicly announced that Linda knows whether Stevie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Lucille can now know whether Stevie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucille","Jennifer","Stevie","Linda"],"index":49422,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Lindsay can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","Lindsay"],"index":50962,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8982061744,"difficulty":0.1017938256}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee knows whether Wallace's forehead is muddy. It is publicly announced that Lee knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Daniel can now know whether Wallace can know that Lee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wallace","Lee","Daniel"],"index":29351,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996774197,"difficulty":0.0003225803}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Vickie can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Vickie","Michael","Daniel"],"index":45610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963546991,"difficulty":0.0036453009}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether George's forehead is muddy. It is publicly announced that Rachel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that Rachel can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rachel","Robert","George","James"],"index":34304,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997567534,"difficulty":0.0002432466}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether George's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ralph can now know that Linnie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Edward","Ralph","Linnie"],"index":49565,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999756515,"difficulty":0.000243485}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Yvonne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Toni can now know that John can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Yvonne","Lynda","Toni","John"],"index":39868,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997641444,"difficulty":0.0002358556}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Sandra's forehead is muddy. It is publicly announced that Todd knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Todd can now know that Sandra can know whether Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Todd","Sandra"],"index":25836,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995498061,"difficulty":0.0004501939}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jared can now know that Ruby can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Pearl","Jared","Ruby"],"index":44238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985263348,"difficulty":0.0014736652}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne knows whether or not everyone's forehead is muddy. It is publicly announced that Marissa's forehead is muddy. It is publicly announced that Emily's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] (Agenta knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Marissa can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marissa","Anne","Emily"],"index":25062,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997830987,"difficulty":0.0002169013}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Genaro can now know whether Andre can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andre","Genaro","Janet"],"index":40036,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996726513,"difficulty":0.0003273487}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Amy can now know that Jorge can know that Jorge's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jorge","Amy","Louis","Janice"],"index":45225,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969879985,"difficulty":0.0030120015}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Michael can now know whether Bryan can know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Mary","Marlene","Bryan"],"index":2599,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997083545,"difficulty":0.0002916455}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances knows whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jerry can now know that Frances can know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Stephanie","Frances","Donna"],"index":38545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997305274,"difficulty":0.0002694726}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Louie can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anna","Louie"],"index":26703,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997423291,"difficulty":0.0002576709}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Evelyn can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marcell","Jeremy","Evelyn","Carrol"],"index":2884,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981770515,"difficulty":0.0018229485}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Veronica knows whether someone's forehead is muddy. It is publicly announced that Cynthia knows whether or not nobody's forehead is muddy. It is publicly announced that Cynthia knows whether Veronica's forehead is muddy. It is publicly announced that Helen knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Helen can now know that Cynthia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Veronica","Helen","Cynthia"],"index":9756,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983779192,"difficulty":0.0016220808}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Paul can now know that Larry can know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","John","Larry","Paul"],"index":46965,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997474551,"difficulty":0.0002525449}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Wayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Patricia can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Charles","Wayne"],"index":57383,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984894991,"difficulty":0.0015105009}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy. It is publicly announced that Jennifer knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Billy can now know that Pamela can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Billy","Pamela","Jennifer"],"index":58743,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983273149,"difficulty":0.0016726851}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Betty can now know whether Marion can know whether Marion's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Leslie","Marion","Betty"],"index":35408,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995802045,"difficulty":0.0004197955}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara knows whether Tamara's forehead is muddy. It is publicly announced that Jimmie knows whether Eric's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Eric can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Tamara","Jimmie","Setsuko"],"index":33570,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982722998,"difficulty":0.0017277002}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Justin can now know whether Stephanie can know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Justin","Stephanie"],"index":66603,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996744394,"difficulty":0.0003255606}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carlos can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carlos","Andrew","Earl"],"index":8518,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983009696,"difficulty":0.0016990304}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theodore knows whether Delores's forehead is muddy. It is publicly announced that Jesse knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jesse can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesse","Russel","Theodore","Delores"],"index":59196,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982871413,"difficulty":0.0017128587}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know that Kevin can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Geraldine","Mary","David"],"index":49908,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9819277525,"difficulty":1.9819277525}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Manuel can now know that David can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Manuel","David"],"index":60048,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984556437,"difficulty":0.0015443563}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Melvin can now know that Annette can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melvin","Annette","David","Sarah"],"index":28011,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997841716,"difficulty":0.0002158284}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Edith can now know whether Ronda can know that Edith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Edith","Frances","Ronda"],"index":52971,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992927313,"difficulty":0.0007072687}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Emile's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Carl can now know whether Lois can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Richard","Lois","Emile"],"index":7882,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996017814,"difficulty":0.0003982186}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Blanca can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Blanca","Robert","Amy"],"index":22792,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983689189,"difficulty":0.0016310811}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Darryl can now know whether Joseph can know that Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darryl","Joseph","Jose"],"index":1158,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996864796,"difficulty":0.0003135204}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Robert can know whether Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Amado","Michael","Frances"],"index":63196,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997243285,"difficulty":0.0002756715}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Patricia can now know that Stanley can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Lucille","Stanley","Henry"],"index":57558,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997590184,"difficulty":0.0002409816}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa knows whether Chad's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know whether Theresa can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Theresa","Chad","William"],"index":50196,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995725751,"difficulty":0.0004274249}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"James can now know whether Sheila can know that Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Pierre","Sheila","Betty"],"index":33534,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996253252,"difficulty":0.0003746748}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Evelyn's forehead is muddy. It is publicly announced that Teresa knows whether Evelyn's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Evelyn can now know that Teresa can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Teresa","Evelyn"],"index":62188,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983075857,"difficulty":0.0016924143}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lula can now know that Kimberly can know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mohammad","Kimberly","Lula","Ruby"],"index":43527,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961154461,"difficulty":0.0038845539}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Bryan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Sean can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bryan","Sean"],"index":51885,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9938812256,"difficulty":0.0061187744}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Linda can now know whether Beverly can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alex","Natasha","Beverly","Linda"],"index":18561,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997193217,"difficulty":0.0002806783}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Joe knows whether Joe's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Joe can now know that Misty can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joe","Misty"],"index":26456,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dolores knows whether Robert's forehead is muddy. It is publicly announced that Robert knows whether Dolores's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Dolores can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Dolores"],"index":37315,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998352766,"difficulty":0.001647234}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know whether Jesse can know that Naomi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stefania","Naomi","Jesse","Thomas"],"index":42121,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996722937,"difficulty":0.0003277063}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy. It is publicly announced that Kenneth knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentd knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Kenneth can now know that Mary can know whether Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Agnes","George","Mary","Kenneth"],"index":58454,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997161031,"difficulty":0.0002838969}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Larry can now know whether Leroy can know that Melva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leroy","Lori","Melva","Larry"],"index":66153,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996688366,"difficulty":0.0003311634}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether or not everyone's forehead is muddy. It is publicly announced that Ruth knows whether or not nobody's forehead is muddy. It is publicly announced that Grace knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Ruth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ruth","Grace"],"index":59297,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998390913,"difficulty":0.001609087}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether Ashley's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jessica can now know that Ashley can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ashley","Jessica"],"index":50884,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997426867,"difficulty":0.0002573133}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kathleen can now know that Elva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathleen","Elva","Jeffery","Peter"],"index":62676,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996733427,"difficulty":0.003266573}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Twila knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Crystal can now know that Twila can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Twila","Jennie"],"index":60623,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996478558,"difficulty":0.0003521442}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Bryant's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentd knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Billy can now know that Lula can know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lula","Bryant","Charles","Billy"],"index":29569,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997201562,"difficulty":0.0002798438}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Daphne can now know that Karen can know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Randall","Maria","Daphne"],"index":54724,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9306603074,"difficulty":0.0693396926}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jay knows whether Jay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jay can now know that Jay's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jay","Robert","Edgardo","Paul"],"index":24803,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972449541,"difficulty":0.0027550459}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Florence can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lon","Florence"],"index":6369,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983590245,"difficulty":0.0016409755}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jacob can now know that Cheryl can know that Casey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Lourdes","Casey","Jacob"],"index":37348,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986458421,"difficulty":0.0013541579}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Lisa can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mabel","Lisa"],"index":63081,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997556806,"difficulty":0.0002443194}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Evan's forehead is muddy. It is publicly announced that Pamela's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Viola can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Viola","Pamela","John","Evan"],"index":23098,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997689128,"difficulty":0.0002310872}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] 0","hypothesis":"Carol can now know that Monique can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Monique","Carol"],"index":26878,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Susan can now know whether Mary can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Susan"],"index":14690,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Karen can now know whether Eva can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eva","Karen","Debra"],"index":20906,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bryce can now know whether Carol can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Carol","Chelsea","Bryce"],"index":6558,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997510314,"difficulty":0.0002489686}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Ruth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Kenneth can now know that Ruth can know that Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Ruth","Robert"],"index":1674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9902982116,"difficulty":0.0097017884}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Donald can now know that Ann can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donald","Ann"],"index":42188,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983782768,"difficulty":0.0016217232}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know whether John can know that Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Timothy","Barbara","John"],"index":32114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996831417,"difficulty":0.0003168583}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Osvaldo knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jeffrey's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Jeffrey can now know whether Osvaldo can know whether Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Jeffrey","Osvaldo"],"index":55504,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997283816,"difficulty":0.0002716184}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vernon knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Vernon can now know that Mary can know whether Denise's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vernon","Denise","Mary"],"index":36590,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997172952,"difficulty":0.0002827048}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Betty can now know that Gail's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gail","Betty","Shirley","Renee"],"index":27767,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998664856,"difficulty":0.001335144}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Shawn can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shawn","Brittany","Rosalind","Dennis"],"index":33423,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997084737,"difficulty":0.0002915263}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Bryan can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Bryan","Gerald"],"index":59112,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.998206377,"difficulty":0.001793623}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Wade can now know whether Ellis can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wade","Clark","Christopher","Ellis"],"index":6706,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997290969,"difficulty":0.0002709031}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aubrey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Aubrey can now know whether Sonia can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Aubrey","Sonia","Laura"],"index":37944,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997522235,"difficulty":0.0002477765}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois knows whether Lois's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Devin can now know that Devin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Devin","Lois"],"index":40995,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982889295,"difficulty":0.0017110705}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kathleen can now know that Muriel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Muriel","Kathleen","David","Todd"],"index":32265,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9973288774,"difficulty":0.0026711226}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Martha can now know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Christopher","Martha"],"index":42338,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984543324,"difficulty":0.0015456676}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Marguerite can know that Rene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irving","Marguerite","Robert","Rene"],"index":45205,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996671677,"difficulty":0.0003328323}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marianne knows whether or not nobody's forehead is muddy. It is publicly announced that Kelly's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Marianne can now know whether Kelly can know that Kelly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Kelly","Marianne","Albert"],"index":36570,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997089505,"difficulty":0.0002910495}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvette's forehead is muddy. It is publicly announced that Janet knows whether Yvette's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Janet can now know whether Micah can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Micah","Jack","Yvette","Janet"],"index":64550,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997858405,"difficulty":0.0002141595}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerome's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jerome can now know that Jamie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerome","Jamie","Ellen","James"],"index":55008,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983792305,"difficulty":0.0016207695}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gustavo knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Thomas can now know whether John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Gustavo","John"],"index":43398,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996091723,"difficulty":0.0003908277}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether someone's forehead is muddy. It is publicly announced that Terry's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Terry"],"index":14533,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937784076,"difficulty":0.0062215924}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Daniel can now know whether Cecilia can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joyce","Daniel","Cecilia"],"index":7918,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry knows whether Barry's forehead is muddy. It is publicly announced that Barry's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Roger can now know whether Barry can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barry","Roger"],"index":14327,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether John's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"William can now know whether John can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Brian","Amy","William"],"index":2256,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995394945,"difficulty":0.0004605055}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Veronica can now know that Veronica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Kennith","Veronica"],"index":15156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980571866,"difficulty":0.0019428134}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether Craig's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Angela can now know whether Craig can know whether Craig's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Craig","Kelsey"],"index":1699,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996002316,"difficulty":0.0003997684}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy. It is publicly announced that Stephanie knows whether Brooke's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Stephanie can now know whether Brooke can know whether Brooke's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brooke","Pamela","Stephanie"],"index":20280,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996581078,"difficulty":0.0003418922}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Janet can now know that Cynthia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janet","Danielle","Cynthia","Addie"],"index":5276,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.772090435,"difficulty":1.772090435}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Marcus can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Marcus","Margaret","Brian"],"index":13965,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997847676,"difficulty":0.0002152324}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tonya knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Veronica can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Veronica","Tonya","Jimmy"],"index":18230,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996987581,"difficulty":0.0003012419}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ralph can now know whether Joshua can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ralph","Joshua","Michelle"],"index":18904,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999597609,"difficulty":0.000402391}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rickey knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Rickey can now know that Dennis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rickey","Dennis","Robert"],"index":49249,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979166389,"difficulty":0.0020833611}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether Rita's forehead is muddy. It is publicly announced that Connie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Kenneth can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Connie","Arthur","Kenneth","Rita"],"index":36093,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Maureen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Maureen can now know whether Maureen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Steven","Maureen"],"index":37547,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993498921,"difficulty":0.0006501079}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Jennifer can now know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Albert","Ma","Derek","Jennifer"],"index":243,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9434598088,"difficulty":0.0565401912}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Abigail