{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Nathaniel. Raymond's card is shown to Raymond. Andrew's card is shown to Willie. Willie's card is shown to Andrew. Andrew's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Willie does not know whether Willie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Andrew can now know whether Willie can know that Willie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nathaniel","Raymond","Willie","Andrew"],"index":55199,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9405223131,"difficulty":0.0594776869}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Joseph. Joseph's card is shown to Sally. It is publicly announced that someone picked a red card. It is publicly announced that Sally does not know whether Sally picked a red card. It is publicly announced that Sally does not know whether Sally picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Joseph can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Sally","Donna"],"index":52384,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Michael. Michael's card is shown to Michael. Thomas's card is shown to Dani. Michael's card is shown to Dani. Dani's card is shown to Dani. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether or not nobody picked a red card. It is publicly announced that Thomas knows whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Michael can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Michael","Dani"],"index":58320,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997238517,"difficulty":0.0002761483}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christina's card is shown to Robert. Clyde's card is shown to Robert. Christina's card is shown to Nancee. Robert's card is shown to Christina. Clyde's card is shown to Christina. Robert's card is shown to Clyde. Clyde's card is shown to Clyde. It is publicly announced that someone picked a red card. It is publicly announced that Nancee does not know whether Clyde picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 Agentd:1,4 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:3,4 Agentb:3 Agentc:1,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Christina can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Nancee","Christina","Clyde"],"index":36638,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998611331,"difficulty":0.001388669}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harry's card is shown to Harry. Kay's card is shown to Harry. Harry's card is shown to Kay. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 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 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Kay can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harry","Kay"],"index":16860,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Debora's card is shown to Patricia. Patricia's card is shown to William. William's card is shown to William. Clemente's card is shown to William. Debora's card is shown to William. Patricia's card is shown to Clemente. William's card is shown to Debora. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Debora can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","William","Clemente","Debora"],"index":34283,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997824192,"difficulty":0.002175808}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Laurie. Laurie's card is shown to Jane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jane can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laurie","Jane","Christopher","Gary"],"index":62431,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984951019,"difficulty":0.0015048981}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zachary's card is shown to John. Zachary's card is shown to Zachary. Jason's card is shown to Zachary. Terry's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Zachary does not know whether Terry picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Zachary can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Zachary","Jason","Terry"],"index":19259,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9814903736,"difficulty":0.0185096264}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacob's card is shown to Neil. Frankie's card is shown to Frankie. Jacob's card is shown to Frankie. Frankie's card is shown to Charlotte. Neil's card is shown to Jacob. It is publicly announced that someone picked a red card. It is publicly announced that Frankie picked a black card. It is publicly announced that Frankie does not know whether Neil picked a red card. It is publicly announced that Frankie knows whether someone picked a red card. It is publicly announced that Frankie does not know whether Neil picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentd knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Frankie can now know whether Jacob can know that Jacob picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Neil","Frankie","Charlotte","Jacob"],"index":61026,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9578191638,"difficulty":0.0421808362}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Neva. Sarah's card is shown to Neva. Sarah's card is shown to William. Neva's card is shown to Sarah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sarah can now know that William can know whether William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Neva","William","Sarah"],"index":28416,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9279150367,"difficulty":1.9279150367}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Latasha's card is shown to Ida. Jack's card is shown to Latasha. Latasha's card is shown to Jack. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ida can now know whether Ida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ida","Latasha","Jack"],"index":57954,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9546145797,"difficulty":0.0453854203}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alexander's card is shown to Lupe. Henry's card is shown to Alexander. Alexander's card is shown to Henry. Henry's card is shown to Henry. It is publicly announced that someone picked a red card. It is publicly announced that Lupe knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Lupe can now know that Henry can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lupe","Alexander","Henry"],"index":15349,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9870170951,"difficulty":0.0129829049}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tim's card is shown to George. Bruce's card is shown to George. George's card is shown to Tim. Tim's card is shown to Bruce. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bruce can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Tim","Bruce"],"index":18534,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947792292,"difficulty":0.0052207708}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chad's card is shown to Roy. Robert's card is shown to Robert. Robert's card is shown to Chad. Chad's card is shown to Chad. Chad's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Roy knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Roy can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roy","Robert","Chad","Linda"],"index":63538,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977869987,"difficulty":0.0022130013}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Anna. Morgan's card is shown to Anna. Anna's card is shown to Howard. It is publicly announced that someone picked a red card. It is publicly announced that Anna does not know whether or not everyone picked a red card. It is publicly announced that Anna knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Howard can now know that Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anna","Howard","Morgan"],"index":21449,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5774366856,"difficulty":1.5774366856}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Ronald. Jeanette's card is shown to Jeanette. Melissa's card is shown to Sharon. Jeanette's card is shown to Sharon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Melissa","Jeanette","Sharon"],"index":28453,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983389378,"difficulty":0.0016610622}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Gerald. Gerald's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Gerald picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"David can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gerald","David"],"index":20346,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7212927938,"difficulty":0.2787072062}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gina's card is shown to Gina. Gina's card is shown to Phyllis. Phyllis's card is shown to James. James's card is shown to Fredrick. Fredrick's card is shown to Fredrick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fredrick can now know that Gina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gina","Phyllis","James","Fredrick"],"index":29971,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982433319,"difficulty":0.0017566681}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Gordon. Tommie's card is shown to Gordon. Gordon's card is shown to Anna. Anna's card is shown to Anna. Anna's card is shown to Tommie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anna can now know that Tommie can know that Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gordon","Anna","Tommie"],"index":16538,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960313439,"difficulty":0.0039686561}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kellie's card is shown to Kellie. Kellie's card is shown to Alan. Alan's card is shown to Eric. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kellie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kellie","Alan","Eric"],"index":29666,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Claudia's card is shown to Heather. Suzanne's card is shown to Heather. Heather's card is shown to Claudia. Claudia's card is shown to Claudia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heather can now know that Frank picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Heather","Claudia","Suzanne"],"index":1566,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982725382,"difficulty":0.0017274618}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristina's card is shown to Bernard. Kristina's card is shown to Kristina. Kristina's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Kristina does not know whether or not everyone picked a red card. It is publicly announced that Kristina does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Bernard can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kevin","Bernard","Kristina","Karen"],"index":44456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Tamika. Tamika's card is shown to Jacquelin. It is publicly announced that someone picked a red card. It is publicly announced that Tamika does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jacquelin can now know that Tamika can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tamika","Jacquelin","Matthew","Richard"],"index":58103,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.506816566,"difficulty":1.506816566}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alden's card is shown to David. David's card is shown to Alden. Jack's card is shown to Alden. Alden's card is shown to Alden. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jack can now know that David can know whether Jack picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Jack","Alden"],"index":51834,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6564028859,"difficulty":0.3435971141}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alicia's card is shown to Steven. Alicia's card is shown to Wilma. Steven's card is shown to Alicia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know whether Alicia can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Wilma","Alicia"],"index":65294,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997788072,"difficulty":0.0002211928}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jill's card is shown to James. James's card is shown to Gabrielle. James's card is shown to Jill. It is publicly announced that someone picked a red card. It is publicly announced that Jill does not know whether Jill picked a red card. It is publicly announced that Gabrielle knows whether or not everyone picked a red card. It is publicly announced that Gabrielle picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 2 ] (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Jill can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Gabrielle","Jill"],"index":29910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6182409525,"difficulty":0.3817590475}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Genevieve's card is shown to Blanche. Blanche's card is shown to Mary. Genevieve's card is shown to Mary. Blanche's card is shown to Genevieve. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Genevieve can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Blanche","Mary","Genevieve"],"index":19134,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983640313,"difficulty":0.0016359687}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joshua's card is shown to Xavier. Margaret's card is shown to Xavier. Xavier's card is shown to Joshua. Xavier's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Joshua does not know whether Joshua picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Joshua can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Xavier","Joshua","Margaret"],"index":53864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9741904736,"difficulty":0.0258095264}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Phillip. Dane's card is shown to Dane. Robert's card is shown to Dane. Robert's card is shown to Justin. Justin's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Dane can know whether Phillip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phillip","Dane","Justin","Robert"],"index":37850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986153841,"difficulty":0.0013846159}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessie's card is shown to Jessie. Ella's card is shown to Ella. Jessie's card is shown to Max. It is publicly announced that someone picked a red card. It is publicly announced that Max does not know whether Max picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ella can now know whether Ella picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jessie","Ella","Max"],"index":18643,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9451605678,"difficulty":0.0548394322}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Benjamin's card is shown to Benjamin. Mary's card is shown to Carol. Benjamin's card is shown to Carol. Rena's card is shown to Carol. Mary's card is shown to Rena. Rena's card is shown to Rena. It is publicly announced that someone picked a red card. It is publicly announced that Carol does not know whether Carol picked a red card. It is publicly announced that Benjamin does not know whether Carol picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Mary can now know that Benjamin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Benjamin","Carol","Rena"],"index":34126,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9853255153,"difficulty":0.0146744847}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luis's card is shown to Luis. Darrell's card is shown to Luis. Luis's card is shown to Mary. Luis's card is shown to Darrell. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know whether Darrell picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Luis","Mary","Darrell"],"index":57172,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8734334111,"difficulty":1.8734334111}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julia's card is shown to Ophelia. Ophelia's card is shown to Todd. Julia's card is shown to Todd. Ophelia's card is shown to Julia. It is publicly announced that someone picked a red card. It is publicly announced that Ophelia does not know whether Ophelia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Julia can now know whether Todd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ophelia","Todd","Julia"],"index":6853,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9103986621,"difficulty":0.0896013379}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Buford's card is shown to Alfred. Suzanne's card is shown to Alfred. Buford's card is shown to Paul. Suzanne's card is shown to Paul. Paul's card is shown to Suzanne. Suzanne's card is shown to Suzanne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paul can now know whether Buford can know whether Suzanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfred","Paul","Buford","Suzanne"],"index":62846,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983536005,"difficulty":0.0016463995}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bertha's card is shown to Bertha. Bertha's card is shown to Rita. Tyson's card is shown to Rita. Rita's card is shown to Tyson. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rita can now know that Bertha can know that Rita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bertha","Rita","Tyson"],"index":42513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964283109,"difficulty":0.0035716891}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Anna. Anna's card is shown to Beryl. It is publicly announced that someone picked a red card. It is publicly announced that Beryl knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Anna can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Anna","Beryl"],"index":18828,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983341098,"difficulty":0.0016658902}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clifford's card is shown to Justin. Justin's card is shown to Mirta. Mirta's card is shown to Mirta. Justin's card is shown to Clifford. Mirta's card is shown to Clifford. Clifford's card is shown to Clifford. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mirta can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Justin","Mirta","Clifford"],"index":28957,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.986803472,"difficulty":0.013196528}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Michael's card is shown to Lisa. Michael's card is shown to Kira. It is publicly announced that someone picked a red card. It is publicly announced that Kira does not know whether Lisa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Kira can now know that Kira picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Lisa","Kira"],"index":48231,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949643612,"difficulty":0.0050356388}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dona's card is shown to Dona. Dona's card is shown to Leona. It is publicly announced that someone picked a red card. It is publicly announced that Leona does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Dona can now know whether Leona can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dona","Leona"],"index":65014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994997978,"difficulty":0.0005002022}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Rose. Robert's card is shown to Robert. Patricia's card is shown to Robert. Robert's card is shown to Rita. Rita's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rose can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rose","Robert","Rita","Patricia"],"index":5144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olga's card is shown to Olga. Michael's card is shown to Olga. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether Michael picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Olga can now know that Michael can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Olga","Michael"],"index":25852,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983357787,"difficulty":0.0016642213}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to William. Karen's card is shown to Karen. Sergio's card is shown to Karen. Karen's card is shown to Sergio. William's card is shown to Antonio. Karen's card is shown to Antonio. Antonio's card is shown to Antonio. It is publicly announced that someone picked a red card. It is publicly announced that Antonio picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Karen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Karen","Sergio","Antonio"],"index":53830,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Lewis. Rosemary's card is shown to Lewis. Rosemary's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Lewis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lewis","Thomas","Rosemary"],"index":11082,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983545542,"difficulty":0.0016454458}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwight's card is shown to Sally. Bobby's card is shown to Billy. Dwight's card is shown to Dwight. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sally can now know that Dwight can know whether Dwight picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sally","Billy","Dwight","Bobby"],"index":11131,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9877564907,"difficulty":0.0122435093}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Dorothy's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] (Agentb knows whether (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dorothy","Mary"],"index":58395,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999763906,"difficulty":0.000236094}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to Bobby. Monica's card is shown to Monica. Christian's card is shown to Christian. It is publicly announced that someone picked a red card. It is publicly announced that Monica does not know whether Bobby picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Christian can now know that Monica can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bobby","Monica","Christian"],"index":9132,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Suzanne's card is shown to Suzanne. Gary's card is shown to Gary. Gabriel's card is shown to Gary. Gary's card is shown to Gabriel. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Gabriel does not know whether Gabriel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Suzanne can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Suzanne","Gary","Gabriel"],"index":51884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986363053,"difficulty":0.0013636947}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ira's card is shown to Ira. Danielle's card is shown to Danielle. Danielle's card is shown to Hazel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ira can now know whether Hazel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ira","Danielle","Hazel"],"index":4515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9496871233,"difficulty":0.0503128767}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Leah. Shirley's card is shown to Leah. Leah's card is shown to Lynn. Richard's card is shown to Lynn. Shirley's card is shown to Lynn. Leah's card is shown to Richard. Lynn's card is shown to Shirley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Shirley can know whether Leah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leah","Lynn","Richard","Shirley"],"index":57286,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5462184548,"difficulty":1.5462184548}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jon's card is shown to Linda. Jon's card is shown to Jon. Jennifer's card is shown to Jon. Joel's card is shown to Jon. Joel's card is shown to Jennifer. Jon's card is shown to Joel. Joel's card is shown to Joel. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Linda picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Jon can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Jon","Jennifer","Joel"],"index":22390,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940152764,"difficulty":0.0059847236}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Joseph's card is shown to Delores. Joseph's card is shown to Janice. Delores's card is shown to Janice. William's card is shown to Janice. Delores's card is shown to William. Janice's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Delores can know whether Janice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Delores","Janice","William"],"index":15120,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5185596943,"difficulty":1.5185596943}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeff's card is shown to Julie. Julie's card is shown to Michael. Michael's card is shown to Joseph. Julie's card is shown to Jeff. Jeff's card is shown to Jeff. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Joseph picked a red card. It is publicly announced that Julie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jeff can now know that Julie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Michael","Joseph","Jeff"],"index":2723,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6789783239,"difficulty":0.3210216761}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Richard. Richard's card is shown to Richard. Harold's card is shown to Richard. Ronald's card is shown to Harold. Alisa's card is shown to Harold. Alisa's card is shown to Alisa. It is publicly announced that someone picked a red card. It is publicly announced that Alisa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Harold can now know that Ronald can know that Harold picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Richard","Harold","Alisa"],"index":29950,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9162185788,"difficulty":0.0837814212}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Maria. Irma's card is shown to Maria. Irma's card is shown to Claretha. Richard's card is shown to Richard. Claretha's card is shown to Irma. Irma's card is shown to Irma. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether someone picked a red card. It is publicly announced that Maria picked a red card. It is publicly announced that Claretha does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Richard can now know that Claretha can know whether Claretha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Claretha","Richard","Irma"],"index":24412,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6484274268,"difficulty":0.3515725732}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to Dolly. Dolly's card is shown to Janice. Claudia's card is shown to Janice. Dolly's card is shown to Claudia. It is publicly announced that someone picked a red card. It is publicly announced that Dolly does not know whether Claudia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Claudia can now know that Janice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dolly","Janice","Claudia"],"index":44076,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949871302,"difficulty":0.0050128698}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Anna. Anna's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Anna knows whether John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anna","John"],"index":3580,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997224212,"difficulty":0.0002775788}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Cynthia. Jamie's card is shown to Cynthia. Charles's card is shown to Cynthia. Jamie's card is shown to Jamie. Charles's card is shown to Jamie. Cynthia's card is shown to Charles. Annette's card is shown to Annette. It is publicly announced that someone picked a red card. It is publicly announced that Jamie does not know whether Annette picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Charles can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cynthia","Jamie","Charles","Annette"],"index":22427,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9414127469,"difficulty":1.9414127469}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to James. Mark's card is shown to James. Leslie's card is shown to Leslie. It is publicly announced that someone picked a red card. It is publicly announced that Leslie knows whether Leslie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Leslie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Leslie","Mark"],"index":35103,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984841943,"difficulty":0.0015158057}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a black card. It is publicly announced that Michael knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Peter"],"index":14039,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7689444423,"difficulty":1.7689444423}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robbie's card is shown to Robbie. Tammy's card is shown to Robbie. Aaron's card is shown to Tammy. Aaron's card is shown to Aaron. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robbie can now know that Tammy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robbie","Tammy","Aaron"],"index":52146,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983640313,"difficulty":0.0016359687}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Joan's card is shown to Leslie. Leslie's card is shown to Leslie. Leslie's card is shown to Ruth. Joan's card is shown to Emma. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Emma picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Emma can now know whether Joan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joan","Leslie","Ruth","Emma"],"index":41747,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8969265819,"difficulty":0.1030734181}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Jerry. Jerry's card is shown to Jason. Jason's card is shown to Jason. Jeffrey's card is shown to Jason. Jason's card is shown to Nichole. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know that Nichole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Jason","Nichole","Jeffrey"],"index":24702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974370003,"difficulty":0.0025629997}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Paul's card is shown to Stephen. Stephen's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephen","Paul","Mark"],"index":66927,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997722507,"difficulty":0.0002277493}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Carolyn. Stephanie's card is shown to Carolyn. Linda's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carolyn can now know whether Stephanie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carolyn","Stephanie","Linda"],"index":12004,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9165451527,"difficulty":0.0834548473}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Malena's card is shown to Richard. Malena's card is shown to Malena. Leon's card is shown to Malena. Malena's card is shown to Lisa. Lisa's card is shown to Lisa. Leon's card is shown to Leon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Leon can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Malena","Lisa","Leon"],"index":59811,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999773562,"difficulty":0.000226438}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Frank's card is shown to Mark. Rhonda's card is shown to Dawn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","Dawn","Rhonda","Frank"],"index":42494,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997687936,"difficulty":0.0002312064}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wallace's card is shown to Jessica. Samantha's card is shown to Jessica. Wallace's card is shown to Melissa. Melissa's card is shown to Melissa. Samantha's card is shown to Melissa. Jessica's card is shown to Samantha. Wallace's card is shown to Samantha. Samantha's card is shown to Samantha. It is publicly announced that someone picked a red card. It is publicly announced that Melissa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Melissa can now know whether Wallace can know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Wallace","Melissa","Samantha"],"index":19050,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982950091,"difficulty":0.0017049909}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Lisa. Catherine's card is shown to Lisa. Bruce's card is shown to Bruce. Catherine's card is shown to Bruce. Bruce's card is shown to Michael. Michael's card is shown to Michael. Lisa's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Catherine picked a red card. It is publicly announced that Lisa does not know whether Bruce picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Bruce can now know whether Lisa can know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Bruce","Michael","Catherine"],"index":45539,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9078022242,"difficulty":1.9078022242}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Christopher. Carol's card is shown to Carol. Marvin's card is shown to Marvin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Carol","Marvin"],"index":38895,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955588579,"difficulty":0.0044411421}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelia's card is shown to Millicent. Leila's card is shown to Willie. Millicent's card is shown to Willie. Willie's card is shown to Angelia. It is publicly announced that someone picked a red card. It is publicly announced that Leila knows whether Angelia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Willie can now know that Millicent can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leila","Millicent","Willie","Angelia"],"index":48600,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998457551,"difficulty":0.001542449}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Laura. Geoffrey's card is shown to Laura. Laura's card is shown to Geoffrey. Alan's card is shown to Geoffrey. Laura's card is shown to Alan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Geoffrey can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Laura","Geoffrey","Alan"],"index":41081,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997252822,"difficulty":0.0002747178}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Elizabeth. Debra's card is shown to Debra. Elizabeth's card is shown to Maria. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Debra does not know whether Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Maria can now know that Debra can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","Debra","Maria"],"index":7302,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997783303,"difficulty":0.0002216697}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Billy. Wesley's card is shown to Billy. Billy's card is shown to Wesley. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Billy can now know that Billy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Billy","James","Wesley"],"index":55799,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9806720614,"difficulty":0.0193279386}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hilda's card is shown to Lester. Jose's card is shown to Hilda. Lester's card is shown to Jose. Hilda's card is shown to Jose. Jose's card is shown to Jose. It is publicly announced that someone picked a red card. It is publicly announced that Hilda knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jose can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lester","Hilda","Jose"],"index":24896,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984978437,"difficulty":0.0015021563}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Brian. Reba's card is shown to James. James's card is shown to James. Brian's card is shown to Genevieve. James's card is shown to Genevieve. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know that Reba picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Reba","Brian","James","Genevieve"],"index":38629,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981421232,"difficulty":0.0018578768}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adelaide's card is shown to Adelaide. Kevin's card is shown to Adelaide. Adelaide's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Kevin does not know whether Kevin picked a red card. It is publicly announced that Kevin does not know whether or not everyone picked a red card. It is publicly announced that Kevin picked a red card. It is publicly announced that Kevin picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] [ ! 2 ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Adelaide can now know whether Kevin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Adelaide","Kevin"],"index":45659,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9865356088,"difficulty":0.0134643912}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Arianne. Robert's card is shown to Robert. Arianne's card is shown to Maxine. Maxine's card is shown to Maxine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maxine can now know whether Maxine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Arianne","Robert","Maxine"],"index":11444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9828621745,"difficulty":0.0171378255}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Shirley. Robert's card is shown to Robert. Bobby's card is shown to Robert. Shirley's card is shown to Bobby. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Judy picked a red card. It is publicly announced that Judy does not know whether Judy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Robert can now know whether Judy can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Judy","Robert","Bobby"],"index":53014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970811009,"difficulty":0.0029188991}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. Kathy's card is shown to Gregory. Gregory's card is shown to Kathy. Julie's card is shown to Avis. Kathy's card is shown to Avis. Avis's card is shown to Avis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Julie can now know that Gregory can know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julie","Gregory","Kathy","Avis"],"index":61546,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.938996017,"difficulty":0.061003983}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Verona's card is shown to Jamie. Jamie's card is shown to Verona. Jamie's card is shown to Allison. Verona's card is shown to Allison. Allison's card is shown to Allison. It is publicly announced that someone picked a red card. It is publicly announced that Allison knows whether Verona picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Allison can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jamie","Verona","Allison"],"index":11181,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Estelle's card is shown to Timothy. Patricia's card is shown to Matthew. Matthew's card is shown to Estelle. Estelle's card is shown to Estelle. Patricia's card is shown to Estelle. Matthew's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Estelle can now know whether Timothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Matthew","Estelle","Patricia"],"index":18463,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8242865801,"difficulty":0.1757134199}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Justin. Justin's card is shown to Josefa. Richard's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know that Justin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Richard","Josefa","Lisa"],"index":40480,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974271655,"difficulty":0.0025728345}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Paula. Paula's card is shown to Theresa. Theresa's card is shown to Theresa. Theresa's card is shown to John. Theresa's card is shown to April. John's card is shown to April. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"April can now know whether Paula can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Theresa","John","April"],"index":34398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995651841,"difficulty":0.0004348159}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Shari. Shari's card is shown to John. Fred's card is shown to John. William's card is shown to John. Shari's card is shown to Fred. Fred's card is shown to Fred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fred can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shari","John","Fred","William"],"index":61602,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983862638,"difficulty":0.0016137362}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Virginia. Melvin's card is shown to Virginia. Melvin's card is shown to Melvin. Oscar's card is shown to Melvin. Christopher's card is shown to Oscar. Oscar's card is shown to Oscar. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know whether Oscar picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Virginia","Melvin","Christopher","Oscar"],"index":12997,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.871288836,"difficulty":0.128711164}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Lee. Lee's card is shown to Ashli. Ashli's card is shown to Ashli. Lee's card is shown to Frederick. Ashli's card is shown to Frederick. Lee's card is shown to Jennifer. Jennifer's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Ashli picked a black card. It is publicly announced that Ashli does not know whether Jennifer picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lee can now know that Frederick can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lee","Ashli","Frederick","Jennifer"],"index":32963,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6836388111,"difficulty":0.3163611889}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alexandria's card is shown to Joyce. Joyce's card is shown to Marina. Alexandria's card is shown to Marina. Marina's card is shown to Rosa. Joyce's card is shown to Alexandria. Rosa's card is shown to Alexandria. It is publicly announced that someone picked a red card. It is publicly announced that Alexandria does not know whether Alexandria picked a red card. It is publicly announced that Joyce knows whether or not nobody picked a red card. It is publicly announced that Rosa picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentc knows that (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Rosa can now know that Alexandria can know that Alexandria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Marina","Rosa","Alexandria"],"index":25880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7472211123,"difficulty":0.2527788877}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Jeffrey. Luis's card is shown to Jeffrey. Jeffrey's card is shown to Bruce. Bruce's card is shown to Bruce. Luis's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Bruce knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc: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:2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jeffrey can now know whether Bruce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffrey","Bruce","Luis"],"index":21540,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6863513589,"difficulty":1.6863513589}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Danielle. John's card is shown to Barbara. Danielle's card is shown to John. Barbara's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb: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 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Barbara can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Danielle","Barbara","John"],"index":43017,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guillermo's card is shown to Guillermo. Marie's card is shown to Marie. Guillermo's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Marie can now know that David can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Guillermo","Marie","David"],"index":39544,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9430311322,"difficulty":0.0569688678}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Jessica. Robert's card is shown to Jessica. Michael's card is shown to Michael. Jessica's card is shown to Joan. Michael's card is shown to Joan. Jessica's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Joan picked a red card. It is publicly announced that Joan does not know whether Joan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Robert can now know whether Michael can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Michael","Joan","Robert"],"index":13402,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995589852,"difficulty":0.0004410148}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Horace. Horace's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Timothy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Horace can now know whether Timothy can know whether Timothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Horace","Timothy"],"index":12646,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9951964021,"difficulty":0.0048035979}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vincent's card is shown to Ginger. Kathleen's card is shown to Ginger. Kathleen's card is shown to Kathleen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vincent can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vincent","Ginger","Ruby","Kathleen"],"index":65720,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949087501,"difficulty":0.0050912499}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Ann. George's card is shown to Ann. George's card is shown to Paula. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Paula does not know whether or not everyone picked a red card. It is publicly announced that George does not know whether Paula picked a red card. It is publicly announced that George does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"George can now know that Ann picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ann","Paula","George"],"index":23245,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5521969199,"difficulty":0.4478030801}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamela's card is shown to Mitchell. Mitchell's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Mitchell does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mitchell can now know whether Richard can know that Mitchell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mitchell","Richard","Pamela"],"index":49453,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9609717727,"difficulty":1.9609717727}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arleen's card is shown to Mary. Louis's card is shown to Arleen. Arleen's card is shown to Arleen. Kenneth's card is shown to Arleen. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth picked a red card. It is publicly announced that Louis knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (1&2&3&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:3 Agentb:1,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Arleen can now know that Mary can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Louis","Mary","Arleen","Kenneth"],"index":58825,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978681803,"difficulty":0.0021318197}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Joseph. Joseph's card is shown to Eva. Joseph's card is shown to Araceli. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eva can now know that Joseph can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Eva","Araceli"],"index":37712,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984397292,"difficulty":0.0015602708}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brianna's card is shown to Brianna. Marian's card is shown to Jonah. Jonah's card is shown to Marian. Marian's card is shown to Marian. Brianna's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Joshua knows whether Brianna picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Joshua can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brianna","Jonah","Marian","Joshua"],"index":44080,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Michael's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Margaret does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Margaret can now know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Margaret"],"index":20713,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9640715122,"difficulty":1.9640715122}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grady's card is shown to Grady. Frank's card is shown to Robert. Eloise's card is shown to Frank. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Grady picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eloise","Grady","Robert","Frank"],"index":4026,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7152653933,"difficulty":1.7152653933}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Dale. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Dale picked a red card. It is publicly announced that Dale knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Michael can now know that Dale can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dale","Michael"],"index":55267,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5243933797,"difficulty":1.5243933797}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristie's card is shown to Katherine. Anna's card is shown to Anna. Dwayne's card is shown to Anna. Kristie's card is shown to Dwayne. Anna's card is shown to Kristie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Katherine can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Katherine","Anna","Dwayne","Kristie"],"index":42218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9928863645,"difficulty":0.0071136355}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darlene's card is shown to Darlene. Thomas's card is shown to Thomas. Thomas's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Darlene picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Andre can now know whether Thomas can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlene","Thomas","Andre","Michael"],"index":15079,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.994189024,"difficulty":0.005810976}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herman's card is shown to Tanner. Tanner's card is shown to Herman. Shirley's card is shown to Brenda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Herman can now know whether Tanner picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","Tanner","Herman","Brenda"],"index":51526,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6720391512,"difficulty":0.3279608488}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sophie's card is shown to Joan. Douglas's card is shown to Joan. Joan's card is shown to Stacie. Stacie's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Sophie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Joan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sophie","Joan","Stacie","Douglas"],"index":47618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9843450189,"difficulty":0.0156549811}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Archie. Archie's card is shown to Sharon. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether or not everyone picked a red card. It is publicly announced that Sharon does not know whether Sharon picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Sharon can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Archie","Sharon"],"index":10651,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Trent. Evelyn's card is shown to Evelyn. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Trent can now know whether Mary can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Trent","Evelyn","Nancy"],"index":62982,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999538064,"difficulty":0.000461936}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Randall. Derek's card is shown to Randall. Randall's card is shown to Derek. Frederick's card is shown to Derek. Randall's card is shown to Frederick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Derek can now know whether Derek picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Randall","Derek","Frederick"],"index":54589,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7189929485,"difficulty":1.7189929485}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffany's card is shown to Roberto. Tiffany's card is shown to Tiffany. It is publicly announced that someone picked a red card. It is publicly announced that Roberto does not know whether or not everyone picked a red card. It is publicly announced that Roberto does not know whether or not everyone picked a red card. It is publicly announced that Roberto knows whether someone picked a red card. It is publicly announced that Tiffany knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Roberto can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roberto","Tiffany"],"index":15305,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997133613,"difficulty":0.0002866387}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sonja's card is shown to Cheryl. Sonja's card is shown to Sonja. Ruthie's card is shown to Ruthie. Sonja's card is shown to Jean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruthie can now know that Jean can know that Jean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Sonja","Ruthie","Jean"],"index":650,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979168773,"difficulty":0.0020831227}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felicita's card is shown to Felicita. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Felicita can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Felicita","David"],"index":12927,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997783303,"difficulty":0.0002216697}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Evelyn. Helen's card is shown to Evelyn. Evelyn's card is shown to John. John's card is shown to Matthew. Helen's card is shown to Matthew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Evelyn can know whether Helen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Evelyn","John","Helen","Matthew"],"index":36523,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.62172997,"difficulty":1.62172997}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jon's card is shown to Monique. Carla's card is shown to Monique. Jon's card is shown to Carla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Monique","Jon","Carla"],"index":12729,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999722898,"difficulty":0.000277102}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Brian. John's card is shown to Brian. Brian's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 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:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know that Brian can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Karen","John"],"index":16356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925691485,"difficulty":0.0074308515}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Mavis. Christopher's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Christopher can now know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mavis","Christopher","Margaret"],"index":40531,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6061878204,"difficulty":1.6061878204}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Myrtle. Rose's card is shown to Benjamin. Benjamin's card is shown to Rose. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Benjamin can now know that Myrtle can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Myrtle","Benjamin","Rose"],"index":65066,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985886216,"difficulty":0.0014113784}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Evelyn. Louis's card is shown to Evelyn. Matthew's card is shown to Matthew. Matthew's card is shown to Louis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Matthew can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Matthew","Louis"],"index":59513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985057116,"difficulty":0.0014942884}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeana's card is shown to Jeana. Patricia's card is shown to Jeana. Maxine's card is shown to Jeana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeana can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeana","Patricia","Maxine"],"index":5181,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998334229,"difficulty":0.001665771}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Mark's card is shown to Martha. Martha's card is shown to Martha. Martha's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mark can now know whether Martha can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Martha","Michael"],"index":36158,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999524951,"difficulty":0.000475049}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norma's card is shown to Cynthia. Carroll's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether Cynthia picked a red card. It is publicly announced that Carroll knows whether Norma picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Cynthia can now know that Carroll can know whether Carroll picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carroll","Cynthia","William","Norma"],"index":39497,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9840754867,"difficulty":1.9840754867}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nia's card is shown to Michael. Nia's card is shown to Mary. Nia's card is shown to Nia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Mary","Nia"],"index":64126,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983287454,"difficulty":0.0016712546}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Alonzo. Alonzo's card is shown to Harry. Harry's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Alonzo does not know whether Harry picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Alonzo can now know whether Mary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alonzo","Mary","Harry"],"index":42160,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9955940843,"difficulty":0.0044059157}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurine's card is shown to Dale. Todd's card is shown to Dale. Todd's card is shown to Glenn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dale can now know whether Maurine can know that Dale picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dale","Maurine","Glenn","Todd"],"index":17136,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6449739933,"difficulty":1.6449739933}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adriana's card is shown to Lillian. Lillian's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Adriana knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Lillian can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adriana","Lillian","Mary"],"index":981,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983657002,"difficulty":0.0016342998}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Clark. Clark's card is shown to James. Gertrude's card is shown to James. Gertrude's card is shown to Gertrude. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc: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:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clark can now know that James can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clark","James","Gertrude"],"index":66863,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9847988486,"difficulty":0.0152011514}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rowena's card is shown to Rowena. Ashley's card is shown to David. Ashley's card is shown to Kurt. Rowena's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that Kurt picked a red card. It is publicly announced that Kurt does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Rowena can now know that David can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rowena","David","Kurt","Ashley"],"index":4305,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985468984,"difficulty":0.0014531016}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobby's card is shown to Bobby. Bobby's card is shown to Paulina. Bobby's card is shown to Laura. Brian's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Bobby knows whether or not everyone picked a red card. It is publicly announced that Paulina knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Bobby can now know that Bobby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bobby","Paulina","Laura","Brian"],"index":53947,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9243687987,"difficulty":1.9243687987}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christina's card is shown to Christina. Kelly's card is shown to Christina. Christina's card is shown to Greg. Greg's card is shown to Greg. Kelly's card is shown to Greg. Christina's card is shown to Kelly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Greg can now know that Kelly can know whether Kelly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christina","Greg","Kelly"],"index":7602,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9669226408,"difficulty":1.9669226408}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Paula. Amber's card is shown to Chris. Paula's card is shown to Elizabeth. Amber's card is shown to Elizabeth. Amber's card is shown to Amber. It is publicly announced that someone picked a red card. It is publicly announced that Paula knows whether Chris picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Chris can now know whether Amber can know whether Paula picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Chris","Elizabeth","Amber"],"index":3941,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980194569,"difficulty":0.0019805431}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Mark. Osvaldo's card is shown to Osvaldo. Mark's card is shown to Darrell. Osvaldo's card is shown to Edith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know whether Darrell can know that Osvaldo picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Osvaldo","Darrell","Edith"],"index":39910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.871088922,"difficulty":0.128911078}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Charles. Andrea's card is shown to Charles. Andrea's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Andrea picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb: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:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Clarence can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Clarence","Andrea"],"index":26914,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyung's card is shown to Kyung. Kyung's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Willie does not know whether Willie picked a red card. It is publicly announced that Kyung does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 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 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Kyung can now know that Willie can know that Kyung picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kyung","Willie"],"index":46105,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6786722541,"difficulty":0.3213277459}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Roy. James's card is shown to Roy. Roy's card is shown to Sarah. Sarah's card is shown to Sarah. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sarah can now know that James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roy","Sarah","James"],"index":19011,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964093566,"difficulty":0.0035906434}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Andrea. Andrea's card is shown to James. James's card is shown to Brett. Brett's card is shown to Brett. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Andrea can now know whether Brett can know whether Andrea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Andrea","James","Brett"],"index":1836,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9978269935,"difficulty":1.9978269935}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sonya's card is shown to Sam. Sam's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. Sam's card is shown to Sonya. Jeffrey's card is shown to Sharon. Sharon's card is shown to Sharon. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether Sonya picked a red card. It is publicly announced that Sam knows whether Sonya picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Sam can now know that Jeffrey can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sam","Jeffrey","Sonya","Sharon"],"index":41894,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997830987,"difficulty":0.0002169013}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denis's card is shown to Donald. Denis's card is shown to Edmund. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Denis can now know that Donald can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Denis","Edmund"],"index":6822,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9901245236,"difficulty":0.0098754764}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to George. Arthur's card is shown to Jesus. George's card is shown to Arthur. Arthur's card is shown to Arthur. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jesus can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Jesus","Arthur"],"index":22199,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983248115,"difficulty":0.0016751885}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Annie. David's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Annie can now know that David can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Annie","David","Patricia"],"index":9140,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Chas's card is shown to Chas. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb: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:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Helen can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Helen","Chas"],"index":41620,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984667897,"difficulty":0.0015332103}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Deborah. Juanita's card is shown to Linda. Juanita's card is shown to Marcos. Linda's card is shown to Marcos. Marcos's card is shown to Marcos. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Juanita can now know that Juanita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Juanita","Linda","Marcos"],"index":59348,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8463759422,"difficulty":0.1536240578}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilber's card is shown to Wayne. Douglas's card is shown to Wayne. Wilber's card is shown to Wilber. Douglas's card is shown to Wilber. Douglas's card is shown to Jamie. Wilber's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Jamie does not know whether Wilber picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentd knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Douglas can now know whether Wilber can know that Douglas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wayne","Wilber","Jamie","Douglas"],"index":21728,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.873093307,"difficulty":1.873093307}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jamie's card is shown to Jamie. Kathleen's card is shown to Jamie. Margarita's card is shown to Jamie. Jamie's card is shown to Barbara. Kathleen's card is shown to Barbara. Margarita's card is shown to Kathleen. Jamie's card is shown to Margarita. Kathleen's card is shown to Margarita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Jamie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jamie","Barbara","Kathleen","Margarita"],"index":11809,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997807145,"difficulty":0.0002192855}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Emil. Jared's card is shown to Jared. It is publicly announced that someone picked a red card. It is publicly announced that Jared does not know whether or not everyone picked a red card. It is publicly announced that Emil picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Emil can now know that Jared can know that Jared picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Emil","Jared"],"index":14989,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.976744473,"difficulty":0.023255527}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Billy. William's card is shown to Billy. Billy's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"William can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Billy","William"],"index":42682,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9955174327,"difficulty":0.0044825673}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Kevin. Naomi's card is shown to Naomi. Boyd's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Boyd does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Boyd can now know that Boyd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Boyd","Kevin","Naomi","Harold"],"index":25045,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8338783979,"difficulty":1.8338783979}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Earl's card is shown to Michael. Robert's card is shown to Michael. Earl's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Francis does not know whether Francis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Francis can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Michael","Earl","Robert"],"index":57932,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997105002,"difficulty":0.0002894998}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Doris. David's card is shown to Doris. Nathaniel's card is shown to Nancy. David's card is shown to David. David's card is shown to Nathaniel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nathaniel can now know whether Doris can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Nancy","David","Nathaniel"],"index":65390,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8897590041,"difficulty":0.1102409959}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Bonnie. Jack's card is shown to Bonnie. Mark's card is shown to Jack. Mark's card is shown to Roger. Jack's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jack can now know that Bonnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bonnie","Jack","Roger","Mark"],"index":67584,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981909394,"difficulty":0.0018090606}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Robert. Alfonso's card is shown to Robert. Robert's card is shown to Richard. Richard's card is shown to Richard. Alfonso's card is shown to Richard. Robert's card is shown to Alfonso. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Alfonso can now know that Richard can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Richard","Alfonso"],"index":46452,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967903495,"difficulty":0.0032096505}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugenia's card is shown to Eugenia. Eugenia's card is shown to Ramona. Eugenia's card is shown to Darrin. It is publicly announced that someone picked a red card. It is publicly announced that Darrin does not know whether Ramona picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Darrin can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eugenia","Ramona","Darrin"],"index":8057,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997256398,"difficulty":0.0002743602}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Joshua's card is shown to Donald. Barbara's card is shown to Joshua. Donald's card is shown to Sal. Sal's card is shown to Sal. It is publicly announced that someone picked a red card. It is publicly announced that Joshua picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Donald can now know that Joshua can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Donald","Joshua","Sal"],"index":41753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985327721,"difficulty":0.0014672279}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Craig. James's card is shown to Craig. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Craig picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"James can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Craig","James"],"index":64766,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999720633,"difficulty":0.000279367}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Sarah. Sarah's card is shown to Teresa. David's card is shown to Teresa. Sarah's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know that Teresa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Teresa","David"],"index":33569,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983680844,"difficulty":0.0016319156}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Raquel. Raquel's card is shown to Kimberly. Erin's card is shown to Kimberly. Raquel's card is shown to Erin. Kimberly's card is shown to Erin. It is publicly announced that someone picked a red card. It is publicly announced that Raquel knows whether or not nobody picked a red card. It is publicly announced that Erin does not know whether Erin picked a red card. It is publicly announced that Erin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Raquel can now know that Erin can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raquel","Kimberly","Erin","Sarah"],"index":6493,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnold's card is shown to Arnold. Joaquin's card is shown to Arnold. Joaquin's card is shown to Joaquin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Arnold can now know whether Joaquin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arnold","Joaquin"],"index":30116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997084737,"difficulty":0.0002915263}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lida's card is shown to Lida. Lida's card is shown to Louis. Kurt's card is shown to Louis. Kurt's card is shown to Kurt. Kurt's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd: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 Agentb:1,3 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kurt can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lida","Louis","Kurt","Patricia"],"index":25531,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andy's card is shown to Randy. Kenneth's card is shown to Randy. Andy's card is shown to Andy. Jamie's card is shown to Andy. Randy's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Randy's card is shown to Jamie. Kenneth's card is shown to Jamie. It is publicly announced that someone picked a red card. It is publicly announced that Andy does not know whether Kenneth picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1,3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1,3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Andy can now know whether Randy can know that Randy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Andy","Kenneth","Jamie"],"index":22553,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8993630409,"difficulty":0.1006369591}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Warren's card is shown to Warren. Donald's card is shown to Warren. Warren's card is shown to Heriberto. Warren's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Heriberto can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Warren","Heriberto","Donald"],"index":48621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997733235,"difficulty":0.0002266765}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emma's card is shown to Anna. Anna's card is shown to Stephan. Stephan's card is shown to Stephan. Bertha's card is shown to Stephan. Emma's card is shown to Stephan. Stephan's card is shown to Bertha. Emma's card is shown to Emma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bertha can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anna","Stephan","Bertha","Emma"],"index":19743,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997802377,"difficulty":0.0002197623}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rafael's card is shown to Rafael. Ellen's card is shown to Maria. Maria's card is shown to Chris. Ellen's card is shown to Chris. Chris's card is shown to Chris. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Rafael picked a red card. It is publicly announced that Maria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 2 ] Agentc knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Ellen can now know whether Maria can know that Chris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rafael","Maria","Ellen","Chris"],"index":26532,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9482775331,"difficulty":0.0517224669}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Christoper. Wayne's card is shown to Wayne. Christoper's card is shown to Diane. Wayne's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Diane picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Wayne can now know that Diane can know whether Wayne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christoper","Wayne","Diane","Melissa"],"index":18426,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9643449187,"difficulty":1.9643449187}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lessie's card is shown to Lessie. Ruth's card is shown to Lessie. Helen's card is shown to Nevada. Ruth's card is shown to Nevada. Lessie's card is shown to Helen. Ruth's card is shown to Helen. Lessie's card is shown to Ruth. Nevada's card is shown to Ruth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know whether Lessie can know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lessie","Nevada","Helen","Ruth"],"index":63019,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8457663059,"difficulty":1.8457663059}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Lisa's card is shown to Henry. Henry's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta 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 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Henry can now know whether Henry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathleen","Henry","Andrew","Lisa"],"index":15419,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9954679012,"difficulty":1.9954679012}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lewis's card is shown to Joseph. Alisha's card is shown to Joseph. Joseph's card is shown to Anthony. Lewis's card is shown to Anthony. Alisha's card is shown to Anthony. Joseph's card is shown to Lewis. Anthony's card is shown to Alisha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know that Alisha can know whether Lewis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Anthony","Lewis","Alisha"],"index":28618,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6553108692,"difficulty":1.6553108692}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Matthew. Jonathan's card is shown to Matthew. Matthew's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Robert picked a red card. It is publicly announced that Matthew knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Robert can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Robert","Jonathan"],"index":2255,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9882931113,"difficulty":0.0117068887}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mickie's card is shown to Anne. Mickie's card is shown to Mickie. Donna's card is shown to Mickie. Anne's card is shown to Donna. Donna's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anne can now know that Mickie can know that Anne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anne","Mickie","Donna"],"index":32360,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976186156,"difficulty":0.0023813844}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gaynelle's card is shown to Betty. Kristen's card is shown to Kristen. It is publicly announced that someone picked a red card. It is publicly announced that Betty picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb: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:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Betty can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betty","Gaynelle","Kristen"],"index":15100,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984679818,"difficulty":0.0015320182}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Craig. Cruz's card is shown to Craig. Edwin's card is shown to Craig. Cruz's card is shown to Cruz. Edwin's card is shown to Cruz. Cruz's card is shown to Wesley. Craig's card is shown to Edwin. Cruz's card is shown to Edwin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Craig can now know whether Edwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Craig","Cruz","Wesley","Edwin"],"index":25875,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5345227122,"difficulty":0.4654772878}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ezekiel's card is shown to Lisa. Lisa's card is shown to Jonelle. Jonelle's card is shown to Jonelle. Ezekiel's card is shown to Jonelle. Jonelle's card is shown to Ezekiel. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jonelle can now know whether Ezekiel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Jonelle","Ezekiel"],"index":27940,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7471250296,"difficulty":0.2528749704}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Scott's card is shown to Scott. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know whether Andrew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Scott","Dominique","Andrew"],"index":30618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9607226253,"difficulty":0.0392773747}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aldo's card is shown to Kathleen. Gabriel's card is shown to Kathleen. Gabriel's card is shown to Richard. Aldo's card is shown to Aldo. Richard's card is shown to Gabriel. Gabriel's card is shown to Gabriel. It is publicly announced that someone picked a red card. It is publicly announced that Aldo knows whether someone picked a red card. It is publicly announced that Kathleen picked a red card. It is publicly announced that Richard does not know whether Aldo picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Richard can now know that Gabriel can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","Richard","Aldo","Gabriel"],"index":19742,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997852445,"difficulty":0.0002147555}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Miriam's card is shown to Miriam. Marla's card is shown to Miriam. Jose's card is shown to Jose. Jose's card is shown to Marla. Marla's card is shown to Marla. Jose's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Miriam does not know whether Harry picked a red card. It is publicly announced that Marla picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(3) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(3) ] 0","hypothesis":"Miriam can now know that Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Miriam","Jose","Marla","Harry"],"index":45688,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9463752508,"difficulty":0.0536247492}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelly's card is shown to Theresa. Shelly's card is shown to Shelly. Alan's card is shown to Shelly. It is publicly announced that someone picked a red card. It is publicly announced that Theresa does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Theresa can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Theresa","Shelly","Lucille","Alan"],"index":49396,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlene's card is shown to Charlene. Ethel's card is shown to Charlene. Carol's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlene can now know whether Ethel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charlene","Ethel","Michael","Carol"],"index":24517,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9005775452,"difficulty":1.9005775452}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Shannon. Paul's card is shown to Shannon. Rickie's card is shown to Shannon. Shannon's card is shown to Paul. Rickie's card is shown to Paul. Rickie's card is shown to Rickie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rickie can now know that Rickie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shannon","Paul","Rickie"],"index":43333,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9913860559,"difficulty":0.0086139441}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Paul. Wanda's card is shown to Paul. Jonathan's card is shown to Paul. Paul's card is shown to Wanda. Wanda's card is shown to Wanda. Wanda's card is shown to Jonathan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wanda can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Debra","Wanda","Jonathan"],"index":67238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983587861,"difficulty":0.0016412139}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Roosevelt. Brenda's card is shown to Mark. Roosevelt's card is shown to Brenda. Mark's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Brenda does not know whether Brenda picked a red card. It is publicly announced that Roosevelt knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Roosevelt can now know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roosevelt","Mark","Brenda"],"index":9131,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6980827451,"difficulty":0.3019172549}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandy's card is shown to Brandy. William's card is shown to Brandy. William's card is shown to William. Thomas's card is shown to William. Brandy's card is shown to Thomas. William's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brandy can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brandy","William","Thomas"],"index":34435,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997788072,"difficulty":0.0002211928}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joy's card is shown to Anita. Donna's card is shown to Joy. Anita's card is shown to Donna. Joy's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anita can now know whether Donna can know whether Joy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anita","Joy","Donna"],"index":44021,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987693429,"difficulty":0.0012306571}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Anthony's card is shown to Marjorie. Marjorie's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether someone picked a red card. It is publicly announced that Anthony does not know whether Marjorie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Marjorie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Anthony","Marjorie"],"index":15974,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985561967,"difficulty":0.0014438033}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Corey. Corey's card is shown to Mercedes. John's card is shown to Mercedes. Emil's card is shown to Mercedes. Corey's card is shown to Emil. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card. It is publicly announced that John does not know whether Mercedes picked a red card. It is publicly announced that Corey knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"John can now know that Mercedes can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Corey","Mercedes","John","Emil"],"index":42735,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8215059638,"difficulty":0.1784940362}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Mary. William's card is shown to William. Wanda's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Mary can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","William","Wanda"],"index":60912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953839183,"difficulty":0.0046160817}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Salvatore's card is shown to Bess. Jimmy's card is shown to Jimmy. Matthew's card is shown to Jimmy. Salvatore's card is shown to Jimmy. Jimmy's card is shown to Matthew. Matthew's card is shown to Salvatore. It is publicly announced that someone picked a red card. It is publicly announced that Salvatore does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jimmy can now know that Bess picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bess","Jimmy","Matthew","Salvatore"],"index":40224,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8476005793,"difficulty":0.1523994207}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Sally. Sally's card is shown to Sharon. Sharon's card is shown to Sharon. Sally's card is shown to Kendall. Sharon's card is shown to Kendall. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wayne can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sally","Sharon","Wayne","Kendall"],"index":55501,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984028935,"difficulty":0.0015971065}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Jarvis. Jarvis's card is shown to Paul. Paul's card is shown to Steven. Mark's card is shown to Steven. Steven's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether Jarvis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mark can now know that Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jarvis","Paul","Steven","Mark"],"index":42814,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967767596,"difficulty":0.0032232404}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cody's card is shown to Lindsay. Mary's card is shown to Marie. Marie's card is shown to Cody. Cody's card is shown to Cody. Lindsay's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Lindsay does not know whether Mary picked a red card. It is publicly announced that Marie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(2) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that Marie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lindsay","Marie","Cody","Mary"],"index":11254,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.954249382,"difficulty":0.045750618}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurice's card is shown to Mary. Patrick's card is shown to Patrick. Daniel's card is shown to Patrick. Maurice's card is shown to Daniel. Patrick's card is shown to Maurice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Patrick","Daniel","Maurice"],"index":26466,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997703433,"difficulty":0.0002296567}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Iris's card is shown to James. Iris's card is shown to Rita. Darlene's card is shown to Iris. Iris's card is shown to Iris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darlene can now know that Rita can know that Darlene picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darlene","James","Rita","Iris"],"index":18665,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99775213,"difficulty":0.00224787}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Earl's card is shown to Dorothy. Dorothy's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Earl does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Earl can now know that Dorothy can know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Earl"],"index":66928,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8667244315,"difficulty":0.1332755685}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leo's card is shown to Leo. William's card is shown to Leo. Frank's card is shown to William. Frank's card is shown to Frank. Frank's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Frank picked a red card. It is publicly announced that Leo picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(1) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(1) ] 0","hypothesis":"William can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leo","William","Frank","Robert"],"index":53695,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8630063534,"difficulty":0.1369936466}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phyllis's card is shown to Phyllis. James's card is shown to Phyllis. Phyllis's card is shown to Kevin. Kevin's card is shown to Kevin. James's card is shown to James. Phyllis's card is shown to Bertha. Kevin's card is shown to Bertha. It is publicly announced that someone picked a red card. It is publicly announced that Phyllis does not know whether Bertha picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"James can now know whether Phyllis can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phyllis","Kevin","James","Bertha"],"index":19357,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candace's card is shown to Candace. Jessie's card is shown to Candace. Candace's card is shown to Jessie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessie can now know whether Candace can know that Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Candace","Jessie","Carol"],"index":45434,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9397929907,"difficulty":1.9397929907}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Maria. Wilhelmina's card is shown to Wilhelmina. Maria's card is shown to Christina. Howard's card is shown to Howard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christina can now know whether Howard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Wilhelmina","Christina","Howard"],"index":21691,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8275219202,"difficulty":1.8275219202}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Ted. Ted's card is shown to Ted. Henry's card is shown to Ted. Ted's card is shown to Henry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Ted","Henry"],"index":27417,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997698665,"difficulty":0.0002301335}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Gertrude. Jesus's card is shown to Michael. Michael's card is shown to Michael. Jesus's card is shown to Cindy. Gertrude's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Gertrude knows whether or not everyone picked a red card. It is publicly announced that Jesus picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Michael can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jesus","Gertrude","Michael","Cindy"],"index":29332,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Benjamin's card is shown to John. Jennifer's card is shown to John. Jennifer's card is shown to Benjamin. John's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that John picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card. It is publicly announced that Jennifer does not know whether Benjamin picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Benjamin can now know that John can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Benjamin","Jennifer"],"index":11520,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6917074323,"difficulty":1.6917074323}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Fernando. Anthony's card is shown to James. Wanda's card is shown to James. Fernando's card is shown to Anthony. James's card is shown to Anthony. James's card is shown to Wanda. Anthony's card is shown to Wanda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know that Fernando can know that Wanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Fernando","James","Anthony","Wanda"],"index":42963,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978567958,"difficulty":0.0021432042}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denise's card is shown to Allen. Debra's card is shown to Allen. Allen's card is shown to Denise. Denise's card is shown to Denise. Allen's card is shown to Debra. Denise's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Allen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Allen can now know that Trudy can know that Trudy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Allen","Denise","Trudy","Debra"],"index":56895,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9264578819,"difficulty":0.0735421181}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Natalie's card is shown to Jeffery. Natalie's card is shown to Staci. Staci's card is shown to Natalie. It is publicly announced that someone picked a red card. It is publicly announced that Jeffery does not know whether or not everyone picked a red card. It is publicly announced that Staci does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Staci can now know that Natalie can know that Jeffery picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffery","Staci","Natalie"],"index":10256,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5144587159,"difficulty":1.5144587159}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Barry. Rebecca's card is shown to Bryce. Bryce's card is shown to Rebecca. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bryce can now know whether Rebecca picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barry","Bryce","Rebecca"],"index":19420,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.625764966,"difficulty":1.625764966}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephan's card is shown to Stephan. Owen's card is shown to Stephan. Alan's card is shown to Owen. Owen's card is shown to Alan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephan","Owen","Alan"],"index":22702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983758926,"difficulty":0.0016241074}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karla's card is shown to Mathew. Patricia's card is shown to Patricia. Mathew's card is shown to Karla. Patricia's card is shown to Karla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know whether Mathew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mathew","Patricia","Karla"],"index":56881,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997709394,"difficulty":0.0002290606}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emma's card is shown to William. Carla's card is shown to Emma. William's card is shown to Carla. Emma's card is shown to Carla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Carla can know that Carla picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Emma","Carla"],"index":719,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955170751,"difficulty":0.0044829249}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Brenda. Christine's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Brenda knows whether or not nobody picked a red card. It is publicly announced that Christine knows whether Brenda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brenda can now know whether Christine can know whether Christine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brenda","Christine"],"index":16717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9954511523,"difficulty":0.0045488477}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Betty's card is shown to Stephen. Stephen's card is shown to Betty. Jena's card is shown to Betty. Betty's card is shown to Jena. Stephen's card is shown to Harriet. It is publicly announced that someone picked a red card. It is publicly announced that Betty knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Betty picked a black card. It is publicly announced that Stephen does not know whether Harriet picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Jena can now know that Harriet can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Betty","Jena","Harriet"],"index":55013,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Pat. Elizabeth's card is shown to Jeff. Jeff's card is shown to Jeff. Jeff's card is shown to Ralph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pat can now know whether Jeff can know whether Ralph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pat","Elizabeth","Jeff","Ralph"],"index":43840,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982410669,"difficulty":0.0017589331}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vergie's card is shown to Vergie. Vickie's card is shown to Samantha. Vergie's card is shown to Samantha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vergie can now know whether Vickie can know whether Vickie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vickie","Vergie","Samantha"],"index":19322,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9943585992,"difficulty":0.0056414008}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tammy's card is shown to Tammy. Julio's card is shown to Tammy. Aileen's card is shown to Tammy. Tammy's card is shown to Julio. Julio's card is shown to Julio. Tammy's card is shown to Aileen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Aileen can now know that Tammy can know that Aileen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tammy","Julio","Aileen"],"index":13051,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967233539,"difficulty":0.0032766461}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Grace. Grace's card is shown to Inez. It is publicly announced that someone picked a red card. It is publicly announced that Inez does not know whether Inez picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Grace can now know that Grace picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Grace","Inez"],"index":15669,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9675891399,"difficulty":1.9675891399}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Leo. Keith's card is shown to Keith. John's card is shown to Keith. John's card is shown to John. Leo's card is shown to Daisy. It is publicly announced that someone picked a red card. It is publicly announced that Leo does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta 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:3 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Leo can now know that Keith can know that Leo picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leo","Keith","John","Daisy"],"index":49688,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5483937263,"difficulty":1.5483937263}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Michael. Kiera's card is shown to Gerald. Gerald's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that Kiera knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kiera can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kiera","Michael","Gerald"],"index":3299,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968978167,"difficulty":0.0031021833}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcos's card is shown to Marcos. John's card is shown to Marcos. Ashley's card is shown to Ashley. Marcos's card is shown to John. Ashley's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Marcos knows whether Marcos picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 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:1,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"John can now know that Marcos can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marcos","Ashley","John"],"index":44467,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940108657,"difficulty":0.0059891343}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Louise. Mary's card is shown to Louise. Francisco's card is shown to Francisco. Louise's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Francisco can now know whether Louise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Louise","Francisco","Mary"],"index":40568,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6271041632,"difficulty":0.3728958368}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Jesse's card is shown to Linda. Jerrod's card is shown to Jerrod. It is publicly announced that someone picked a red card. It is publicly announced that Jesse does not know whether or not everyone picked a red card. It is publicly announced that Jerrod picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Jesse can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Jesse","Linda","Jerrod"],"index":20162,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7091971636,"difficulty":1.7091971636}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachal's card is shown to Matt. Margaret's card is shown to Matt. Debra's card is shown to Matt. Matt's card is shown to Margaret. Margaret's card is shown to Margaret. Margaret's card is shown to Debra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Matt can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matt","Rachal","Margaret","Debra"],"index":50655,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983869791,"difficulty":0.0016130209}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Bianca. Bianca's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Bianca does not know whether Bianca picked a red card. It is publicly announced that Bianca does not know whether Bianca picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Bianca can now know whether Nancy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bianca","Nancy"],"index":38198,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997035861,"difficulty":0.0002964139}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leonard's card is shown to Ashley. Ashley's card is shown to Leonard. Ashley's card is shown to Leah. Leonard's card is shown to Leah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ashley can now know whether Leah can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ashley","Leonard","Leah"],"index":62569,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9953014851,"difficulty":0.0046985149}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francisco's card is shown to Francisco. Mary's card is shown to Francisco. Francisco's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Earnest knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Francisco can now know whether Earnest can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Earnest","Francisco","Mary"],"index":18593,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999022603,"difficulty":0.000977397}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gladys's card is shown to Gladys. James's card is shown to Gladys. Nicholas's card is shown to Gladys. James's card is shown to James. Nicholas's card is shown to James. Gladys's card is shown to Nicholas. Darryl's card is shown to Darryl. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Darryl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Darryl can now know whether Nicholas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gladys","James","Nicholas","Darryl"],"index":19905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8706453443,"difficulty":0.1293546557}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Cynthia. Charles's card is shown to Mary. Mary's card is shown to Mary. Mary's card is shown to Sharon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know that Mary can know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Charles","Mary","Sharon"],"index":40945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9123696685,"difficulty":0.0876303315}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Dennis. Dennis's card is shown to Toni. Toni's card is shown to Toni. Jerry's card is shown to Toni. Toni's card is shown to Jerry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Toni can now know that Dennis can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Toni","Jerry"],"index":5859,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984467626,"difficulty":0.0015532374}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eleanor's card is shown to Eleanor. Eleanor's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Elizabeth can now know that Eleanor can know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eleanor","Elizabeth"],"index":66564,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7233832479,"difficulty":1.7233832479}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Raymond's card is shown to John. John's card is shown to Albert. Lee's card is shown to Lee. Albert's card is shown to Raymond. Lee's card is shown to Raymond. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lee can now know whether Raymond picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Albert","Lee","Raymond"],"index":12517,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6863503456,"difficulty":1.6863503456}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vicki's card is shown to Dirk. Dirk's card is shown to Vicki. It is publicly announced that someone picked a red card. It is publicly announced that Dirk does not know whether Dirk picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dirk can now know that Vicki can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dirk","Vicki"],"index":37835,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999781549,"difficulty":0.000218451}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Earl. Rebecca's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Earl","David","Rebecca"],"index":28267,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997658134,"difficulty":0.0002341866}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Sidney. Sidney's card is shown to Mark. Mark's card is shown to Mark. Henrietta's card is shown to Mark. Mark's card is shown to Henrietta. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Sidney picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Sidney can now know that Mark can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sidney","Rebecca","Mark","Henrietta"],"index":31713,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979979396,"difficulty":0.0020020604}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Joni's card is shown to Stephen. Stephen's card is shown to Joni. It is publicly announced that someone picked a red card. It is publicly announced that Will does not know whether Will picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Stephen can now know whether Joni picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephen","Will","Joni"],"index":10734,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9226631522,"difficulty":1.9226631522}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodore's card is shown to Sherry. Lloyd's card is shown to Theodore. Theodore's card is shown to Lloyd. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lloyd can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherry","Theodore","Lloyd"],"index":36577,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983704686,"difficulty":0.0016295314}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Clara. John's card is shown to John. Catherine's card is shown to John. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Wayne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Clara can now know whether Clara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clara","John","Catherine","Wayne"],"index":53797,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7110053897,"difficulty":0.2889946103}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Teresa. Teresa's card is shown to Kim. Teresa's card is shown to April. Kim's card is shown to April. It is publicly announced that someone picked a red card. It is publicly announced that Teresa does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"April can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Teresa","Kim","April"],"index":14686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janis's card is shown to Ronald. Bryan's card is shown to Bryan. Janis's card is shown to Janis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ronald can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ronald","Bryan","Janis"],"index":41235,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997612834,"difficulty":0.0002387166}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcus's card is shown to Marcus. Gia's card is shown to Marcus. Elin's card is shown to Marcus. Marcus's card is shown to Gia. Gia's card is shown to Gia. Albert's card is shown to Gia. Elin's card is shown to Gia. Marcus's card is shown to Albert. Elin's card is shown to Albert. Marcus's card is shown to Elin. It is publicly announced that someone picked a red card. It is publicly announced that Elin does not know whether Gia picked a red card. It is publicly announced that Elin does not know whether Albert picked a red card. It is publicly announced that Marcus does not know whether Albert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Albert can now know whether Gia can know whether Albert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcus","Gia","Albert","Elin"],"index":28703,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9966737032,"difficulty":0.0033262968}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paige's card is shown to Paige. Adrianne's card is shown to Paige. Adrianne's card is shown to Darius. Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darius can now know whether Paige can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paige","Adrianne","Darius","Gregory"],"index":57548,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debbie's card is shown to Debbie. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Debbie picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Francis can now know whether Debbie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debbie","Francis","Evelyn"],"index":43875,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9819552302,"difficulty":0.0180447698}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Bernadine. Kandi's card is shown to Bernadine. Kandi's card is shown to Joanne. Bernadine's card is shown to Kandi. Agnes's card is shown to Kandi. It is publicly announced that someone picked a red card. It is publicly announced that Joanne picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Kandi can now know that Agnes picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernadine","Joanne","Kandi","Agnes"],"index":59450,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9712923169,"difficulty":0.0287076831}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Brent. Brent's card is shown to Lauren. Herbert's card is shown to Lauren. Sarah's card is shown to Herbert. Lauren's card is shown to Herbert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brent","Sarah","Lauren","Herbert"],"index":59647,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9694645405,"difficulty":1.9694645405}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Edwin. Edwin's card is shown to Donald. Donald's card is shown to Donald. Mary's card is shown to Donald. Donald's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether Donald picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Edwin can now know that Mary can know that Edwin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edwin","Donald","Mary"],"index":38121,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951785803,"difficulty":0.0048214197}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denise's card is shown to Denise. Charlotte's card is shown to Denise. Denise's card is shown to Angela. Charlotte's card is shown to Angela. Angela's card is shown to Charlotte. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charlotte can now know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Denise","Angela","Charlotte"],"index":28719,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9911319613,"difficulty":0.0088680387}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to James. James's card is shown to James. Wilbert's card is shown to James. Thomas's card is shown to Wilbert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that James can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","James","Wilbert"],"index":14761,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9831526875,"difficulty":0.0168473125}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Marie's card is shown to Jennifer. Ellen's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Marie picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jennifer can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ellen","Jennifer","Marie"],"index":64074,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997853637,"difficulty":0.0002146363}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Frederick. Mary's card is shown to Mary. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Frederick can now know that Frederick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frederick","Mary","James"],"index":19036,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982261062,"difficulty":0.0017738938}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Sara's card is shown to Ronald. Sara's card is shown to Sara. It is publicly announced that someone picked a red card. It is publicly announced that Sara does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Ronald","Sara"],"index":10144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997057319,"difficulty":0.0002942681}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cortez's card is shown to Angla. Maurice's card is shown to Angla. Maurice's card is shown to Cortez. Angla's card is shown to Benjamin. Maurice's card is shown to Maurice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Benjamin can now know that Benjamin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angla","Cortez","Benjamin","Maurice"],"index":32257,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979712367,"difficulty":0.0020287633}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Pricilla. Dean's card is shown to Dean. Julie's card is shown to Dean. Pricilla's card is shown to Melissa. Melissa's card is shown to Melissa. Julie's card is shown to Melissa. Pricilla's card is shown to Julie. Julie's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:1,3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:1,3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Pricilla can now know that Melissa can know whether Pricilla picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pricilla","Dean","Melissa","Julie"],"index":62809,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6191657186,"difficulty":1.6191657186}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Susan. Jasper's card is shown to Susan. James's card is shown to Susan. Susan's card is shown to Jasper. Jasper's card is shown to Jasper. It is publicly announced that someone picked a red card. It is publicly announced that Jasper knows whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Jasper can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Susan","Jasper","James"],"index":49931,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.839732945,"difficulty":1.839732945}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myrtle's card is shown to Michael. Michael's card is shown to Roger. Roger's card is shown to Roger. Michael's card is shown to Myrtle. Roger's card is shown to Myrtle. It is publicly announced that someone picked a red card. It is publicly announced that Roger knows whether Roger picked a red card. It is publicly announced that Michael does not know whether Roger picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Roger can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Roger","Myrtle"],"index":36720,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9852804542,"difficulty":0.0147195458}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Lisa. Winston's card is shown to Lisa. Lisa's card is shown to Winston. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Lisa can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lisa","Winston"],"index":50650,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985798597,"difficulty":0.0014201403}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Geraldine. Geraldine's card is shown to Roy. Dennis's card is shown to Roy. Geraldine's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Roy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Roy can now know that Geraldine can know whether Dennis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geraldine","Roy","Dennis"],"index":35196,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7493456006,"difficulty":0.2506543994}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gearldine's card is shown to Patricia. Gearldine's card is shown to John. Gearldine's card is shown to Gladys. John's card is shown to Gladys. Gladys's card is shown to Gladys. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Gearldine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Gearldine","John","Gladys"],"index":65905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980304837,"difficulty":0.0019695163}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edgar's card is shown to Edgar. Victoria's card is shown to Richard. Beth's card is shown to Victoria. Richard's card is shown to Beth. It is publicly announced that someone picked a red card. It is publicly announced that Edgar knows whether or not nobody picked a red card. It is publicly announced that Richard knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (Agentb 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 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Edgar can now know that Richard can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edgar","Richard","Victoria","Beth"],"index":33429,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9064071774,"difficulty":0.0935928226}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Laurette. Steve's card is shown to Laurette. Nicole's card is shown to Shannon. Shannon's card is shown to Shannon. Steve's card is shown to Shannon. Laurette's card is shown to Steve. Nicole's card is shown to Steve. Steve's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Shannon picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Nicole can now know whether Shannon can know whether Nicole picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laurette","Nicole","Shannon","Steve"],"index":48905,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982130527,"difficulty":0.0017869473}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Jack. Donna's card is shown to Donna. Donna's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"William can now know whether Donna can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jack","Donna","William"],"index":54791,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996826649,"difficulty":0.0003173351}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Donald. Bernice's card is shown to Donald. Tracy's card is shown to Michael. Michael's card is shown to Bernice. Donald's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donald","Michael","Bernice","Tracy"],"index":48248,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997733235,"difficulty":0.0002266765}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Wayne. Wayne's card is shown to Johnny. It is publicly announced that someone picked a red card. It is publicly announced that Johnny does not know whether Johnny picked a red card. It is publicly announced that Johnny knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Johnny can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wayne","Johnny"],"index":61855,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984627962,"difficulty":0.0015372038}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herbert's card is shown to Herbert. Herbert's card is shown to Mike. Mike's card is shown to Gladys. It is publicly announced that someone picked a red card. It is publicly announced that Gladys does not know whether Gladys picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mike can now know that Gladys picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Herbert","Mike","Gladys"],"index":45891,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996258378,"difficulty":0.003741622}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marguerite's card is shown to Marguerite. Rebecca's card is shown to Rebecca. Kathryn's card is shown to Rebecca. Marguerite's card is shown to Kathryn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marguerite can now know that Rebecca can know that Rebecca picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marguerite","Rebecca","Kathryn"],"index":56054,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977512956,"difficulty":0.0022487044}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carlos's card is shown to Mark. Carlos's card is shown to Gloria. Gloria's card is shown to Carlos. It is publicly announced that someone picked a red card. It is publicly announced that Gloria does not know whether Mark picked a red card. It is publicly announced that Gloria picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(2) ] Agenta knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Mark can now know that Carlos can know whether Carlos picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Gloria","Carlos"],"index":22648,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9875850677,"difficulty":1.9875850677}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Roy. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether Roy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roy","David","Anthony"],"index":12837,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.610471487,"difficulty":0.389528513}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Mary's card is shown to Helen. Mary's card is shown to Mary. Anton's card is shown to Anton. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Anton can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","Mary","Anton"],"index":43466,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983422756,"difficulty":0.0016577244}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Victor. Julie's card is shown to Victor. Julie's card is shown to James. Victor's card is shown to Julie. Susan's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that James picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Julie can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","James","Julie","Susan"],"index":59864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9739698172,"difficulty":0.0260301828}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luis's card is shown to Anthony. Anthony's card is shown to Leroy. Luis's card is shown to Leroy. Leroy's card is shown to Loretta. Anthony's card is shown to Luis. Loretta's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Luis does not know whether Luis picked a red card. It is publicly announced that Anthony knows whether or not nobody picked a red card. It is publicly announced that Loretta picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentd knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Luis can now know whether Leroy can know that Leroy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Leroy","Loretta","Luis"],"index":66354,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7277582884,"difficulty":1.7277582884}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margret's card is shown to Margret. Prudence's card is shown to Margret. Margret's card is shown to Prudence. It is publicly announced that someone picked a red card. It is publicly announced that Prudence knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Prudence can now know that Margret can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Margret","Prudence"],"index":38625,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9926604033,"difficulty":0.0073395967}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vernon's card is shown to Vernon. Vernon's card is shown to Seymour. Seymour's card is shown to Seymour. Stephen's card is shown to Seymour. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vernon can now know whether Seymour picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vernon","Seymour","Stephen"],"index":25667,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7751299143,"difficulty":0.2248700857}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herbert's card is shown to Herbert. Herbert's card is shown to Kevin. Kevin's card is shown to Kevin. Barry's card is shown to Kevin. Kevin's card is shown to Barry. Barry's card is shown to Barry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barry can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Herbert","Kevin","Barry"],"index":40525,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dana's card is shown to Jayne. Jayne's card is shown to Owen. It is publicly announced that someone picked a red card. It is publicly announced that Owen picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Dana can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jayne","Dana","Owen"],"index":46167,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Calvin's card is shown to Marilyn. Marilyn's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Calvin picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Marilyn can now know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Calvin","Marilyn","Susan"],"index":51490,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8302906156,"difficulty":0.1697093844}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emily's card is shown to Christin. Christin's card is shown to Eugene. Eugene's card is shown to Emily. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eugene can now know that Emily can know whether Christin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christin","Eugene","Emily"],"index":20336,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6539701819,"difficulty":0.3460298181}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Daryl. Craig's card is shown to Craig. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Craig can now know whether Daryl can know that Daryl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daryl","Craig"],"index":26854,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9796143174,"difficulty":0.0203856826}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandy's card is shown to Brandy. Brandy's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Brandy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Brandy can now know that David can know whether Brandy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brandy","David","Dennis"],"index":35170,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973395467,"difficulty":0.0026604533}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rodney's card is shown to Joyce. Rebecca's card is shown to Joyce. Joyce's card is shown to Rebecca. Rebecca's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Joyce can now know whether Rodney can know that Rodney picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rodney","Joyce","Rebecca","Janet"],"index":18227,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8821001053,"difficulty":1.8821001053}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Holly's card is shown to Holly. Sherri's card is shown to Sherri. Sherri's card is shown to Beverley. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card. It is publicly announced that Sherri does not know whether Holly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Richard can now know whether Sherri can know whether Holly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Holly","Sherri","Beverley"],"index":39089,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978237152,"difficulty":0.0021762848}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bill's card is shown to Lynn. Lynn's card is shown to Margaret. Bill's card is shown to Margaret. Margaret's card is shown to Bill. It is publicly announced that someone picked a red card. It is publicly announced that Lynn does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(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:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lynn can now know whether Bill can know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lynn","Margaret","Bill"],"index":33205,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9651818871,"difficulty":1.9651818871}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heather's card is shown to Daniel. Daniel's card is shown to Beth. Heather's card is shown to Leslie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know whether Heather can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Beth","Heather","Leslie"],"index":13850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997715354,"difficulty":0.0002284646}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Edward. Charles's card is shown to Edward. Oscar's card is shown to Diane. Oscar's card is shown to Charles. Diane's card is shown to Charles. Charles's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Diane can now know whether Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Oscar","Edward","Diane","Charles"],"index":11807,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5007836223,"difficulty":1.5007836223}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandra's card is shown to Ronda. Ronda's card is shown to Sandra. Mark's card is shown to Sandra. Sandra's card is shown to Sandra. It is publicly announced that someone picked a red card. It is publicly announced that Mark knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Ronda can now know whether Mark can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronda","Mark","Sandra"],"index":38180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999710381,"difficulty":0.000289619}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marianela's card is shown to Marianela. Marianela's card is shown to Edwin. It is publicly announced that someone picked a red card. It is publicly announced that Marianela knows whether Marianela picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Pauline can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marianela","Pauline","Edwin"],"index":48671,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9444442987,"difficulty":0.0555557013}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kaye's card is shown to Emilio. Ronald's card is shown to Emilio. Ronald's card is shown to Marianne. Kaye's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marianne can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emilio","Kaye","Marianne","Ronald"],"index":34908,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997683167,"difficulty":0.0002316833}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Jesse. Pamela's card is shown to Jesse. Ann's card is shown to Ann. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Pamela does not know whether Jesse picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Pamela can now know whether Jesse can know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesse","Ann","Pamela"],"index":56345,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9140103459,"difficulty":0.0859896541}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Eleanor's card is shown to James. Hubert's card is shown to James. James's card is shown to Eleanor. Eleanor's card is shown to Eleanor. Cassie's card is shown to Eleanor. Hubert's card is shown to Eleanor. James's card is shown to Cassie. Hubert's card is shown to Cassie. James's card is shown to Hubert. It is publicly announced that someone picked a red card. It is publicly announced that Hubert does not know whether Eleanor picked a red card. It is publicly announced that Hubert does not know whether Cassie picked a red card. It is publicly announced that James does not know whether Cassie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Eleanor can now know that Cassie can know whether Eleanor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Eleanor","Cassie","Hubert"],"index":36379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8722646832,"difficulty":0.1277353168}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kerry's card is shown to Otis. Julian's card is shown to Julian. John's card is shown to John. John's card is shown to Kerry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Otis can now know that Kerry can know that Julian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Otis","Julian","John","Kerry"],"index":63237,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981086254,"difficulty":0.0018913746}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Manuel. Manuel's card is shown to Robert. Loren's card is shown to Robert. Arthur's card is shown to Robert. Robert's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Manuel does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Manuel","Robert","Loren","Arthur"],"index":32384,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9939919114,"difficulty":0.0060080886}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Roy can now know that Roy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roy","Andrea"],"index":50116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978969097,"difficulty":0.0021030903}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorraine's card is shown to Venus. Charise's card is shown to Venus. Charise's card is shown to Lorraine. Venus's card is shown to Jesus. Charise's card is shown to Charise. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Venus can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Venus","Lorraine","Jesus","Charise"],"index":3618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9922229648,"difficulty":0.0077770352}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wm's card is shown to Charles. Michael's card is shown to Charles. Charles's card is shown to Wm. Wm's card is shown to Wm. Wm's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Michael can now know whether Wm picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Wm","Michael"],"index":65729,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7320919633,"difficulty":0.2679080367}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to John. Craig's card is shown to John. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that Craig picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Mary","Craig"],"index":12787,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996113658,"difficulty":0.003886342}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lester's card is shown to Lester. Katherine's card is shown to Lester. Lester's card is shown to Katherine. Katherine's card is shown to Katherine. Christy's card is shown to Katherine. Lester's card is shown to Christy. Jackie's card is shown to Christy. It is publicly announced that someone picked a red card. It is publicly announced that Lester picked a black card. It is publicly announced that Jackie does not know whether Katherine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jackie can now know whether Katherine can know whether Christy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lester","Katherine","Jackie","Christy"],"index":21955,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997615695,"difficulty":0.002384305}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Jennifer. Jennifer's card is shown to Michelle. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card. It is publicly announced that Michelle knows whether Michelle picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Michelle can now know whether Jennifer can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Michelle"],"index":15741,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8952473402,"difficulty":0.1047526598}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Florence's card is shown to Florence. Glenn's card is shown to Florence. Glenn's card is shown to Glenn. Michael's card is shown to Edgar. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Glenn can now know that Florence can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florence","Glenn","Michael","Edgar"],"index":4576,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998385787,"difficulty":0.001614213}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shana's card is shown to Shana. Shana's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that Shana does not know whether Annie picked a red card. It is publicly announced that Shana does not know whether Annie picked a red card. It is publicly announced that Annie does not know whether or not everyone picked a red card. It is publicly announced that Shana does not know whether Annie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Annie can now know whether Shana can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shana","Annie"],"index":65700,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997729659,"difficulty":0.0002270341}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamela's card is shown to Pamela. Mae's card is shown to Pamela. Pamela's card is shown to Mae. Mae's card is shown to Mae. It is publicly announced that someone picked a red card. It is publicly announced that Pamela knows whether Mae picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 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 2) ] 0","hypothesis":"Pamela can now know whether Mae can know that Mae picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pamela","Mae"],"index":41378,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8772711754,"difficulty":0.1227288246}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Beverley. Franklin's card is shown to Beverley. Franklin's card is shown to Cynthia. Beverley's card is shown to Franklin. It is publicly announced that someone picked a red card. It is publicly announced that Beverley picked a red card. It is publicly announced that Franklin does not know whether or not everyone picked a red card. It is publicly announced that Franklin does not know whether Cynthia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Beverley can now know whether Franklin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beverley","Cynthia","Franklin"],"index":32537,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9792366028,"difficulty":0.0207633972}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlene's card is shown to Marlene. Mary's card is shown to Marlene. Oscar's card is shown to Mary. Mary's card is shown to Oscar. It is publicly announced that someone picked a red card. It is publicly announced that Marlene does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know whether Marlene can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marlene","Mary","Oscar"],"index":469,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999768436,"difficulty":0.000231564}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Gloria. Gloria's card is shown to Elizabeth. Mandy's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mandy can now know that Gloria can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Mandy","Elizabeth"],"index":31997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983488321,"difficulty":0.0016511679}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Clarence. Darrell's card is shown to Suzanne. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Clarence does not know whether Suzanne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Clarence can now know whether Clarence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darrell","Clarence","Nicholas","Suzanne"],"index":2332,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9977194667,"difficulty":1.9977194667}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jane's card is shown to Marcelle. Rosalie's card is shown to Jane. Margo's card is shown to Jane. Marcelle's card is shown to Rosalie. Jane's card is shown to Margo. Rosalie's card is shown to Margo. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jane can now know that Marcelle can know whether Jane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcelle","Jane","Rosalie","Margo"],"index":66965,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9763529897,"difficulty":0.0236470103}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Kimberly. Dorothy's card is shown to Kimberly. Katherine's card is shown to Dorothy. Kimberly's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Katherine can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kimberly","Dorothy","Katherine"],"index":62444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997189641,"difficulty":0.0002810359}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Faye's card is shown to Scott. Scott's card is shown to Faye. Faye's card is shown to Faye. Scott's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Scott knows whether Faye picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Faye can now know that Christopher can know whether Faye picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Faye","Christopher","Guadalupe"],"index":45606,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9017184377,"difficulty":1.9017184377}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Angelica. Ralph's card is shown to Ralph. Cecile's card is shown to Ralph. Angelica's card is shown to Cecile. It is publicly announced that someone picked a red card. It is publicly announced that Cecile picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Ralph can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Angelica","Roy","Ralph","Cecile"],"index":6993,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997834563,"difficulty":0.0002165437}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terry's card is shown to Carl. Charity's card is shown to Carl. Carl's card is shown to Charity. Charity's card is shown to Charity. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terry can now know that Carl can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carl","Terry","Charity"],"index":14112,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984098673,"difficulty":0.0015901327}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Fred's card is shown to James. Dale's card is shown to Joseph. James's card is shown to Dale. Dale's card is shown to Dale. James's card is shown to Fred. Dale's card is shown to Fred. Fred's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Fred does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,3 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,3 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Joseph can now know that Fred can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Joseph","Dale","Fred"],"index":30820,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9259734154,"difficulty":0.0740265846}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Brenda. Louise's card is shown to Brenda. Kenneth's card is shown to Kenneth. Gary's card is shown to Kenneth. Brenda's card is shown to Louise. Louise's card is shown to Louise. Brenda's card is shown to Gary. Louise's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Louise picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1,3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1,3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Kenneth can now know whether Gary can know that Brenda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brenda","Kenneth","Louise","Gary"],"index":33772,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9527429342,"difficulty":1.9527429342}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Patrick. Victoria's card is shown to Patrick. Patrick's card is shown to Todd. Denise's card is shown to Todd. Denise's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Todd does not know whether Todd picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patrick can now know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","Todd","Victoria","Denise"],"index":66661,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8080064058,"difficulty":0.1919935942}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Teresa. Michael's card is shown to Teresa. Teresa's card is shown to Alice. Michael's card is shown to Alice. Teresa's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Teresa can know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Teresa","Alice","Michael"],"index":22083,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978466034,"difficulty":0.0021533966}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Steve. Gretta's card is shown to Gretta. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gretta can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steve","Gretta","Annie"],"index":6272,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985067248,"difficulty":0.0014932752}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Herminia's card is shown to Herminia. Marcia's card is shown to Herminia. Herminia's card is shown to Marcia. Herminia's card is shown to Billy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Billy can now know whether Marcia can know whether Herminia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Herminia","Marcia","Billy"],"index":46378,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981842637,"difficulty":0.0018157363}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Alice. Shannon's card is shown to Lashawnda. Alice's card is shown to Shannon. Lashawnda's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether Alice picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Lashawnda can now know that Shannon can know that Shannon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alice","Lashawnda","Shannon"],"index":30184,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9363413453,"difficulty":0.0636586547}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louis's card is shown to Louis. Latoya's card is shown to Sam. Mary's card is shown to Latoya. Sam's card is shown to Latoya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sam can now know that Louis can know whether Latoya picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Louis","Sam","Latoya"],"index":25073,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8213190436,"difficulty":1.8213190436}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victor's card is shown to William. William's card is shown to Aaron. It is publicly announced that someone picked a red card. It is publicly announced that Victor picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"William can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Victor","William","Aaron"],"index":3481,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997254014,"difficulty":0.0002745986}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Betty. Sheila's card is shown to Jose. Sheila's card is shown to Sandy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandy can now know whether Jose can know whether Sheila picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Jose","Sandy","Sheila"],"index":66609,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987257123,"difficulty":0.0012742877}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christin's card is shown to Christin. George's card is shown to Christin. Christin's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Christin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Warren can now know that Christin can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Warren","Christin","George"],"index":1381,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9779734015,"difficulty":0.0220265985}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cecil's card is shown to Anna. Cecil's card is shown to Cecil. Cecil's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Cecil can now know whether Anna can know whether Cecil picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anna","Cecil","James"],"index":5280,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986197948,"difficulty":0.0013802052}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Cheryl. Cheryl's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Cheryl can now know that Cheryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Cheryl","William","Adam"],"index":54266,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6850787997,"difficulty":1.6850787997}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Diana. Diana's card is shown to Tracie. Ann's card is shown to Tracie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tracie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diana","Tracie","Ann"],"index":15526,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997783303,"difficulty":0.0002216697}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marla's card is shown to Candace. Marla's card is shown to Dawn. Jeffrey's card is shown to Jeffrey. Jeffrey's card is shown to Marla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dawn can now know that Marla can know whether Candace picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Candace","Dawn","Jeffrey","Marla"],"index":49651,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8734132648,"difficulty":0.1265867352}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stanley's card is shown to Stanley. Stanley's card is shown to Daniel. Daniel's card is shown to Daniel. Stanley's card is shown to Francis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know whether Stanley can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stanley","Daniel","Helen","Francis"],"index":14660,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8716275692,"difficulty":1.8716275692}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Russell's card is shown to Heidi. Michelle's card is shown to Russell. Robert's card is shown to Russell. Michelle's card is shown to Michelle. Robert's card is shown to Michelle. Russell's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Michelle does not know whether Russell picked a red card. It is publicly announced that Michelle does not know whether Russell picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Michelle can now know that Russell can know whether Russell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heidi","Russell","Michelle","Robert"],"index":16068,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9274314046,"difficulty":0.0725685954}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Max's card is shown to James. James's card is shown to Maryellen. Maryellen's card is shown to Maryellen. Max's card is shown to Maryellen. Maryellen's card is shown to Max. It is publicly announced that someone picked a red card. It is publicly announced that Max knows whether someone picked a red card. It is publicly announced that Maryellen picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] 0","hypothesis":"Max can now know that James can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Maryellen","Max"],"index":34597,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6938930154,"difficulty":1.6938930154}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Susan. Thelma's card is shown to Susan. Rachelle's card is shown to Rachelle. Susan's card is shown to Thelma. Thelma's card is shown to Thelma. It is publicly announced that someone picked a red card. It is publicly announced that Brandon knows whether Thelma picked a red card. It is publicly announced that Brandon does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Susan can now know that Rachelle can know whether Brandon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brandon","Susan","Rachelle","Thelma"],"index":63837,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.589143157,"difficulty":1.589143157}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobby's card is shown to Nichole. Genaro's card is shown to Bobby. Nichole's card is shown to Genaro. Genaro's card is shown to Genaro. It is publicly announced that someone picked a red card. It is publicly announced that Bobby does not know whether Nichole picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 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:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Bobby can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nichole","Bobby","Genaro"],"index":2746,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984788299,"difficulty":0.0015211701}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Elizabeth. Irene's card is shown to David. David's card is shown to Linda. Irene's card is shown to Linda. Elizabeth's card is shown to Irene. David's card is shown to Irene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Irene can now know that Linda can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","David","Linda","Irene"],"index":43704,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997802377,"difficulty":0.0002197623}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elsa's card is shown to Elsa. Steven's card is shown to Daniel. Elsa's card is shown to Raymond. Steven's card is shown to Raymond. Raymond's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymond can now know that Elsa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elsa","Daniel","Raymond","Steven"],"index":65805,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Christopher's card is shown to Branden. Branden's card is shown to Ronald. Ronald's card is shown to Ronald. Christopher's card is shown to Jaclyn. Jaclyn's card is shown to Jaclyn. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether or not everyone picked a red card. It is publicly announced that Christopher picked a red card. It is publicly announced that Christopher does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jaclyn can now know that Branden can know whether Ronald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Branden","Ronald","Jaclyn"],"index":23760,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9142730832,"difficulty":1.9142730832}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gina's card is shown to Patricia. Gina's card is shown to Lori. Patricia's card is shown to Gina. Lori's card is shown to Gina. Gina's card is shown to Gina. It is publicly announced that someone picked a red card. It is publicly announced that Lori does not know whether or not everyone picked a red card. It is publicly announced that Lori does not know whether Lori picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know whether Lori picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Lori","Gina"],"index":36277,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.805817306,"difficulty":1.805817306}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to John. Anna's card is shown to Anna. Larry's card is shown to Anna. John's card is shown to Larry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Norman can now know that Norman picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Norman","Anna","Larry"],"index":54678,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982378483,"difficulty":0.0017621517}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Anne. Anna's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Anne does not know whether Anna picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Anna can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anne","Anna"],"index":61287,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997809529,"difficulty":0.0002190471}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allan's card is shown to Helen. Helen's card is shown to Allan. Allan's card is shown to Philip. Helen's card is shown to Michael. Allan's card is shown to Michael. Philip's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Helen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Allan","Philip","Michael"],"index":12,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.935559988,"difficulty":0.064440012}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Christine. Mary's card is shown to Christine. Lisa's card is shown to Mary. Christine's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Christine knows whether or not everyone picked a red card. It is publicly announced that Christine does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Lisa can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Christine","Mary"],"index":62240,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dianne's card is shown to Dianne. Elena's card is shown to Dianne. Marlene's card is shown to Dianne. Elena's card is shown to Elena. Marlene's card is shown to Marlene. It is publicly announced that someone picked a red card. It is publicly announced that Elena does not know whether Marlene picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 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:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Marlene can now know whether Elena can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dianne","Elena","Marlene"],"index":21322,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9946846366,"difficulty":0.0053153634}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vance's card is shown to Vance. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Margaret can now know that Vance can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Vance","Margaret"],"index":66116,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9875427485,"difficulty":0.0124572515}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Paul. William's card is shown to William. William's card is shown to Gladys. Gladys's card is shown to Gladys. It is publicly announced that someone picked a red card. It is publicly announced that William picked a black card. It is publicly announced that Gladys picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 3 ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 3 ] 0","hypothesis":"Gladys can now know that Paul can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paul","William","Gladys"],"index":8961,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5100713968,"difficulty":1.5100713968}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Carolyn. Carolyn's card is shown to Karen. Karen's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Carolyn can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carolyn","Karen"],"index":64903,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985153079,"difficulty":0.0014846921}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Naomi's card is shown to Essie. Essie's card is shown to Helen. Helen's card is shown to Helen. Naomi's card is shown to Helen. Essie's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Naomi can now know that Helen can know that Naomi picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Essie","Helen","Naomi","David"],"index":52679,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9883104563,"difficulty":0.0116895437}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Kimberly. Kimberly's card is shown to John. Jacquelyn's card is shown to Jacquelyn. It is publicly announced that someone picked a red card. It is publicly announced that Jacquelyn picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(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:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"John can now know that Jerry can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Jerry","John","Jacquelyn"],"index":23476,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997820258,"difficulty":0.0002179742}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aaron's card is shown to Aaron. Traci's card is shown to Aaron. Aaron's card is shown to Traci. Jeff's card is shown to Keith. Traci's card is shown to Keith. Keith's card is shown to Keith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeff can now know whether Aaron can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeff","Aaron","Traci","Keith"],"index":67105,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Willie. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Willie can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Willie","John"],"index":11966,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976844788,"difficulty":0.0023155212}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Krystyna. Krystyna's card is shown to Matthew. Matthew's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Brian knows whether Matthew picked a red card. It is publicly announced that Matthew does not know whether Brian picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Brian can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Krystyna","Matthew","Brian"],"index":11503,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986097813,"difficulty":0.0013902187}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Mary. Angela's card is shown to Mary. Mary's card is shown to Joseph. Joseph's card is shown to Angela. Angela's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Joseph picked a black card. It is publicly announced that Joseph picked a black card. It is publicly announced that Paula knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know whether Paula can know that Angela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Joseph","Paula","Angela"],"index":53971,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9775505066,"difficulty":1.9775505066}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Catherine. Jacob's card is shown to Jacob. It is publicly announced that someone picked a red card. It is publicly announced that Catherine does not know whether or not everyone picked a red card. It is publicly announced that Jacob knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jacob can now know that Catherine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Catherine","Jacob"],"index":1608,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9797567725,"difficulty":0.0202432275}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Keith","Richard","James","Martha"],"index":26354,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997609258,"difficulty":0.0002390742}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Helen. Cassandra's card is shown to William. Helen's card is shown to Cassandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlie can now know that Helen can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Charlie","William","Cassandra"],"index":67130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalie's card is shown to Barbara. Rosalie's card is shown to Patricia. Debra's card is shown to Rosalie. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Barbara can now know that Patricia can know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Debra","Barbara","Patricia","Rosalie"],"index":53095,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7921487689,"difficulty":0.2078512311}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Adam. Forrest's card is shown to Forrest. Forrest's card is shown to Jennifer. Adam's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adam","Forrest","Jennifer","James"],"index":10777,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981065989,"difficulty":0.0018934011}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geraldine's card is shown to Geraldine. Laurie's card is shown to Laurie. Christine's card is shown to Laurie. Laurie's card is shown to Christine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Laurie can now know whether Laurie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Geraldine","Laurie","Christine"],"index":38108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9793435335,"difficulty":0.0206564665}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Raymond. Robert's card is shown to Raymond. Raymond's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Raymond knows whether Robert picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Raymond can now know that Robert can know that Raymond picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Raymond","Robert"],"index":25140,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9850177169,"difficulty":0.0149822831}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Kenneth's card is shown to Stephen. Kimberly's card is shown to Stephen. Kenneth's card is shown to Kenneth. Kimberly's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kimberly can now know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephen","Kenneth","Kimberly"],"index":39880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979659319,"difficulty":0.0020340681}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Jesse. Tom's card is shown to Jesse. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jesse knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jesse can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jesse","Tom"],"index":28513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961621761,"difficulty":0.0038378239}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pam's card is shown to Thomas. Joan's card is shown to Joan. Thomas's card is shown to Barbara. Thomas's card is shown to Pam. Joan's card is shown to Pam. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know that Joan can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Joan","Barbara","Pam"],"index":14960,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9778617024,"difficulty":0.0221382976}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Helen's card is shown to Jill. Frederick's card is shown to Jill. Beverly's card is shown to Beverly. Jill's card is shown to Frederick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Frederick can now know that Beverly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Jill","Beverly","Frederick"],"index":62675,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998263061,"difficulty":0.001736939}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Frances's card is shown to Charles. Frances's card is shown to Frances. Antonio's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Antonio can now know whether Frances can know that Nancy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Frances","Antonio","Nancy"],"index":34247,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8565730453,"difficulty":0.1434269547}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rick's card is shown to Joseph. James's card is shown to Rick. Rick's card is shown to Rick. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Joseph does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know whether Joseph can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","James","Rick"],"index":17344,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.861337781,"difficulty":0.138662219}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Anne. Anne's card is shown to Roberto. Gloria's card is shown to Roberto. Anne's card is shown to Gloria. Donald's card is shown to Gloria. Roberto's card is shown to Gloria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether Roberto picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anne","Donald","Roberto","Gloria"],"index":41661,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5753680468,"difficulty":0.4246319532}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Michael. Sylvia's card is shown to Maria. Beverly's card is shown to Maria. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Michael picked a red card. It is publicly announced that Sylvia does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Maria can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sylvia","Michael","Maria","Beverly"],"index":3523,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997207522,"difficulty":0.0002792478}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Sarah. Sarah's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Mark knows whether Sarah picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Mark can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sarah","Mark"],"index":32684,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986147881,"difficulty":0.0013852119}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Coy's card is shown to Richard. Coy's card is shown to Coy. Richard's card is shown to Kimberly. Kimberly's card is shown to Kimberly. It is publicly announced that someone picked a red card. It is publicly announced that Coy does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Richard can now know that Coy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Coy","Kimberly"],"index":6670,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981321692,"difficulty":0.0018678308}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Benton's card is shown to Joseph. May's card is shown to Joseph. Benton's card is shown to Benton. May's card is shown to Benton. Benton's card is shown to May. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Benton","May"],"index":53116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997279048,"difficulty":0.0002720952}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vincent's card is shown to David. Kevin's card is shown to David. Vincent's card is shown to Kevin. David's card is shown to Kevin. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jill can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vincent","Jill","David","Kevin"],"index":52994,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997264743,"difficulty":0.0002735257}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Jessica's card is shown to Thomas. Thomas's card is shown to Robin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robin can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Robin","Jessica"],"index":57847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997728467,"difficulty":0.0002271533}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keri's card is shown to Karl. Karl's card is shown to Keri. Keri's card is shown to Keri. Keri's card is shown to Monica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Keri can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karl","Keri","Monica"],"index":64370,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997234941,"difficulty":0.0002765059}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Suzan's card is shown to Suzan. Rueben's card is shown to Suzan. Rueben's card is shown to Rueben. Richard's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Janet can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Suzan","Rueben","Janet"],"index":26172,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9486598372,"difficulty":0.0513401628}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Eric. Eric's card is shown to Sunday. It is publicly announced that someone picked a red card. It is publicly announced that Sunday knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Sunday can now know whether Sunday picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eric","Sunday"],"index":17080,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9716620445,"difficulty":1.9716620445}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Belinda's card is shown to Lisa. Donald's card is shown to Lisa. Belinda's card is shown to Beatrice. Beatrice's card is shown to Beatrice. Beatrice's card is shown to Donald. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Belinda does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Belinda can now know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Belinda","Beatrice","Donald"],"index":49842,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9631119967,"difficulty":0.0368880033}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Joanne. Scott's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Joanne can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joanne","Linda","Patricia","Scott"],"index":61327,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917572141,"difficulty":0.0082427859}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tomas's card is shown to Kristin. Ashley's card is shown to Kristin. Kristin's card is shown to Tomas. Ashley's card is shown to Ashley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kristin can now know that Ashley can know whether Kristin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kristin","Tomas","Ashley"],"index":25731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6652867198,"difficulty":0.3347132802}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nichole's card is shown to Betty. Betty's card is shown to Nichole. It is publicly announced that someone picked a red card. It is publicly announced that Nichole does not know whether or not everyone picked a red card. It is publicly announced that Nichole knows whether or not nobody picked a red card. It is publicly announced that Betty picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 1 ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 1 ] 0","hypothesis":"Nichole can now know whether Betty can know that Betty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Betty","Nichole"],"index":26766,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9311510921,"difficulty":0.0688489079}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candida's card is shown to Bruce. Bruce's card is shown to Candida. Morris's card is shown to Candida. Bruce's card is shown to Morris. Candida's card is shown to Morris. Morris's card is shown to Timmy. It is publicly announced that someone picked a red card. It is publicly announced that Timmy knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Candida can now know whether Bruce can know that Candida picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bruce","Candida","Morris","Timmy"],"index":58653,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8544653058,"difficulty":1.8544653058}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Francine. George's card is shown to George. George's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Francine picked a red card. It is publicly announced that Francine knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Richard can now know whether George can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Francine","George","Richard"],"index":11648,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Robin. Lynn's card is shown to Robin. Mario's card is shown to Robin. Robin's card is shown to Lynn. Dana's card is shown to Lynn. Robin's card is shown to Mario. Dana's card is shown to Dana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:1 Agentd: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 Agentb:1,4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dana can now know that Robin can know that Mario picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robin","Lynn","Mario","Dana"],"index":22679,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974621534,"difficulty