can now know whether Douglas can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","Valerie","Abigail","Nona"],"index":11776,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999740541,"difficulty":0.000259459}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sabrina can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tammy","Lewis","Sabrina","Howard"],"index":15457,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983049631,"difficulty":0.0016950369}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] 0","hypothesis":"Lorenzo can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Lorenzo","Teri"],"index":45646,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984477758,"difficulty":0.0015522242}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether Donna's forehead is muddy. It is publicly announced that James knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"James can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Donna","Leonardo","James"],"index":48529,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995849729,"difficulty":0.0004150271}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenn knows whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Glenn can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Frances","Glenn","Mary"],"index":11257,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984840751,"difficulty":0.0015159249}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether Marc's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Barbara can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michelle","Barbara","Marc","Lee"],"index":21816,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997557998,"difficulty":0.0002442002}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Joseph can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Milton","Leon"],"index":28770,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9942820072,"difficulty":0.0057179928}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delores knows whether Estella's forehead is muddy. It is publicly announced that Estella knows whether Estella's forehead is muddy. It is publicly announced that Delores knows whether Delores's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Estella can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Delores","Estella"],"index":23369,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather knows whether or not nobody's forehead is muddy. It is publicly announced that Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Jennifer can now know that Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Jennifer","Heather","Willie"],"index":46691,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9634585381,"difficulty":0.0365414619}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether or not nobody's forehead is muddy. It is publicly announced that Amy knows whether Amy's forehead is muddy. It is publicly announced that Dorthy's forehead is muddy. It is publicly announced that Steven knows whether Dorthy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Dorthy can now know whether Amy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorthy","Amy","Steven","Jessica"],"index":42447,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997450709,"difficulty":0.0002549291}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ashley","Norman","Michael"],"index":8421,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99976331,"difficulty":0.00023669}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Marcus"],"index":62538,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985301495,"difficulty":0.0014698505}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sean knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Sean can now know that Michelle can know that Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Michelle","Sean"],"index":13030,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99836272,"difficulty":0.00163728}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Robert can now know whether Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Gene","Walter","Robert"],"index":12915,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997275472,"difficulty":0.0002724528}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn's forehead is muddy. It is publicly announced that Shawn knows whether Joan's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Joan can now know that Shawn can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joan","Bradley","Shawn"],"index":10714,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996650219,"difficulty":0.0003349781}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Alicia can now know that Samantha can know that Samantha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Samantha","Margaret","Michelle","Alicia"],"index":32413,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983878136,"difficulty":0.0016121864}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Greg's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Paul can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","Vincent","Greg","Mark"],"index":48421,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997649789,"difficulty":0.0002350211}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Carol can now know whether Joseph can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","James","Carol"],"index":52079,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996520281,"difficulty":0.0003479719}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether or not nobody's forehead is muddy. It is publicly announced that Sandra knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Sandra can now know whether Joyce can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sandra","Joyce"],"index":30414,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995835423,"difficulty":0.0004164577}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Becky's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Becky can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Becky","Karen"],"index":31308,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983805418,"difficulty":0.0016194582}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Mary can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","David"],"index":61202,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9547320604,"difficulty":0.0452679396}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Ruth can now know that Ariel can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ariel","Ruth"],"index":56690,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996352196,"difficulty":0.0003647804}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy. It is publicly announced that George knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Mary can now know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Mary","Robert","George"],"index":26161,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979445338,"difficulty":0.0020554662}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Donna can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["April","Donna"],"index":27139,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977825284,"difficulty":0.0022174716}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Gary can now know that Jane can know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jane","Gary","Steven","Douglas"],"index":35096,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984961748,"difficulty":0.0015038252}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Kerry can now know that Walter can know that Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephanie","Kerry","Walter"],"index":51733,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9896097183,"difficulty":0.0103902817}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether Pamela's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Pamela can now know that Kenneth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pamela","Kenneth"],"index":994,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998329699,"difficulty":0.001670301}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Larry can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Larry","Patricia"],"index":30106,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984290004,"difficulty":0.0015709996}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emily knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Zachary can now know that Emily can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Randi","Zachary","Emily"],"index":53766,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996870756,"difficulty":0.0003129244}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Norma can now know that Norma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norma","Carlos","Damaris","Ramona"],"index":34947,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980003238,"difficulty":0.0019996762}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Catherine can now know whether Patricia can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Patricia"],"index":22385,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999612987,"difficulty":0.000387013}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Joshua knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Daniel can now know that Ruth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joshua","Ruth","Daniel","Thomas"],"index":43042,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984993935,"difficulty":0.0015006065}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not nobody's forehead is muddy. It is publicly announced that Hildred's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Hildred can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Hildred","Jennifer"],"index":48066,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984523058,"difficulty":0.0015476942}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Steven's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Mary can now know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cesar","Claudia","Steven","Mary"],"index":54851,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996958971,"difficulty":0.003041029}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Frances can now know whether Jack can know whether Jack's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","Anita","Bradley","Jack"],"index":57322,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996836185,"difficulty":0.0003163815}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Velma can now know that Kathy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cynthia","Kathy","Velma"],"index":20685,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983531237,"difficulty":0.0016468763}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether someone's forehead is muddy. It is publicly announced that Scott knows whether someone's forehead is muddy. It is publicly announced that Lawrence knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Scott can now know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Jason","Frank","Scott"],"index":12754,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977703094,"difficulty":0.0022296906}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy. It is publicly announced that Rhoda's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Rhoda can now know whether Donna can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rhoda","Donna"],"index":12866,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999409318,"difficulty":0.000590682}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] 0","hypothesis":"Donald can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Isabel","Matthew"],"index":35101,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998518765,"difficulty":0.001481235}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Anne can now know that Mark can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Anne","Mark"],"index":66383,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982878566,"difficulty":0.0017121434}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Oliver can now know whether Leona can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Leona","Lessie","Oliver"],"index":50708,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997021556,"difficulty":0.0002978444}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Richard can now know that Joan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Johnathon","Joan"],"index":33015,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981016517,"difficulty":0.0018983483}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether Gregory's forehead is muddy. It is publicly announced that Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Gregory can now know that Luis can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gregory","Luis"],"index":51594,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997859597,"difficulty":0.0002140403}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether Charles's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Charles can now know whether Diana can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Moshe","Charles","Terry","Diana"],"index":8355,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995720983,"difficulty":0.0004279017}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catharine knows whether or not nobody's forehead is muddy. It is publicly announced that Pauline knows whether Catharine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Catharine can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Catharine","Pauline"],"index":21739,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982749224,"difficulty":0.0017250776}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rod knows whether Carol's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Robert can now know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rod","Robert","Carol","Frank"],"index":5230,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9988652468,"difficulty":0.0011347532}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Omar can now know that John can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Omar","John","Lee","Lana"],"index":1319,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Leonard can now know that Jacob can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amy","Jacob","Leonard"],"index":35146,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948155284,"difficulty":0.0051844716}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Treva can now know whether Shirley can know whether Treva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tamara","Jodi","Shirley","Treva"],"index":38736,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996938705,"difficulty":0.0003061295}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether someone's forehead is muddy. It is publicly announced that Martha's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Bobby can now know whether Martha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bobby","Martha"],"index":41035,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997238517,"difficulty":0.0002761483}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Eleanor","Paul"],"index":64968,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928193688,"difficulty":0.0071806312}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abbey knows whether Abbey's forehead is muddy. It is publicly announced that Abbey's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Abbey can now know whether Remedios can know whether Abbey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Abbey","Remedios"],"index":30058,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997224212,"difficulty":0.0002775788}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Athena knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Michael can now know that Athena's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Athena","Dorothy","Michael"],"index":48347,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969661832,"difficulty":0.0030338168}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether Eric's forehead is muddy. It is publicly announced that John knows whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Eric","Edward","John"],"index":45193,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982640147,"difficulty":0.0017359853}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"William can now know whether Morgan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Morgan","William","Jeanna","Aaron"],"index":42470,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997343421,"difficulty":0.0002656579}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hector's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Edward can now know whether Hector can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ernest","Edward","Elmer","Hector"],"index":55630,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997153878,"difficulty":0.0002846122}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Travis knows whether Diana's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Diana can now know that Travis can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Travis","Mark","Diana"],"index":47180,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9871610999,"difficulty":0.0128389001}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amos's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Jason can now know that Amos can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clifford","Jason","Amos"],"index":44001,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997829795,"difficulty":0.0002170205}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Christopher's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Justin can now know whether Christopher can know that Cynthia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Christopher","Richard","Cynthia"],"index":14478,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996688366,"difficulty":0.0003311634}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Lisa can now know that Cynthia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cynthia","Lisa"],"index":29103,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984089732,"difficulty":0.0015910268}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Terry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Myrtle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","Peter","Linda","Myrtle"],"index":43926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982734919,"difficulty":0.0017265081}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"William can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","William","Martha"],"index":60435,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996298552,"difficulty":0.0003701448}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Eugene can now know that Shawn can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Eugene","Shawn","Charlene"],"index":63307,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996109605,"difficulty":0.0003890395}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether Gloria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Thomas can now know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gloria","Terry","Thomas","Fredrick"],"index":51653,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998329103,"difficulty":0.001670897}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Connie can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Connie","Frances"],"index":419,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984099865,"difficulty":0.0015900135}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether or not everyone's forehead is muddy. It is publicly announced that Mike knows whether Larry's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Mike can now know whether Larry can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Larry","Mike"],"index":19030,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996900558,"difficulty":0.0003099442}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reynaldo knows whether or not everyone's forehead is muddy. It is publicly announced that Angela's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Joseph can now know that Byron's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Byron","Angela","Reynaldo"],"index":1048,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.962492466,"difficulty":0.037507534}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Joseph can now know that Allison's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Antonina","Allison","Joseph"],"index":26118,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963032007,"difficulty":0.0036967993}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Ashley can now know that Cherie can know that Cherie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Shannon","Ashley","Cherie"],"index":45278,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983438253,"difficulty":0.0016561747}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Corliss can now know that Richard can know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","Richard","Corliss"],"index":22191,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963693619,"difficulty":0.0036306381}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Francis knows whether Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Francis can now know that Francis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Francis","Debra"],"index":17384,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959394932,"difficulty":0.0040605068}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Shawn can now know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josette","Vicki","Shawn","Margaret"],"index":11477,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8203622103,"difficulty":0.1796377897}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Dean can now know that Mary can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Dean","Marla","Maribel"],"index":35858,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984428287,"difficulty":0.0015571713}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecil knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Cecil can now know that Jose can know whether Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ken","Jose","Cecil","Raymond"],"index":819,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999717772,"difficulty":0.000282228}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Ronnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Thomas can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harold","Thomas","Ronnie"],"index":12513,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995111227,"difficulty":0.0004888773}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Fletcher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katherine","William","Fletcher"],"index":52817,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984925985,"difficulty":0.0015074015}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Mae can now know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Jimmy","John","Mae"],"index":66557,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984498024,"difficulty":0.0015501976}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Alvin can now know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jonathan","Paul","Shalonda","Alvin"],"index":33539,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9771853089,"difficulty":0.0228146911}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Mary can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alvin","Mary","Harley","Jennifer"],"index":47782,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982985854,"difficulty":0.0017014146}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Kimberly can now know whether Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bruce","Kimberly","Mark","Clare"],"index":65480,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994797111,"difficulty":0.0005202889}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether Joe's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joe can now know that Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marilyn","Joe"],"index":56346,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984052777,"difficulty":0.0015947223}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eddie knows whether Eddie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Eddie can now know whether Patricia can know that Eddie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Eddie"],"index":10417,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993969202,"difficulty":0.0006030798}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Margot can now know that Elizabeth can know that Margot's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","Margot","Joel","Elizabeth"],"index":22680,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952706695,"difficulty":0.0047293305}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fay knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Fay can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Fay","Dawn"],"index":41628,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Jamie can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverly","Richard","Cleo","Jamie"],"index":63135,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996007085,"difficulty":0.0003992915}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Nancy can now know that Elizabeth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","James","Nancy"],"index":56660,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983237386,"difficulty":0.0016762614}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know whether Seymour can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Seymour","Ruth","Sandra"],"index":40667,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Scott can now know that Richard can know that Zachary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Zachary","Denise","Scott"],"index":543,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.967792213,"difficulty":0.032207787}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michele's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Robert can now know that Michele can know that Marlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frank","Marlene","Michele","Robert"],"index":27370,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.994771421,"difficulty":0.005228579}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eileen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Eileen can now know whether Juliet can know that Oswaldo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Eileen","Oswaldo","Juliet"],"index":5303,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996680021,"difficulty":0.0003319979}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Mary can now know that James can know whether Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","James","Nina","Mary"],"index":35965,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997310042,"difficulty":0.0002689958}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jean can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jean","James"],"index":32633,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997496009,"difficulty":0.0002503991}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jarrod's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Christine can now know whether Jarrod can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrin","Jarrod","Christine","James"],"index":67433,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether Janet's forehead is muddy. It is publicly announced that Janet knows whether Ernestine's forehead is muddy. It is publicly announced that Brian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Ernestine can now know that Janet can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ernestine","Janet","Brian"],"index":35932,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983731508,"difficulty":0.0016268492}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Livia can now know that Carl can know that Jordan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Livia","Jordan","Carl","Sabrina"],"index":7985,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996420145,"difficulty":0.003579855}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edward","John"],"index":26156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983147383,"difficulty":0.0016852617}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Denise can now know that Jeffery can know whether Denise's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Jeffrey","Jeffery","Denise"],"index":42451,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997169375,"difficulty":0.0002830625}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether Rebecca's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"William can now know whether Sylvester can know that Sylvester's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Jonathan","William","Sylvester"],"index":48686,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996266365,"difficulty":0.0003733635}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Barbara can now know whether Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patrick","Barbara","Karen","Brendan"],"index":36967,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997346997,"difficulty":0.0002653003}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Edward can now know whether Ignacio can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Ignacio","Edward"],"index":23059,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996660948,"difficulty":0.0003339052}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] 0","hypothesis":"Robert can now know whether Rosalie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Rosalie"],"index":13967,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999787271,"difficulty":0.000212729}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felicia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Felicia can now know that James can know that Whitney's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Felicia","James","Whitney"],"index":30863,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9476923943,"difficulty":0.0523076057}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy. It is publicly announced that Mary knows whether Beatrice's forehead is muddy. It is publicly announced that Joseph knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mary can now know that Richard can know whether Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Joseph","Mary","Beatrice"],"index":64962,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996985197,"difficulty":0.0003014803}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Phyllis can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sandra","Leonard","Phyllis"],"index":42604,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997606874,"difficulty":0.0002393126}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"William can now know whether Lola can know that Gerald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gerald","Lola","William"],"index":63515,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996773005,"difficulty":0.0003226995}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"David can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tyler","Terry","David"],"index":20345,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979959726,"difficulty":0.0020040274}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marie can now know that Bonnie can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Mary","Bonnie","Tamara"],"index":38626,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996180534,"difficulty":0.0003819466}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Travis can now know that Tyrone can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tyrone","Inez","Darlene","Travis"],"index":12654,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997703433,"difficulty":0.0002296567}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know whether Frank can know that Anne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Clarissa","Anne","Christopher"],"index":39666,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996724129,"difficulty":0.0003275871}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Angela knows whether Leslie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Joseph can now know that Angela can know that Angela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Joseph","Leslie"],"index":27954,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9740415812,"difficulty":0.0259584188}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sherry can now know whether Angelica can know that Angelica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carlos","Sherry","Alesia","Angelica"],"index":2739,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999671936,"difficulty":0.000328064}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether Kecia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kecia can now know that Michael can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Anthony","Kecia"],"index":2057,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996054769,"difficulty":0.0003945231}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karla knows whether or not nobody's forehead is muddy. It is publicly announced that Angelo knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Angelo can now know that Karla can know that Karla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Angelo","Karla"],"index":34209,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7923565507,"difficulty":0.2076434493}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barry can now know that Meredith can know that Brendon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brendon","Meredith","Barry"],"index":4039,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986112118,"difficulty":0.0013887882}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Howard can now know whether Sue can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Howard","Kim","Elizabeth","Sue"],"index":26387,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996114373,"difficulty":0.0003885627}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Marie can now know that Frederick can know that Frederick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frederick","Dan","Marie"],"index":24047,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9592051506,"difficulty":0.0407948494}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kristie can now know whether Denver can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Harold","Denver","Kristie"],"index":36311,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997091889,"difficulty":0.0002908111}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremiah knows whether or not nobody's forehead is muddy. It is publicly announced that Fred knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Fred can now know that Jeremiah can know whether Jeremiah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Fred","Jeremiah"],"index":53616,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995293617,"difficulty":0.0004706383}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pablo's forehead is not muddy. It is publicly announced that Patsy knows whether Marsha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Marsha can now know that Patsy can know that Pablo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marsha","Patsy","Pablo"],"index":7226,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948248863,"difficulty":0.0051751137}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Damon knows whether Jeanette's forehead is muddy. It is publicly announced that Jeanette's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Jeanette can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Damon","Jeanette"],"index":42169,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974609613,"difficulty":0.0025390387}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Richard can now know that Willie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Richard","Margaret","Willie"],"index":57069,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979249239,"difficulty":0.0020750761}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valeria knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Valeria can now know that Stephen can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Valeria","Stephen","Robert"],"index":16417,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983160496,"difficulty":0.0016839504}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Emil knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michel can now know whether Elizabeth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emil","Karol","Elizabeth","Michel"],"index":49145,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997127652,"difficulty":0.0002872348}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not nobody's forehead is muddy. It is publicly announced that Tracy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Joseph can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Felicia","Tracy","Joseph"],"index":10263,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984169006,"difficulty":0.0015830994}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tommie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Melissa can now know that Barbara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Melissa","Betty","Tommie"],"index":29252,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982681274,"difficulty":0.0017318726}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie knows whether Elizabeth's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Elizabeth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jamie","Elizabeth"],"index":34987,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984809756,"difficulty":0.0015190244}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ebony's forehead is not muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ebony can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Ebony","Silvia"],"index":28055,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984600544,"difficulty":0.0015399456}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oscar knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Chauncey can now know that Oscar can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Oscar","Chauncey","Marta"],"index":21664,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Patricia can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Joseph","Eugene"],"index":47663,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9692980647,"difficulty":0.0307019353}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Christina can now know that Regina can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Regina","Thomas","Christina"],"index":10555,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984971285,"difficulty":0.0015028715}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bessie knows whether someone's forehead is muddy. It is publicly announced that Bessie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Bessie can now know whether Melissa can know whether Melissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bessie","Melissa"],"index":11114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996628761,"difficulty":0.0003371239}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether Emmett's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Donna can now know whether Emmett can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sonia","Emmett","Donna","Brian"],"index":25111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997659326,"difficulty":0.0002340674}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know whether Linda can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Thelma","Antonio","William"],"index":19757,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996846914,"difficulty":0.0003153086}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine knows whether someone's forehead is muddy. It is publicly announced that Patrick knows whether Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Charles can now know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patrick","Charles","Katherine","Adam"],"index":15745,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9984560013,"difficulty":0.0015439987}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Alesha can now know that Alesha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Joel","Alesha"],"index":52166,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980600476,"difficulty":0.0019399524}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene knows whether Irene's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Dean can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Helen","Dean","Irene"],"index":4813,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997342229,"difficulty":0.0002657771}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"David can now know that Robert can know that Laverna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Laverna","Robert","Wilford"],"index":7108,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985479712,"difficulty":0.0014520288}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Max can now know whether Alice can know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Peter","Velma","Max"],"index":53783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999673605,"difficulty":0.000326395}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roberta's forehead is not muddy. It is publicly announced that Alexander knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Roberta can now know that Roberta's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alexander","Roberta","Robert"],"index":27319,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9750928879,"difficulty":0.0249071121}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence knows whether Ellis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ellis can now know that Susan can know that Ellis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ellis","Clarence","Susan"],"index":63026,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99725914,"difficulty":0.00274086}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julius knows whether or not nobody's forehead is muddy. It is publicly announced that Benito's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Julius can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tom","Benito","Julius"],"index":21761,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996153116,"difficulty":0.0003846884}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lauran can now know that Cleo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","Cleo","Frank","Lauran"],"index":43743,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984698892,"difficulty":0.0015301108}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jennifer can now know that Linda can know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Catherine","Jennifer"],"index":58876,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995440841,"difficulty":0.0004559159}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Frances can now know that Karen can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Frances","Shawn","Chad"],"index":41712,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Renea can now know that Ruth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Renea","Ruth","Thomas"],"index":41286,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985539317,"difficulty":0.0014460683}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether or not everyone's forehead is muddy. It is publicly announced that Shelia's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Joshua can now know whether Shelia can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joshua","Shelia"],"index":53299,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997834563,"difficulty":0.0002165437}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy. It is publicly announced that Ethel knows whether someone's forehead is muddy. It is publicly announced that Johnny knows whether Ethel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Daniel can now know that Ethel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Gary","Daniel","Ethel"],"index":22384,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973444343,"difficulty":0.0026555657}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marlene knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Kimberly can now know that Marlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marlene","Kimberly"],"index":1418,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979423881,"difficulty":0.0020576119}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Angla can now know that Angla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angla","Terry","Richard","Marie"],"index":36781,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9868663549,"difficulty":0.0131336451}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steve knows whether Cora's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Cora can now know that Steve can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cora","Marilyn","Steve"],"index":51850,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991802573,"difficulty":0.0008197427}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexandra knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Alexandra can now know that Phyllis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robbie","Alexandra","Phyllis","Dan"],"index":20191,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981307387,"difficulty":0.0018692613}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlie knows whether or not nobody's forehead is muddy. It is publicly announced that Susan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Susan can now know that Floyd's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charlie","Floyd","Susan"],"index":34245,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978992939,"difficulty":0.0021007061}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jaquelyn can now know whether Frances can know whether Jaquelyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jaquelyn","Frances","Theodore"],"index":53238,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993940592,"difficulty":0.0006059408}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Dedra knows whether Dedra's forehead is muddy. It is publicly announced that Fletcher knows whether Fletcher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Christopher can now know that Dedra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dedra","Fletcher","Fernando","Christopher"],"index":5343,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9981237054,"difficulty":0.0018762946}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Heath can now know whether Heath's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leonard","Troy","Ashton","Heath"],"index":62683,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993013144,"difficulty":0.0006986856}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Bernice can now know that James can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bernice","James"],"index":44373,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853231907,"difficulty":0.0146768093}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is not muddy. It is publicly announced that Gene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Gene can now know that Chad can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gene","John","Chad"],"index":10711,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990006089,"difficulty":0.0009993911}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce knows whether or not nobody's forehead is muddy. It is publicly announced that Jesse's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Jesse can now know that Jesse's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jesse","Joyce"],"index":37693,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9838693738,"difficulty":0.0161306262}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Marguerite can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gabriela","George","Marguerite"],"index":11121,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993599057,"difficulty":0.0006400943}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dolores knows whether Aaron's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Cristopher can now know that Aaron can know that Dolores's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cristopher","Dolores","Dana","Aaron"],"index":37484,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983193278,"difficulty":0.0016806722}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tonia knows whether Anna's forehead is muddy. It is publicly announced that Tonia's forehead is not muddy. It is publicly announced that George knows whether Tonia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Tonia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tonia","Anna","George"],"index":51629,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989939332,"difficulty":0.0010060668}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Celia can now know whether Richard can know whether Kathy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eula","Kathy","Celia","Richard"],"index":63322,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994537234,"difficulty":0.0005462766}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Liza knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Danielle can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kristie","Liza","Danielle"],"index":40781,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9981284738,"difficulty":0.0018715262}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jay knows whether Jay's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jay can now know that Karie can know that Karie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carlos","Karie","Jay"],"index":11281,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971477389,"difficulty":0.0028522611}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether Ardath's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Gregory can now know that Sylvia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sylvia","Gregory","Shawn","Ardath"],"index":6208,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983108044,"difficulty":0.0016891956}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie knows whether or not everyone's forehead is muddy. It is publicly announced that George's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Carrie can now know that George can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carrie","George"],"index":20239,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990142584,"difficulty":0.0009857416}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Robert can now know whether Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Timothy","Bertha"],"index":56044,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994105101,"difficulty":0.0005894899}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Debra can now know that Clementine can know that Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vivian","Frances","Clementine","Debra"],"index":26845,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974870682,"difficulty":0.0025129318}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether Sheila's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Travis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sheila","Annette","Travis","Robert"],"index":10915,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987334609,"difficulty":0.0012665391}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jay knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Terry can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","Jay","Terry","Kimberly"],"index":61016,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999369204,"difficulty":0.000630796}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Adele's forehead is muddy. It is publicly announced that Adele knows whether Amanda's forehead is muddy. It is publicly announced that Patricia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Amanda can now know whether Adele can know that Adele's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Adele","Patricia"],"index":4115,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993206263,"difficulty":0.0006793737}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly knows whether Eugene's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kelly can now know whether Paul can know that Eugene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","Paul","Kelly"],"index":7145,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994723201,"difficulty":0.0005276799}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rebecca can now know that Edna can know that Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebecca","Edna","Russell"],"index":63587,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986043572,"difficulty":0.0013956428}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lula can now know that Elizabeth can know that Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lula","Donna","Sharon","Elizabeth"],"index":795,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9894031286,"difficulty":0.0105968714}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] 0","hypothesis":"Taylor can now know that Linda can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Taylor","Linda"],"index":5621,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9910199046,"difficulty":0.0089800954}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Samantha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Samantha can now know whether Ethel can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ethel","John","Samantha","Isaac"],"index":39494,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999248445,"difficulty":0.000751555}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Caroline can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Summer","Crystal","Caroline"],"index":37972,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994009733,"difficulty":0.0005990267}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether or not everyone's forehead is muddy. It is publicly announced that Andre's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Donna can now know that Andre can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donna","Andre"],"index":66139,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994118214,"difficulty":0.0005881786}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oliver knows whether Verna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Oliver can now know that Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Verna","Oliver","Michelle","Sarah"],"index":31385,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982257485,"difficulty":0.0017742515}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhonda knows whether Michael's forehead is muddy. It is publicly announced that Michael knows whether Jose's forehead is muddy. It is publicly announced that Rhonda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agenta knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Jose can now know that Rhonda can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Michael","Rhonda"],"index":56783,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9893499017,"difficulty":0.0106500983}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luke's forehead is muddy. It is publicly announced that Carl knows whether someone's forehead is muddy. It is publicly announced that Carl knows whether Sheila's forehead is muddy. It is publicly announced that Carl knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Carl can now know that Sheila can know whether Sheila's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Luke","Sheila","Carl"],"index":307,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994581342,"difficulty":0.0005418658}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Henry can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Adina","Carolyn","James"],"index":32139,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988754392,"difficulty":0.0011245608}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know whether Darren can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darren","James","Lori","Michael"],"index":2117,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994080067,"difficulty":0.0005919933}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy. It is publicly announced that William's forehead is not muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Dee can now know whether William can know that Vivian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","William","Dee","Vivian"],"index":6176,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994499087,"difficulty":0.0005500913}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Irene's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Irene can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debbie","Irene","Mary"],"index":28780,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999042213,"difficulty":0.000957787}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether Dennis's forehead is muddy. It is publicly announced that Barbara knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Elfriede can now know that Barbara can know that Lillian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Dennis","Elfriede","Lillian"],"index":2682,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982784986,"difficulty":0.0017215014}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kelvin can now know that Kelvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Mary","Kelvin","Charles"],"index":52647,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984019399,"difficulty":0.0015980601}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kevin can now know that Tyler can know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tyler","Kevin","Marjorie"],"index":48453,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.994568944,"difficulty":0.005431056}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy. It is publicly announced that Donna's forehead is muddy. It is publicly announced that Frederick's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Annette can now know that Annette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Annette","Imogene","Frederick","Donna"],"index":57994,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967570901,"difficulty":0.0032429099}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"John can now know that Karen can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Tammy","John"],"index":14423,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993262291,"difficulty":0.0006737709}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Edward can now know that Joel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joel","Edward"],"index":9726,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989680052,"difficulty":0.0010319948}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Selma can now know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Scott","Kristin","Selma","Michael"],"index":65548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973249435,"difficulty":0.0026750565}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Aubrey's forehead is not muddy. It is publicly announced that Pasquale's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agentb knows that (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Aubrey can now know that Pasquale can know that Aubrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pasquale","Aubrey"],"index":67605,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9671320915,"difficulty":0.0328679085}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Henry can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Henry","William"],"index":64744,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992838502,"difficulty":0.0007161498}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Cynthia","Michael"],"index":56932,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992451668,"difficulty":0.0007548332}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roberta knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Roberta can now know that Harold can know that Roberta's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harold","Roberta","Edward"],"index":40787,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979100823,"difficulty":0.0020899177}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wesley knows whether Shirley's forehead is muddy. It is publicly announced that Wesley knows whether Wesley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] Agentc knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Ronald can now know that Wesley can know that Shirley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirley","Irene","Ronald","Wesley"],"index":49028,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967809916,"difficulty":0.0032190084}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agenta knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Norma can now know that Richard can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norma","Juan","Larry","Richard"],"index":7579,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993779659,"difficulty":0.0006220341}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilyn knows whether or not nobody's forehead is muddy. It is publicly announced that Alan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Alan can now know that Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elias","Alan","Marilyn"],"index":64858,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972848892,"difficulty":0.0027151108}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Harriet can now know that Caroline can know that Alvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Caroline","Alvin","Harriet"],"index":335,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974433184,"difficulty":0.0025566816}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Marsha can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Michael","Marsha","Lawrence"],"index":55952,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989815354,"difficulty":0.0010184646}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Jane can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Kenneth","Jane","Linda"],"index":5610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979397655,"difficulty":0.0020602345}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilma can now know whether Michael can know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Linda","Wilma","Michael"],"index":19274,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993834496,"difficulty":0.0006165504}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vincent knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Vincent can now know that Sarah can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Vincent","David","Sarah"],"index":55387,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989441037,"difficulty":0.0010558963}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Daniel can now know that Duane can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lawrence","Daniel","Duane","Andre"],"index":47553,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989468455,"difficulty":0.0010531545}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Virgil can now know whether Patricia can know that Edith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edith","Virgil","Patricia"],"index":45291,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994319081,"difficulty":0.0005680919}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jacqueline can now know that Larry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jacqueline","Larry","Regina"],"index":32674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980074763,"difficulty":0.0019925237}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gene knows whether Natasha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Gene can now know that Natasha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Gene","Natasha"],"index":53647,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9921975732,"difficulty":0.0078024268}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Zoila can now know that Jeffery can know whether Zoila's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Zoila","Jeffery"],"index":151,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993898869,"difficulty":0.0006101131}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Rochelle can now know that Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rochelle","James","Mary","Sarah"],"index":51377,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976862669,"difficulty":0.0023137331}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Timothy can now know that Ann can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Ismael","Timothy","Ann"],"index":18888,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991639853,"difficulty":0.0008360147}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Evangelina can now know whether Karen can know whether Evangelina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Micheal","Karen","Dale","Evangelina"],"index":19799,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993908405,"difficulty":0.0006091595}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackie knows whether or not everyone's forehead is muddy. It is publicly announced that Kevin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know that Jackie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Jackie","Paul","Kevin"],"index":52731,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988615513,"difficulty":0.0011384487}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Pauline can now know that Keith can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pauline","Clare","John","Keith"],"index":51348,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989336133,"difficulty":0.0010663867}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor knows whether or not everyone's forehead is muddy. It is publicly announced that Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Eleanor can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eleanor","Jessica"],"index":58861,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989238381,"difficulty":0.0010761619}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ricardo can now know that David can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Laura","Ricardo"],"index":26111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991349578,"difficulty":0.0008650422}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Trinh knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Trinh can now know whether Edward can know that Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Trinh","Edward"],"index":23509,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993320107,"difficulty":0.0006679893}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruby knows whether Ruby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dominick can now know that John can know that Dominick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruby","John","Dominick","Ruth"],"index":17339,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982113838,"difficulty":0.0017886162}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Melvin can now know whether Karen can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marc","Gregory","Karen","Melvin"],"index":6172,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994294047,"difficulty":0.0005705953}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Viola's forehead is muddy. It is publicly announced that Viola knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Teresa can now know that Donna can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Viola","Scott","Teresa","Donna"],"index":47768,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987437129,"difficulty":0.0012562871}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"John can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vivian","Sandy","John","Sylvia"],"index":58471,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994137287,"difficulty":0.0005862713}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Melva can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","Melva","Ruby"],"index":16918,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99899894,"difficulty":0.00100106}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Desiree knows whether Desiree's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Desiree can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Desiree","John"],"index":16786,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993859529,"difficulty":0.0006140471}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis knows whether or not everyone's forehead is muddy. It is publicly announced that Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Frances can now know that Felix's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frances","Gregory","Louis","Felix"],"index":47381,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947038293,"difficulty":0.0052961707}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frankie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Clifford can now know whether Frankie can know that Frankie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frankie","Clifford"],"index":9795,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993104935,"difficulty":0.0006895065}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Jason can now know whether James can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","James","David"],"index":21943,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994371533,"difficulty":0.0005628467}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kim's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Marisa can now know that Kim can know whether Marisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","David","Marisa"],"index":22707,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994533658,"difficulty":0.0005466342}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kari's forehead is muddy. It is publicly announced that Cindy knows whether Kari's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Douglas can now know that Cindy can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","John","Kari","Cindy"],"index":6161,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994371533,"difficulty":0.0005628467}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jennifer can now know that Paris can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Paris","Gregory"],"index":33380,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989401698,"difficulty":0.0010598302}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mark can now know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Victor","John"],"index":58819,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983922839,"difficulty":0.0016077161}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that Charles can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Perry","Michael","Charles"],"index":51748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984947443,"difficulty":0.0015052557}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vanessa knows whether Luther's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Vanessa can now know that Luther can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Luther","Vanessa"],"index":8655,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989655018,"difficulty":0.0010344982}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loretta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Marguerite can now know that Dennis can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dennis","Marguerite","Loretta"],"index":3779,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994502664,"difficulty":0.0005497336}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly knows whether David's forehead is muddy. It is publicly announced that Bonnie's forehead is not muddy. It is publicly announced that Bonnie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Beverly can now know whether Bonnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Beverly","Bonnie","David"],"index":52709,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994698167,"difficulty":0.0005301833}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not nobody's forehead is muddy. It is publicly announced that Beulah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agenta knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Ronald can now know that Linda can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Beulah","Linda","Michael"],"index":41082,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994254112,"difficulty":0.0005745888}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Ana can now know that Barbara can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ana","Valene","Barbara","Elisa"],"index":46262,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993008375,"difficulty":0.0006991625}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darlene knows whether Julia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Julia can now know that Denis can know that Tracey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Denis","Darlene","Julia","Tracey"],"index":25934,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978073239,"difficulty":0.0021926761}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Chad can now know that John can know whether Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","John","Chad"],"index":15295,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992513061,"difficulty":0.0007486939}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Louise can now know that Alicia can know whether Alicia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alicia","Louise","Brittany"],"index":50114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993465543,"difficulty":0.0006534457}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Barbara can now know that Kenneth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Kenneth","Adrienne"],"index":16408,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989809394,"difficulty":0.0010190606}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dixie knows whether Dixie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dixie can now know that Dixie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christine","Dixie"],"index":46122,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9950090647,"difficulty":0.0049909353}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Chris knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yasmin","Michael","Chris"],"index":42912,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9663139582,"difficulty":0.0336860418}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Willie can now know that Willie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willie","Douglas","Jason","Myra"],"index":20167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974924326,"difficulty":0.0025075674}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Emily"],"index":19596,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.966702342,"difficulty":0.033297658}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Daniel can now know whether Phyllis can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phyllis","Daniel","Jamel"],"index":60064,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993385673,"difficulty":0.0006614327}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Gayle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Helen can now know whether James can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","James","Trevor","Gayle"],"index":47103,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992425442,"difficulty":0.0007574558}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Ronald can now know whether Hector can know whether Hector's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Ronald","Hector","Keith"],"index":55250,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994069338,"difficulty":0.0005930662}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delphia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Amy can now know that Stacey can know that Stacey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Delphia","Amy","Stacey"],"index":11235,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978590608,"difficulty":0.0021409392}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Florence can now know that Chris can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","Thomas","Chris"],"index":13295,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989646673,"difficulty":0.0010353327}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Caroline knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Caroline can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Stephanie","Caroline"],"index":24811,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988872409,"difficulty":0.0011127591}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly knows whether Jesse's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Beverly can now know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Angel","Robert","Beverly","Jesse"],"index":23350,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994714856,"difficulty":0.0005285144}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy. It is publicly announced that Mary knows whether Ruben's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mary can now know that Thomas can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruben","Mary","Thomas"],"index":7676,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965502024,"difficulty":0.0034497976}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Felix's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Kevin","James","Felix"],"index":23675,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9981637597,"difficulty":0.0018362403}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether Edward's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Edward can now know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edward","Peter"],"index":3132,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928576946,"difficulty":0.0071423054}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Alicia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Keith can now know whether Rebecca can know whether Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Monica","Rebecca","Alicia"],"index":29954,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992980957,"difficulty":0.0007019043}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Rebecca can now know that James can know that Arden's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","Arden","Rebecca","James"],"index":60494,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980493784,"difficulty":0.0019506216}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy knows whether someone's forehead is muddy. It is publicly announced that Blythe knows whether Blythe's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Wendy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Blythe can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Blythe","Wendy"],"index":3463,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951811433,"difficulty":0.0048188567}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Walter can now know that Mary can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Walter","Mary"],"index":49562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989696741,"difficulty":0.0010303259}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brittney knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rita can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chad","Brittney","Rita","Curtis"],"index":54693,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988952279,"difficulty":0.0011047721}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lottie's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Lottie can now know that Joann can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lottie","Joann"],"index":1803,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987524748,"difficulty":0.0012475252}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adam knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know whether Adam can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adam","William","Betty"],"index":51323,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992085099,"difficulty":0.0007914901}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether Andrew's forehead is muddy. It is publicly announced that Eric knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Andrew can now know that Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Andrew","Eric","Odell"],"index":4677,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9955073595,"difficulty":0.0044926405}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phyllis knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Ida knows whether Ida's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Daryl can now know whether Fran's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ida","Daryl","Phyllis","Fran"],"index":40310,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994516969,"difficulty":0.0005483031}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phillip's forehead is not muddy. It is publicly announced that Patricia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Patricia can now know that Bernard can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patrick","Phillip","Bernard","Patricia"],"index":621,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989878535,"difficulty":0.0010121465}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether Heidi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Joan can now know that Frank can know that Heidi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joan","Heidi","Ella","Frank"],"index":28983,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980407357,"difficulty":0.0019592643}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Philip can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tiffany","Philip","William"],"index":47570,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978880286,"difficulty":0.0021119714}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurie knows whether Laurie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Laurie can now know that Earl can know whether Earl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Laurie","Earl"],"index":37268,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992899895,"difficulty":0.0007100105}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Katy can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katy","June","Joseph","Corey"],"index":63602,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994754195,"difficulty":0.0005245805}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dawn knows whether Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Dawn can now know that Ruth can know that Karyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karyn","Dawn","Ruth","Erin"],"index":61428,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983021021,"difficulty":0.0016978979}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Peggy can now know that Beth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beth","Patricia","Cathleen","Peggy"],"index":60013,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.6020208001,"difficulty":0.3979791999}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Alicia's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Dennis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dennis","James","Alicia","Robert"],"index":62388,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988107681,"difficulty":0.0011892319}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ada knows whether Ada's forehead is muddy. It is publicly announced that Katrina knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Neva can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Ada","Katrina","Neva"],"index":26536,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998798728,"difficulty":0.001201272}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arturo knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Arturo can now know whether Arturo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bonnie","Arturo","Patricia"],"index":20783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993979931,"difficulty":0.0006020069}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lena knows whether Lena's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mara can now know that Lena can know that Lena's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lena","Mara"],"index":46770,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9941382408,"difficulty":0.0058617592}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Hee can now know that Linda can know whether Hee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hee","Linda","Ronald"],"index":18868,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994117022,"difficulty":0.0005882978}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Heriberto can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Andrew","Heriberto"],"index":57698,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992444515,"difficulty":0.0007555485}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether William's forehead is muddy. It is publicly announced that Terry's forehead is not muddy. It is publicly announced that Terry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jose can now know that Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jose","Terry","William"],"index":51593,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.924038589,"difficulty":0.075961411}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jeffrey can now know that Gene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gene","Jeffrey","Randolph","Christine"],"index":13458,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977873564,"difficulty":0.0022126436}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Mark can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Mark","William","Jaime"],"index":2614,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961159229,"difficulty":0.0038840771}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Edward"],"index":32370,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999435246,"difficulty":0.000564754}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mike knows whether Mike's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Andres can now know that Daniel can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mike","Andres","Daniel","Edward"],"index":4497,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981957078,"difficulty":0.0018042922}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janice can now know that Terrell can know that Julia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julia","Terrell","Janice","Julie"],"index":8711,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978685379,"difficulty":0.0021314621}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mindy knows whether Mindy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"April can now know that Deanna can know that Deanna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mindy","Deanna","April"],"index":39099,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981143475,"difficulty":0.0018856525}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Rosa can now know whether Kate can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rosa","Kate"],"index":31655,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993245602,"difficulty":0.0006754398}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vera knows whether Ellen's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Ellen can now know that Vera can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ellen","Vera"],"index":64928,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993933439,"difficulty":0.0006066561}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Patricia can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Matthew","Betty","Robert"],"index":14269,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989061356,"difficulty":0.0010938644}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Derrick knows whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Derrick can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Shirley","Derrick","Nicole"],"index":29809,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993705153,"difficulty":0.0006294847}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Barbara can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Donna","Barbara"],"index":39562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987518787,"difficulty":0.0012481213}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elmo knows whether Verna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Elmo can now know whether Judith can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elmo","Judith","William","Verna"],"index":42199,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993749261,"difficulty":0.0006250739}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delores's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn knows whether Francisco's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Shawn can now know that Delores can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Francisco","Delores","Shawn"],"index":63117,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988158941,"difficulty":0.0011841059}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether or not everyone's forehead is muddy. It is publicly announced that Susan knows whether someone's forehead is muddy. It is publicly announced that Susan knows whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Susan can now know that Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Susan","Jeffrey"],"index":38275,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977282882,"difficulty":0.0022717118}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis knows whether Amanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Francis can now know whether Francis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amanda","Bobby","Francis"],"index":56928,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993969202,"difficulty":0.0006030798}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Winston's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Cathy can now know that Carol can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carol","Winston","Cathy"],"index":35488,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988578558,"difficulty":0.0011421442}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Paul can now know that Fannie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ida","Paul","Fannie"],"index":62011,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999402523,"difficulty":0.000597477}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Rosa can now know that Peter can know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Peter","Rosa"],"index":61910,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980260134,"difficulty":0.0019739866}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Maud knows whether Maud's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Pam can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maud","Sandra","Ronald","Pam"],"index":53717,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9936774373,"difficulty":0.0063225627}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Stanley can now know that Linda can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harry","Stanley","Linda"],"index":62430,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9935334921,"difficulty":0.0064665079}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Otis can now know that Jim can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Otis","Francis","Jim"],"index":9176,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99941957,"difficulty":0.00058043}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramon knows whether Ramon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Dominique can now know that Charles can know that Dominique's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dominique","Charles","Ramon"],"index":37747,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982885718,"difficulty":0.0017114282}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Harry can now know that Rebecca can know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harry","Patricia","Rebecca"],"index":57319,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993801117,"difficulty":0.0006198883}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Geneva can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Geneva","Justin","James","Tracey"],"index":49985,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988464117,"difficulty":0.0011535883}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence knows whether or not everyone's forehead is muddy. It is publicly announced that Florence knows whether Mark's forehead is muddy. It is publicly announced that Florence knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Mark can now know that Florence can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Florence","Mark"],"index":20592,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963418841,"difficulty":0.0036581159}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Heidi knows whether Rita's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Heidi can now know whether Rita can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Heidi","Rita"],"index":26452,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994364381,"difficulty":0.0005635619}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia knows whether Tyrone's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Tyrone can now know whether Julia can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Julia","Tyrone","Michel"],"index":17279,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994037151,"difficulty":0.0005962849}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guadalupe knows whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Wendy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Guadalupe","Wendy","Daniel","Stanley"],"index":17762,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987131357,"difficulty":0.0012868643}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Joseph","Matthew","Mary"],"index":4050,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998716712,"difficulty":0.001283288}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Daniel can now know that Lisa can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Daniel","Jose","Mary"],"index":27522,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.989151001,"difficulty":0.010848999}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether Kimberely's forehead is muddy. It is publicly announced that Kimberely's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentb knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Jessica can now know whether Kenneth can know that Kimberely's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Jessica","Kimberely"],"index":24812,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994864464,"difficulty":0.0005135536}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Anthony can now know that Bryan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Evelyn","Anthony","Bryan","Jose"],"index":16979,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989699125,"difficulty":0.0010300875}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Susan can now know that George can know that Susan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Fannie","Heather","Susan"],"index":35951,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.8731274009,"difficulty":1.8731274009}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy. It is publicly announced that Simone knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Charles can now know that Simone can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Simone","Charles"],"index":59904,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989889264,"difficulty":0.0010110736}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Margo knows whether Margo's forehead is muddy. It is publicly announced that Edith knows whether Edith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Margo","Edith","Richard","James"],"index":12647,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975086451,"difficulty":0.0024913549}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Evan can now know that Robert can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Evan","Frederick","Robert"],"index":34605,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992497563,"difficulty":0.0007502437}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy knows whether Ayesha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Martin can now know whether Martin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martin","Linda","Randy","Ayesha"],"index":61331,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993904829,"difficulty":0.0006095171}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Galen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Christine can now know that Galen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Douglas","Galen","Christine"],"index":36887,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986330867,"difficulty":0.0013669133}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ginny's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Clyde can now know whether Ginny can know that Clyde's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laverne","Ginny","Anthony","Clyde"],"index":42578,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993636012,"difficulty":0.0006363988}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jana knows whether or not nobody's forehead is muddy. It is publicly announced that Helen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Helen can now know that Jana can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Helen","Jana","Phillip"],"index":38592,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989479184,"difficulty":0.0010520816}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dorthy can now know that Joshua can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","Joshua","Dorthy","Edward"],"index":10259,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989375472,"difficulty":0.0010624528}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor knows whether Samuel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Samuel can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eleanor","Samuel"],"index":32488,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998660326,"difficulty":0.001339674}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Roberta can now know whether Marvin can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marvin","Janice","Roberta"],"index":20404,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993740916,"difficulty":0.0006259084}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Misty knows whether Santos's forehead is muddy. It is publicly announced that Santos's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Misty can now know whether Santos's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Misty","Santos"],"index":39276,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994693398,"difficulty":0.0005306602}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Darlene can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Berta","Darlene"],"index":55610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988636971,"difficulty":0.0011363029}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Francisco can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["George","Francisco"],"index":66323,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99887079,"difficulty":0.00112921}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alison can now know that Quinn can know that Quinn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelvin","Quinn","Alison"],"index":13705,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984192848,"difficulty":0.0015807152}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether or not nobody's forehead is muddy. It is publicly announced that Kenneth knows whether Kenneth's forehead is muddy. It is publicly announced that Brenda's forehead is muddy. It is publicly announced that Verna knows whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kenneth can now know whether Brenda can know whether Verna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Kenneth","Verna","Hazel"],"index":51333,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994495511,"difficulty":0.0005504489}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Paul can now know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Isabel","Brenda","Paul"],"index":743,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993948936,"difficulty":0.0006051064}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] 0","hypothesis":"Raymond can now know that Keith can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Keith"],"index":10643,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992156029,"difficulty":0.0007843971}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Rosie's forehead is muddy. It is publicly announced that Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rosie","Robert","Sandra"],"index":22217,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986276627,"difficulty":0.0013723373}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica's forehead is not muddy. It is publicly announced that Anthony knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Anthony can now know that James can know that Monica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Anthony","Monica"],"index":63391,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975376129,"difficulty":0.0024623871}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Timothy can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Juan","Robert","David"],"index":23772,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994034767,"difficulty":0.0005965233}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Danielle can now know whether David can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Danielle","Michael"],"index":25344,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994556308,"difficulty":0.0005443692}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine knows whether Dolly's forehead is muddy. It is publicly announced that Katherine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Dolly can now know that Katherine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dolly","Katherine"],"index":59599,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990241528,"difficulty":0.0009758472}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffery knows whether Christine's forehead is muddy. It is publicly announced that Christine knows whether Christine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jeffery can now know that Christine can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronny","Christine","Jeffery","Helen"],"index":6027,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993671775,"difficulty":0.0006328225}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Debra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"James can now know that William can know that Debra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Debra","James","William"],"index":64145,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979786277,"difficulty":0.0020213723}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joan can now know whether Jennifer can know whether Katherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bradley","Jennifer","Katherine","Joan"],"index":15070,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993784428,"difficulty":0.0006215572}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Debroah can now know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Debroah","Thomas","Anna"],"index":39624,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982368946,"difficulty":0.0017631054}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether Ryan's forehead is muddy. It is publicly announced that Ivonne knows whether Alberta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Ivonne can now know that Ivonne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alberta","Ryan","Edward","Ivonne"],"index":34961,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.995455265,"difficulty":0.004544735}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether Sarah's forehead is muddy. It is publicly announced that Francis knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Sarah can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sarah","Billie","Francis","David"],"index":23233,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973015785,"difficulty":0.0026984215}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerold knows whether Charles's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] Agentd knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Terry can now know that Charles can know whether Jerold's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucille","Charles","Jerold","Terry"],"index":21824,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993895292,"difficulty":0.0006104708}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Houston knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Teresa can now know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sandra","Houston","Teresa"],"index":5139,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994134903,"difficulty":0.0005865097}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Norma knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Alan can now know that Kevin can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Norma","Alan","Kevin"],"index":48561,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993515611,"difficulty":0.0006484389}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Courtney knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Courtney can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Courtney","Ricky","Joseph"],"index":52783,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987485409,"difficulty":0.0012514591}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Dorothy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dorothy","Jack"],"index":31993,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990206957,"difficulty":0.0009793043}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nora knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Nora can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Nora","David","Ophelia"],"index":12128,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988956451,"difficulty":0.0011043549}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Cristine can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Todd","Cristine","Bobby"],"index":31159,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998891294,"difficulty":0.001108706}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Marian can now know whether Deborah can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marian","Vicky","Deborah","Edgar"],"index":13396,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992284775,"difficulty":0.0007715225}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances knows whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Frances can now know whether Viviana can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Viviana","Frances"],"index":5318,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993243217,"difficulty":0.0006756783}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarice knows whether someone's forehead is muddy. It is publicly announced that Clarice knows whether Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Dennis can now know whether Clarice can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dennis","Albert","Christopher","Clarice"],"index":14360,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994053841,"difficulty":0.0005946159}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether Lester's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Anthony can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lester","Anthony","Thomas"],"index":14257,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993849993,"difficulty":0.0006150007}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ora knows whether Adrian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Adrian can now know whether Louis can know whether Adrian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Ora","Michell","Adrian"],"index":38009,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994051456,"difficulty":0.0005948544}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Norman can now know whether Ellen can know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norman","Ellen","Charles","Edward"],"index":37217,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994133711,"difficulty":0.0005866289}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mike knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Carlos can now know that Michael can know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carlos","Paul","Michael","Mike"],"index":28239,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993392825,"difficulty":0.0006607175}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether Kathy's forehead is muddy. It is publicly announced that Kristin knows whether Kristin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kristin can now know that Maria can know that Kristin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Kristin","Kathy","Vanessa"],"index":10184,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966367483,"difficulty":0.0033632517}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rufus knows whether Rufus's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Rufus can now know that Barbara can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barbara","Rufus"],"index":20296,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989689589,"difficulty":0.0010310411}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jesus can now know whether Krystle can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesus","Donald","Diane","Krystle"],"index":23164,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993651509,"difficulty":0.0006348491}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dwight can now know whether Dwight's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Aimee","Nancy","Freeman","Dwight"],"index":51871,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999392271,"difficulty":0.000607729}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Robert can now know whether Roy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Dana","Roy","Kelley"],"index":16331,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993207455,"difficulty":0.0006792545}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether or not nobody's forehead is muddy. It is publicly announced that Brett's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Paul can now know whether Nelson's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carole","Nelson","Paul","Brett"],"index":25896,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994390607,"difficulty":0.0005609393}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stewart knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Tara can now know that Stewart can know whether Tara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tara","Stewart","Daniel"],"index":55562,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994227886,"difficulty":0.0005772114}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Regina knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Regina can now know whether Carla can know whether Regina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Regina","Thomas","Carla"],"index":49541,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994152784,"difficulty":0.0005847216}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Mario can now know that Kelly can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kelly","Betty","Mario","George"],"index":27660,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993793964,"difficulty":0.0006206036}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wallace knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Donald can now know that Wallace's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Laura","Brandy","Wallace"],"index":878,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983793497,"difficulty":0.0016206503}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Marsha can now know that Robert can know that Marsha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Marsha","Robert"],"index":38355,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998118937,"difficulty":0.001881063}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy. It is publicly announced that Mark knows whether Mark's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Ruth can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mark","Ruth"],"index":54882,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993112087,"difficulty":0.0006887913}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Anthony can now know that Jana can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jana","Jerrie","Anthony"],"index":20468,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9720034003,"difficulty":0.0279965997}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tessa knows whether or not nobody's forehead is muddy. It is publicly announced that Peggy knows whether Tessa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Tessa can now know that Tessa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tessa","Peggy"],"index":31174,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951869845,"difficulty":0.0048130155}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Rebecca can now know that Dale can know that Arthur's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dale","Jesus","Rebecca","Arthur"],"index":21906,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974420071,"difficulty":0.0025579929}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether William can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Phyllis","William","Shane"],"index":37529,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992322922,"difficulty":0.0007677078}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tammy can now know that Zachary can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Zachary","Roxanne","Tammy"],"index":27435,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988817573,"difficulty":0.0011182427}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Lawrence can now know that Richard can know that Lawrence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lawrence","Richard","Kristin"],"index":1668,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978268743,"difficulty":0.0021731257}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Michael can now know whether Linda can know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Michael"],"index":11952,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994016886,"difficulty":0.0005983114}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether Deborah's forehead is muddy. It is publicly announced that George knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"George can now know that Deborah can know whether George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Deborah","Kimberly","Susan"],"index":62257,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994317889,"difficulty":0.0005682111}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Amanda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Alice can now know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Amanda","Alice"],"index":12153,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9986477494,"difficulty":0.0013522506}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renee knows whether Shaniqua's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Shaniqua can now know that Renee can know whether Renee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Renee","Raul","Shaniqua"],"index":25618,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993991852,"difficulty":0.0006008148}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Maureen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether Maureen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maureen","Elizabeth"],"index":54106,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993483424,"difficulty":0.0006516576}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Katrina can now know that Stephen can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katrina","Stephen","Luke","Joseph"],"index":48851,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998881042,"difficulty":0.001118958}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Regina's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Regina can now know that Natalie can know whether Natalie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Natalie","Regina"],"index":9363,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994687438,"difficulty":0.0005312562}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Barbara can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Cory","Barbara","Joseph"],"index":14711,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985820055,"difficulty":0.0014179945}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Alton can now know whether Ruby can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Jeffrey","Alton"],"index":5659,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991440773,"difficulty":0.0008559227}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Dianne can now know that Dianne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dianne","Kathryn","Linda"],"index":63678,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980059266,"difficulty":0.0019940734}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brett's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Brett can now know that Amanda can know that Patrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amanda","Patrick","Brett","Vera"],"index":20567,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978833795,"difficulty":0.0021166205}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Thomas can now know that Margaret can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Natalie","Margaret","Amanda"],"index":64581,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989503026,"difficulty":0.0010496974}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Mike can now know that Lois can know that Mike's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lois","Michelle","Mike"],"index":44062,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978479147,"difficulty":0.0021520853}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Muriel knows whether Muriel's forehead is muddy. It is publicly announced that Muriel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Muriel can now know whether Harvey can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Muriel","Phillip","Harvey","Kevin"],"index":32812,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999443233,"difficulty":0.000556767}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"John can now know that Lily can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lily","John"],"index":38406,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.985617578,"difficulty":0.014382422}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Chad can now know that Chad's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pedro","Chad","Kayla"],"index":16153,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983068705,"difficulty":0.0016931295}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corey knows whether Judith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Nick can now know whether Corey can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Corey","Judith","Nick"],"index":57378,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993607402,"difficulty":0.0006392598}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Ronald can now know that Carolyn can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronald","Carolyn"],"index":16457,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992282391,"difficulty":0.0007717609}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Duane knows whether Pamela's forehead is muddy. It is publicly announced that Eric's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentd knows that (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Lonnie can now know that Eric can know whether Lonnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Duane","Pamela","Lonnie"],"index":6348,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994280934,"difficulty":0.0005719066}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lewis knows whether Dinah's forehead is muddy. It is publicly announced that Lewis knows whether Dinah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Lewis can now know whether Kimberly can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lewis","Dinah","Kimberly","Ryan"],"index":6945,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993630052,"difficulty":0.0006369948}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Blaine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Megan can now know that Blaine can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Megan","Blaine","John","Calvin"],"index":10383,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993829727,"difficulty":0.0006170273}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myra's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Josie can now know that Lisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Yvonne","Lisa","Josie","Myra"],"index":54209,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981535077,"difficulty":0.0018464923}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether or not everyone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Robert can now know that Haley can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ralph","Robert","Kenneth","Haley"],"index":5808,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994219542,"difficulty":0.0005780458}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelina knows whether or not everyone's forehead is muddy. It is publicly announced that Angelina knows whether someone's forehead is muddy. It is publicly announced that Angelina knows whether Angelina's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Angelina can now know that Angelina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Angelina","Elizabeth"],"index":17603,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9940270185,"difficulty":0.0059729815}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Melissa can now know that Kimberly can know whether Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Melissa","Betty","Rebecca"],"index":49929,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993433356,"difficulty":0.0006566644}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nancy can now know whether Ronald can know that Ollie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronald","Ollie","Nancy"],"index":38775,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993264675,"difficulty":0.0006735325}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nina knows whether or not everyone's forehead is muddy. It is publicly announced that Alice's forehead is muddy. It is publicly announced that Tom's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Alice can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alice","Nina","Tom"],"index":46952,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982873797,"difficulty":0.0017126203}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Mark can now know whether Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Lori","Norma"],"index":60633,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994078875,"difficulty":0.0005921125}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sam knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Sam can now know that Ida's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Ida","Sam","George"],"index":35248,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982066154,"difficulty":0.0017933846}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Scott can now know whether Dina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dina","Scott","Bruce"],"index":22693,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993932247,"difficulty":0.0006067753}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Sarah can now know that George can know that Lisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","George","Jesse","Lisa"],"index":16789,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978747368,"difficulty":0.0021252632}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herman knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Sara can now know that Carie can know that Sara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Casey","Herman","Sara","Carie"],"index":61353,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975063205,"difficulty":0.0024936795}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether Christy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Jean can now know that Diana can know that Anna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diana","Anna","Christy","Jean"],"index":856,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998239398,"difficulty":0.001760602}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Annie can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","John","Annie"],"index":29158,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988987446,"difficulty":0.0011012554}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma knows whether Eric's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Eric can now know whether Thelma can know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eric","Thelma"],"index":25342,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994240999,"difficulty":0.0005759001}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Glenn","Jeffery"],"index":63180,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998559773,"difficulty":0.001440227}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cleveland knows whether Merry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Merry can now know whether Manuel can know that Merry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Merry","Alyssa","Manuel","Cleveland"],"index":52619,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994279742,"difficulty":0.0005720258}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lupe's forehead is not muddy. It is publicly announced that Scott's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Frances can now know whether Lupe can know whether Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","Lupe","Michael","Scott"],"index":14194,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994543195,"difficulty":0.0005456805}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Barbara can now know that Neil's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Neil","John"],"index":41104,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980738163,"difficulty":0.0019261837}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joaquin can now know whether Antonio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joaquin","John","Antonio"],"index":19159,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994087219,"difficulty":0.0005912781}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Danelle","Dorothy"],"index":43659,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993129969,"difficulty":0.0006870031}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy. It is publicly announced that James knows whether Juan's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Juan can now know that James can know that Juan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Juan"],"index":16757,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9907671809,"difficulty":1.9907671809}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Brandi can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Corina","John","Brandi"],"index":17542,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999461472,"difficulty":0.000538528}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Edward can now know that Richie can know that Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Edward","Richie"],"index":55227,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998046279,"difficulty":0.001953721}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Warren can now know that Derrick can know that Warren's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Derrick","Brian","Lillian","Warren"],"index":12606,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984971285,"difficulty":0.0015028715}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ivy knows whether Stanley's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Stanley can now know that Ivy can know whether Ivy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ivy","Stanley","Greg"],"index":67086,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994015694,"difficulty":0.0005984306}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma knows whether Kim's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kim can now know whether Michelle can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","Michelle","Thelma"],"index":48486,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994274378,"difficulty":0.0005725622}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Angela can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Sal","Donald"],"index":20832,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989375472,"difficulty":0.0010624528}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Hollis can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Hollis"],"index":20033,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9885411263,"difficulty":0.0114588737}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Victor can now know that Reginald can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Victor","Ester","Reginald","David"],"index":31311,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992524981,"difficulty":0.0007475019}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy. It is publicly announced that Michael knows whether Brandon's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Brandon can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Brandon"],"index":26543,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993721843,"difficulty":0.0006278157}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deanna knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know that Reinaldo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Deanna","Mary","Reinaldo"],"index":60288,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975639582,"difficulty":0.0024360418}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tara knows whether Tara's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Margaret can now know that Tara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tara","Margaret","Richard","Lynda"],"index":8406,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.995773375,"difficulty":0.004226625}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maude's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Gonzalo can now know that Maude can know whether Maude's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leann","Gonzalo","Maude","Joshua"],"index":24407,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994671941,"difficulty":0.0005328059}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Maribel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Linda can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Mac","Maribel","Rachel"],"index":14045,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993656278,"difficulty":0.0006343722}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Doris can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Janet","Doris"],"index":43779,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986513257,"difficulty":0.0013486743}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Mark can now know that Michael can know that Clyde's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clyde","Harvey","Michael","Mark"],"index":50665,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9925588369,"difficulty":0.0074411631}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether Cathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"David can now know whether Kerry can know that Kerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kerry","Terry","David","Cathy"],"index":60340,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992483258,"difficulty":0.0007516742}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Nancy knows whether Bradley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Bradley can now know that Robert can know that Kathryn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bradley","Kathryn","Nancy","Robert"],"index":37673,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9869454503,"difficulty":0.0130545497}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jason can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jason","Kathleen"],"index":62838,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991390705,"difficulty":0.0008609295}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Gregory's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mildred can now know whether Susan can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Susan","David","Mildred"],"index":42589,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993739724,"difficulty":0.0006260276}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Matthew can now know whether Samantha can know whether Lorenzo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lorenzo","Samantha","Matthew"],"index":2246,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999396801,"difficulty":0.000603199}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Katherine knows whether Lindsay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lindsay can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Katherine","Lindsay","Melissa"],"index":22340,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9955080748,"difficulty":0.0044919252}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheri knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Vicki can now know that Cheri can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vicki","Cheri"],"index":42539,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993274212,"difficulty":0.0006725788}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffery","Lois","Robert","David"],"index":45593,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991519451,"difficulty":0.0008480549}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tisha's forehead is not muddy. It is publicly announced that Thelma knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Cynthia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thelma","Tisha","Cynthia"],"index":39247,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989004135,"difficulty":0.0010995865}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Alma's forehead is muddy. It is publicly announced that Kerry knows whether or not nobody's forehead is muddy. It is publicly announced that Alma knows whether Kerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Chong can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Chong","Kerry","Alma"],"index":41835,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994542003,"difficulty":0.0005457997}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Mason can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Mason","Frank"],"index":44955,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989191294,"difficulty":0.0010808706}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Gail can now know whether Darin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Darin","Joan","Gail"],"index":3234,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999401927,"difficulty":0.000598073}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gayle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Gayle can now know that Velma can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Henry","Velma","Gayle"],"index":63038,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993342757,"difficulty":0.0006657243}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Carolyn can now know that Emily can know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emily","Carolyn","Stephanie","Erin"],"index":50656,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968241453,"difficulty":0.0031758547}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois knows whether Lois's forehead is muddy. It is publicly announced that Marisa's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Marisa can now know that Stephanie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephanie","Lois","Marisa"],"index":17651,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9703869224,"difficulty":0.0296130776}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gabriella can now know whether David can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","David","Gabriella","Paul"],"index":41233,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999399066,"difficulty":0.000600934}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Antonia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Robert can now know that Chantel can know that Ronald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chantel","Robert","Ronald","Antonia"],"index":63254,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963311553,"difficulty":0.0036688447}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy. It is publicly announced that Donna knows whether Donna's forehead is muddy. It is publicly announced that Pauline knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","Kenneth","Pauline"],"index":57516,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992610812,"difficulty":0.0007389188}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jesus knows whether Jesus's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jesus can now know whether Michael can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jesus","Michael"],"index":64032,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99923563,"difficulty":0.00076437}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina knows whether Troy's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Troy can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tina","Troy"],"index":12091,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992258549,"difficulty":0.0007741451}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Jackie can now know that Leopoldo can know whether Jeanette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eugene","Jackie","Leopoldo","Jeanette"],"index":62372,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993112087,"difficulty":0.0006887913}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Donna can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Angela","Andrew","Barbara"],"index":33016,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9914426208,"difficulty":0.0085573792}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know that Blanca can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vina","Justin","Ava","Blanca"],"index":64673,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991565943,"difficulty":0.0008434057}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ronald can now know that Melody can know that Melody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Ronald","Melody"],"index":46847,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977462888,"difficulty":0.0022537112}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether or not nobody's forehead is muddy. It is publicly announced that Bruce's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Bruce can now know whether Karri's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffrey","Karri","Bruce"],"index":39927,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994562268,"difficulty":0.0005437732}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether Robert's forehead is muddy. It is publicly announced that Ronald knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ronald can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ronald","Robert"],"index":6283,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9802635312,"difficulty":0.0197364688}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Minnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kimberly can now know whether Minnie can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","John","Minnie","Thomas"],"index":29161,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994540811,"difficulty":0.0005459189}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Shanna can now know whether Donald can know whether Shanna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roy","Donald","Shanna"],"index":42464,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993914366,"difficulty":0.0006085634}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Max knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Max can now know that Clara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beverly","Max","Sarah","Clara"],"index":35143,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976738095,"difficulty":0.0023261905}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Bonnie","Jacklyn","William"],"index":21070,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9894970655,"difficulty":0.0105029345}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobbie knows whether Carmen's forehead is muddy. It is publicly announced that Sean's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Ronald can now know that Carmen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Sean","Bobbie","Carmen"],"index":25349,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977155924,"difficulty":0.0022844076}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Beth can now know whether Marcia can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laura","Wayne","Beth","Marcia"],"index":40783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993157387,"difficulty":0.0006842613}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry knows whether Barry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Barry can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Carolyn","Barry","Josie"],"index":63154,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987609386,"difficulty":0.0012390614}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether Robbie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jean can now know that Jean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Jean","Robbie"],"index":21674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980390668,"difficulty":0.0019609332}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Maria's forehead is not muddy. It is publicly announced that Rolando's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agentb knows whether (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Maria can now know whether Rolando can know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rolando","Maria"],"index":56270,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993630052,"difficulty":0.0006369948}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cathleen knows whether Susie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cathleen","Jimmy","Susie","Robert"],"index":5661,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990112782,"difficulty":0.0009887218}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Alberto can now know that Laronda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Laronda","Alberto"],"index":22297,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978208542,"difficulty":0.0021791458}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Chester can now know that Patricia can know that Chester's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Louise","Patricia","Chester"],"index":3989,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9944434762,"difficulty":0.0055565238}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leanne knows whether or not nobody's forehead is muddy. It is publicly announced that Leanne knows whether Leanne's forehead is muddy. It is publicly announced that Spencer's forehead is muddy. It is publicly announced that Gary knows whether Spencer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Glen can now know whether Leanne can know whether Leanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Spencer","Leanne","Gary","Glen"],"index":49762,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999348104,"difficulty":0.000651896}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentc knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Blake can now know that Lucille can know whether Blake's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aaron","Angela","Blake","Lucille"],"index":11812,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993284941,"difficulty":0.0006715059}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Gerald's forehead is muddy. It is publicly announced that James knows whether Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"James can now know that Teresa can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Gerald","Teresa","Harold"],"index":54567,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993645549,"difficulty":0.0006354451}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Betty can now know that Carl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Larry","Jessica","Carl"],"index":47205,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980064034,"difficulty":0.0019935966}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Rodney knows whether or not nobody's forehead is muddy. It is publicly announced that Lee knows whether Carolyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Rodney can now know that Carolyn can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Rodney","Carolyn","Lee"],"index":50576,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993365407,"difficulty":0.0006634593}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Monica can now know that Margret can know that Monica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Luis","Margret","Mabel","Monica"],"index":29548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985578656,"difficulty":0.0014421344}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Genevieve knows whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Debra can now know whether Genevieve's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carl","Genevieve","Debra"],"index":26976,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994267225,"difficulty":0.0005732775}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Phillip's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Marlon can now know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shannon","Kimberly","Phillip","Marlon"],"index":36082,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9363723993,"difficulty":0.0636276007}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nydia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Michael can now know that Nydia can know that Sonia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Nydia","Sonia"],"index":22867,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980074763,"difficulty":0.0019925237}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Nina can now know that Margaret can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nina","Margaret","Martin"],"index":5147,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9938575625,"difficulty":0.0061424375}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marla knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Charles can now know that Keely's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Marla","Keely"],"index":53892,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9980449677,"difficulty":0.0019550323}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Amanda can now know whether Debra can know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Amanda","Debra"],"index":50233,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993929863,"difficulty":0.0006070137}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Kurt can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kurt","John","Jenifer"],"index":34885,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993551373,"difficulty":0.0006448627}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Fred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Mary can now know whether Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Fred","Julia","Amanda","Mary"],"index":44926,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994338155,"difficulty":0.0005661845}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] 0","hypothesis":"David can now know that Alma can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Alma"],"index":5381,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993688464,"difficulty":0.0006311536}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Irvin can now know whether James can know whether Stacey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alexander","Irvin","James","Stacey"],"index":59084,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994031191,"difficulty":0.0005968809}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene knows whether Janice's forehead is muddy. It is publicly announced that Janice knows whether Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Donald can now know that Janice can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Janice","Arlene","Julia"],"index":54602,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978522062,"difficulty":0.0021477938}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Michael can now know whether Emily can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Emily","Michael"],"index":24251,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993712306,"difficulty":0.0006287694}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know that Howard can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Curt","Robert","Cynthia","Howard"],"index":67554,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993078709,"difficulty":0.0006921291}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy. It is publicly announced that John knows whether Jacqueline's forehead is muddy. It is publicly announced that Billy knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jacqueline can now know whether John can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jacqueline","Billy","John"],"index":31634,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993995428,"difficulty":0.0006004572}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linsey knows whether or not nobody's forehead is muddy. It is publicly announced that Jennifer's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] 0","hypothesis":"Ronald can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Roger","Linsey","Jennifer"],"index":12568,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989326596,"difficulty":0.0010673404}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Paul's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Wade can now know whether Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wade","Paul","Bryan"],"index":16912,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994427562,"difficulty":0.0005572438}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Herbert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Herbert","Dena","Susan","Joann"],"index":16850,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989247918,"difficulty":0.0010752082}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy. It is publicly announced that Billie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Billie can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Billie","William"],"index":19616,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977909327,"difficulty":0.0022090673}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cornelia knows whether Michael's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy. It is publicly announced that Cornelia knows whether Cornelia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Cornelia can now know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cornelia","Michael"],"index":61463,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994444251,"difficulty":0.0005555749}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gail knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Gail can now know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Gail","Cameron"],"index":11901,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994505048,"difficulty":0.0005494952}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Paul can now know whether Clarence can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Clarence","Paul"],"index":62568,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993398786,"difficulty":0.0006601214}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Glen can now know whether James can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Charles","Glen"],"index":7651,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994458556,"difficulty":0.0005541444}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roderick knows whether someone's forehead is muddy. It is publicly announced that Brian knows whether someone's forehead is muddy. It is publicly announced that Diane knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Kimberly can now know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diane","Kimberly","Roderick","Brian"],"index":13380,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980313182,"difficulty":0.0019686818}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton knows whether Milton's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Whitley can now know that Milton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Milton","Catherine","Whitley","Donald"],"index":2925,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.993729949,"difficulty":0.006270051}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mohammed knows whether Vicki's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mohammed can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vicki","Mohammed","George"],"index":4969,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990193844,"difficulty":0.0009806156}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kathleen can now know that Denise can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cristy","Edward","Denise","Kathleen"],"index":58804,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999120295,"difficulty":0.000879705}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Henry can now know whether George can know whether Michele's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Henry","George","Michele"],"index":56871,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993848801,"difficulty":0.0006151199}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Peter can now know that Melvin can know whether Melvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Melvin","Juan","Miguel"],"index":64497,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999215126,"difficulty":0.000784874}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillian's forehead is not muddy. It is publicly announced that Laura's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Shannon can now know that Lillian can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shannon","Laura","Lillian","Gregory"],"index":37963,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989935756,"difficulty":0.0010064244}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Casey knows whether Christopher's forehead is muddy. It is publicly announced that Casey knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Christopher can now know that Casey can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Casey","Christopher","Yvette","Sonya"],"index":40186,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989683628,"difficulty":0.0010316372}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marty knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Jennifer can now know that Anthony can know that Anthony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Pauline","Jennifer","Marty"],"index":38714,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9946405292,"difficulty":0.0053594708}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Linda can now know that Morgan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Linda","Morgan"],"index":15679,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9883382916,"difficulty":0.0116617084}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vanessa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Vanessa can now know that Gary can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Vanessa","Kenneth"],"index":60804,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992789626,"difficulty":0.0007210374}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is not muddy. It is publicly announced that Alisa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Kenneth can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edward","Alisa","Kenneth"],"index":57309,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992794394,"difficulty":0.0007205606}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bret can now know that John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Michael","Bret","Robert"],"index":55109,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986358285,"difficulty":0.0013641715}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"George can now know whether Kendra can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kendra","George"],"index":14330,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993258715,"difficulty":0.0006741285}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether Jacqueline's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Denise can now know whether Michael can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Denise","Jacqueline"],"index":55341,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992076755,"difficulty":0.0007923245}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Herbert can now know that Terry can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elvira","Herbert","Terry","Tommy"],"index":35154,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993102551,"difficulty":0.0006897449}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Anamaria can now know that Dorothy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Dorothy","Anamaria"],"index":41783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991962314,"difficulty":0.0008037686}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Karen can now know that Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Brian","Timothy","Mary"],"index":43805,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9966879487,"difficulty":0.0033120513}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bette knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Bette can now know whether Charles can know that Bette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Zina","Bette","Charles"],"index":1462,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999409318,"difficulty":0.000590682}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renee's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1&2&3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1&2&3) ] 0","hypothesis":"Bruce can now know whether Renee can know whether Brandy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bruce","Renee","Brandy"],"index":60890,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994443059,"difficulty":0.0005556941}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jackson can now know whether Jeanne can know that Jeanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Celesta","Mike","Jackson","Jeanne"],"index":16489,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992291927,"difficulty":0.0007708073}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashlee's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Autumn can now know whether Autumn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Autumn","Ashlee","Chris"],"index":21635,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994164705,"difficulty":0.0005835295}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Allen can now know that Allen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Allen","Jennifer","Vivian"],"index":60929,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998259604,"difficulty":0.001740396}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellis knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Ellis can now know whether Teresa can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellis","David","Teresa"],"index":10523,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994620681,"difficulty":0.0005379319}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Frank can now know that Ryan can know that Victor's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ryan","Angelina","Victor","Frank"],"index":34979,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966285825,"difficulty":0.0033714175}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne's forehead is not muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Shane can now know that William can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Suzanne","Shane"],"index":23540,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998791635,"difficulty":0.001208365}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fay knows whether Fay's forehead is muddy. It is publicly announced that Michelle knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Michelle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Fay","Michelle","Jack"],"index":17809,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987248778,"difficulty":0.0012751222}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bruce can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Roberta","Bruce"],"index":58030,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988074303,"difficulty":0.0011925697}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel knows whether or not everyone's forehead is muddy. It is publicly announced that Anna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Anna can now know that Manuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Iva","Manuel","Lucille"],"index":33548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9730782509,"difficulty":0.0269217491}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick knows whether someone's forehead is muddy. It is publicly announced that Don knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Don can now know that Patrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Don","Patrick"],"index":51188,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979174733,"difficulty":0.0020825267}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Sherman can now know that Lucille can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sherman","Lucille"],"index":56415,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994161129,"difficulty":0.0005838871}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Greg knows whether or not nobody's forehead is muddy. It is publicly announced that Denise's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Danielle can now know that Danielle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danielle","Denise","Greg"],"index":900,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977987409,"difficulty":0.0022012591}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Michael can now know that Clara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Clara"],"index":61307,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977220893,"difficulty":0.0022779107}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Rebecca can now know whether Jasmine can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jasmine","Rebecca","Valentin","Paul"],"index":21956,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993259907,"difficulty":0.0006740093}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Eleanor knows whether Camilla's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Esther can now know that Eleanor can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eleanor","Esther","Erin","Camilla"],"index":67481,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9945018291,"difficulty":0.0054981709}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doyle knows whether Shane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Shane can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rose","Doyle","Shane"],"index":14298,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993909597,"difficulty":0.0006090403}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bret knows whether someone's forehead is muddy. It is publicly announced that Bret's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] 0","hypothesis":"Bret can now know whether Mark can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bret","Mark"],"index":20998,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999422431,"difficulty":0.000577569}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Muriel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Jesus can now know that Laura can know that Laura's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Valda","Muriel","Jesus"],"index":65224,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9958101511,"difficulty":0.0041898489}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jeffrey can now know that Norman can know that Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Norman","Thomas"],"index":34836,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9915322661,"difficulty":0.0084677339}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby knows whether Erica's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Bobby can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christopher","Erica","Douglas","Bobby"],"index":24150,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992635846,"difficulty":0.0007364154}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Karin knows whether Wilfred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Karlene can now know that Wilfred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karlene","Wilfred","Karin","Willie"],"index":4314,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9980377555,"difficulty":0.0019622445}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Christopher can now know whether Steven can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Christopher"],"index":53375,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993377328,"difficulty":0.0006622672}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tiffany can now know that Peter can know that Alberto's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tiffany","Alberto","Peter"],"index":59333,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977378845,"difficulty":0.0022621155}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laurie can now know that David can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tamara","David","Laurie","John"],"index":13454,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989228845,"difficulty":0.0010771155}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amy can now know that David can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Gregory","David","Amy"],"index":31826,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984266758,"difficulty":0.0015733242}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Betsy can now know whether William can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Betsy","William"],"index":31985,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994218349,"difficulty":0.0005781651}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Deborah can now know whether Adeline can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Adeline","George","Deborah","Lisa"],"index":11263,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991447926,"difficulty":0.0008552074}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Lee can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lee","Ronnie","Christoper","Jerry"],"index":29399,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99894315,"difficulty":0.00105685}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Charles can now know that Rose can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Grace","Charles","Richard"],"index":57725,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984676242,"difficulty":0.0015323758}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Margaret knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Margaret can now know that Lesley can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Enrique","Lesley","Carl"],"index":21030,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992341995,"difficulty":0.0007658005}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Marilee can now know whether Kristine can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kristine","Marilee"],"index":66155,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993952513,"difficulty":0.0006047487}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacey knows whether Stacey's forehead is muddy. It is publicly announced that Eleanor knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Rebecca can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stacey","Mara","Eleanor","Rebecca"],"index":13909,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999340117,"difficulty":0.000659883}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Calvin knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Un can now know that Calvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Un","Cathy","Calvin"],"index":40025,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980242252,"difficulty":0.0019757748}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Victoria can now know whether Stephen can know whether Anastacia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Victoria","Quentin","Anastacia"],"index":66018,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999317646,"difficulty":0.000682354}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Daniel can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lela","Hilda","Daniel","Kendra"],"index":47125,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988858104,"difficulty":0.0011141896}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Carolyn can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carolyn","William"],"index":50573,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990179539,"difficulty":0.0009820461}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Richard can now know whether Brandie can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patti","Jeffrey","Richard","Brandie"],"index":52261,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993706346,"difficulty":0.0006293654}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Teodoro","John"],"index":6126,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988930821,"difficulty":0.0011069179}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Maria can now know whether Scott can know whether Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Matthew","Maria"],"index":780,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994220734,"difficulty":0.0005779266}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Dallas can now know whether Dallas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathleen","Carol","Dallas"],"index":17403,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994142056,"difficulty":0.0005857944}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilma knows whether Mathilde's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Virginia can now know whether Wilma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephanie","Mathilde","Virginia","Wilma"],"index":67600,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994407296,"difficulty":0.0005592704}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen knows whether Tonya's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Michael can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Tonya","Carmen"],"index":18707,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990310669,"difficulty":0.0009689331}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Rose can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rose","Lori","Richard"],"index":16993,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990082383,"difficulty":0.0009917617}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Irene can now know that Louis can know whether Irene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Zana","Willard","Irene"],"index":56867,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999345839,"difficulty":0.000654161}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Tyler can now know that Jerry can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tyler","Andy","Jerry"],"index":38996,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993746877,"difficulty":0.0006253123}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether Grace can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Grace","Marvin","Christopher"],"index":10368,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993201494,"difficulty":0.0006798506}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Stella can now know whether Blair can know that Chris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stella","Lisa","Chris","Blair"],"index":57887,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994207621,"difficulty":0.0005792379}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marian knows whether Gordon's forehead is muddy. It is publicly announced that Gordon's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Marian can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marian","Gordon"],"index":12255,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994674325,"difficulty":0.0005325675}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alta knows whether or not nobody's forehead is muddy. It is publicly announced that Manuel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Alta can now know that Manuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Manuel","Alta"],"index":54505,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9925550818,"difficulty":0.0074449182}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Lisa can now know that Monica can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Monica","Hester","Lisa"],"index":33342,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993900061,"difficulty":0.0006099939}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicholas can now know whether Janice can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicholas","Janice","Barbara","Joseph"],"index":7187,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994339347,"difficulty":0.0005660653}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Leanne can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elmer","Donald","Georgia","Leanne"],"index":4080,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988340735,"difficulty":0.0011659265}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry knows whether someone's forehead is muddy. It is publicly announced that Jerry knows whether Jerry's forehead is muddy. It is publicly announced that Peter knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jerry","Robert","Peter"],"index":51547,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967709184,"difficulty":0.0032290816}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carly knows whether Dale's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Antione can now know that Carly can know that Carly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antione","Carly","Dale","Joseph"],"index":12727,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980022311,"difficulty":0.0019977689}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"George can now know that Stanley can know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irving","Stanley","George","Kathleen"],"index":20882,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982300401,"difficulty":0.0017699599}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Donna knows whether David's forehead is muddy. It is publicly announced that David knows whether Derek's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentd knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Derek can now know that Josie can know whether Josie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Derek","David","Josie"],"index":18548,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994008541,"difficulty":0.0005991459}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Karen can now know whether Curtis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Elba","Curtis"],"index":32638,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994245768,"difficulty":0.0005754232}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Ian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Basil can now know whether Teresa can know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Teresa","Susan","Basil","Ian"],"index":9962,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994051456,"difficulty":0.0005948544}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Denise knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Denise can now know that Wanda can know whether Wanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Denise","Wanda"],"index":4798,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992675185,"difficulty":0.0007324815}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Buddy knows whether Buddy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Scott can now know that Buddy can know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Buddy","Elizabeth","Scott"],"index":27167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981003404,"difficulty":0.0018996596}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"James can now know that Kathleen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Thomas","Kathleen","James"],"index":13641,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928289056,"difficulty":0.0071710944}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Brooke can now know that Shari can know that Reginald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shari","Reginald","Mattie","Brooke"],"index":20857,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976522326,"difficulty":0.0023477674}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond's forehead is muddy. It is publicly announced that Danielle knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Raymond can now know whether Danielle can know whether Danielle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Joshua","Raymond","Danielle"],"index":50419,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994501472,"difficulty":0.0005498528}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"John can now know that Thomas can know that Danny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Danny","Mary","John","Thomas"],"index":57739,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972254038,"difficulty":0.0027745962}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco knows whether someone's forehead is muddy. It is publicly announced that Francisco knows whether someone's forehead is muddy. It is publicly announced that Francisco knows whether someone's forehead is muddy. It is publicly announced that Francisco knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Rose can now know that Ted's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francisco","Ted","Rose"],"index":6523,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971394539,"difficulty":0.0028605461}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Patricia can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Patricia","Ronald","Anthony"],"index":38070,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999273479,"difficulty":0.000726521}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Jerome's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jerome can now know that Martin can know that Jerome's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martin","Jerome","Jennifer"],"index":46789,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966470599,"difficulty":0.0033529401}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Katherine can now know that Stacey can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brandon","Katherine","Stacey"],"index":21692,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988634586,"difficulty":0.0011365414}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Heather knows whether Heather's forehead is muddy. It is publicly announced that Kathy knows whether Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Carlos can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Heather","Kathy","Carlos","Elizabeth"],"index":54999,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993672967,"difficulty":0.0006327033}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Mark can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thomas","Mark"],"index":45975,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9595278502,"difficulty":0.0404721498}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Andrew can now know whether Migdalia can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","John","Migdalia"],"index":23298,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993975163,"difficulty":0.0006024837}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether Frieda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Evelyn can now know that Frieda can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Evelyn","Frieda"],"index":50902,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989653826,"difficulty":0.0010346174}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rick can now know that Mamie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rick","Felipe","Lea","Mamie"],"index":61192,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992889166,"difficulty":0.0007110834}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether Floyd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Floyd can now know that Gregory can know that Ann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Douglas","Gregory","Ann","Floyd"],"index":58134,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982625842,"difficulty":0.0017374158}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether Dana's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Tony can now know that Dana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tony","Dana"],"index":51991,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959646463,"difficulty":0.0040353537}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felix knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Felix can now know that Michael can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Dennis","Linda","Felix"],"index":14838,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979300499,"difficulty":0.0020699501}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Debbie can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leonard","Patrick","Joseph","Debbie"],"index":65234,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989752769,"difficulty":0.0010247231}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet knows whether Janet's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Janet can now know that Allen can know that Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Janet","Allen"],"index":50600,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966551065,"difficulty":0.0033448935}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephany's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Timothy can now know that Stephany can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nadine","Stephany","Timothy"],"index":37562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989687204,"difficulty":0.0010312796}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guadalupe knows whether someone's forehead is muddy. It is publicly announced that Guadalupe knows whether Alberta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Alberta can now know that Lyman can know that Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Alberta","Lyman","Guadalupe"],"index":48436,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974478483,"difficulty":0.0025521517}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy knows whether Margaret's forehead is muddy. It is publicly announced that Tammy knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know whether Tammy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tammy","Margaret"],"index":54368,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993991852,"difficulty":0.0006008148}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Barry can now know whether Luann can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barry","Reba","Luann"],"index":53918,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992524981,"difficulty":0.0007475019}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether Billy's forehead is muddy. It is publicly announced that Gloria knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Gail can now know whether Zula can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Billy","Gail","Zula"],"index":58985,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992505908,"difficulty":0.0007494092}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kevin can now know that Cynthia can know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cynthia","Kevin"],"index":63654,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957362413,"difficulty":0.0042637587}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shona knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Matthew can now know that Shona's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elvira","Matthew","Shona"],"index":55881,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998044014,"difficulty":0.001955986}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Agnes's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Agnes can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Agnes","Meghan","Annabelle","Timothy"],"index":16368,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998989284,"difficulty":0.001010716}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Joyce can now know that Maria can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juli","Kimberley","Joyce","Maria"],"index":49293,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993414283,"difficulty":0.0006585717}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Kimberley can now know that Aaron can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberley","Justin","Aaron","Karen"],"index":42008,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989725351,"difficulty":0.0010274649}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darline knows whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Darline can now know that Jose can know that Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Nicole","Darline"],"index":64283,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9320924878,"difficulty":0.0679075122}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know whether Willie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Willie","Larry","Emily","Portia"],"index":47895,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994117022,"difficulty":0.0005882978}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle knows whether Hershel's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Hershel can now know that Lewis can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lewis","Hershel","Danielle"],"index":49748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.993614018,"difficulty":0.006385982}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"John can now know that Leonardo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Nancy","John","Leonardo"],"index":28050,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966358542,"difficulty":0.0033641458}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Katie can now know that Barbara can know whether Katie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katie","Barbara","Darren"],"index":12536,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994670749,"difficulty":0.0005329251}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Barry's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Dewayne can now know whether Leola can know whether Barry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barry","Dewayne","Leola","Christopher"],"index":23336,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994140863,"difficulty":0.0005859137}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilma knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know whether Susan can know whether Wilma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Susan","Tamiko","Wilma"],"index":10319,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994199276,"difficulty":0.0005800724}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Alma can now know whether Velma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wayne","Alma","Velma"],"index":43068,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994775653,"difficulty":0.0005224347}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Alyssa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Nadine can now know that Alyssa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alyssa","Steven","Charles","Nadine"],"index":13213,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989293218,"difficulty":0.0010706782}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether Joe's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ronald can now know that Thomas can know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joe","Thomas","Ronald","John"],"index":48774,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977827668,"difficulty":0.0022172332}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teri knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Marcy can now know that Giovanni can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Teri","Marcy","Giovanni"],"index":63936,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989668131,"difficulty":0.0010331869}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Joseph can now know whether Raymond can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ernest","Jerry","Joseph","Raymond"],"index":20295,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993374944,"difficulty":0.0006625056}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jermaine can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Jermaine","Robin","Anne"],"index":58165,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984120131,"difficulty":0.0015879869}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Robert can now know that Candy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Candy"],"index":52113,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9727023244,"difficulty":0.0272976756}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Nicole knows whether someone's forehead is muddy. It is publicly announced that Nicole knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Peggy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nicole","Peggy","Jennifer"],"index":55296,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.98814255,"difficulty":0.01185745}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Raymond can now know that Carmelo can know whether Tanisha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raymond","Carmelo","Tanisha"],"index":18514,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993562102,"difficulty":0.0006437898}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether Anne's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Rita can now know that Anne can know that Rita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anne","Rita"],"index":48707,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984790683,"difficulty":0.0015209317}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether Rodney's forehead is muddy. It is publicly announced that Rodney knows whether Ryan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ryan can now know whether Rodney can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rodney","Ryan"],"index":38521,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992897511,"difficulty":0.0007102489}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Genevieve can now know whether Lori can know whether Genevieve's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Paul","Lori","Genevieve"],"index":38674,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994485974,"difficulty":0.0005514026}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether someone's forehead is muddy. It is publicly announced that Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] 0","hypothesis":"Justin can now know that Dennis can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dennis","Justin"],"index":6396,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990021586,"difficulty":0.0009978414}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Cory can now know that Eugene can know whether Dale's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cory","Elizabeth","Eugene","Dale"],"index":43992,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999425292,"difficulty":0.000574708}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Percy knows whether Percy's forehead is muddy. It is publicly announced that Bobbie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] Agenta knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Percy can now know that Norma can know whether Hilary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Percy","Norma","Bobbie","Hilary"],"index":11182,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994138479,"difficulty":0.0005861521}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy. It is publicly announced that Anthony knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Teresa can now know whether Anthony can know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Reid","Teresa","Anthony"],"index":22225,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994605184,"difficulty":0.0005394816}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Hazel can now know that Mildred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Hazel","Daniel","Mildred"],"index":26626,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982313514,"difficulty":0.0017686486}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether William's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Donald can now know whether Freddie can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Freddie","William","Donald"],"index":62477,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993951321,"difficulty":0.0006048679}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Priscilla can now know that Patsy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anna","Priscilla","Patsy"],"index":47300,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988749623,"difficulty":0.0011250377}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy. It is publicly announced that Daniella knows whether Daniella's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Linda can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Linda","Daniella"],"index":45581,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989473224,"difficulty":0.0010526776}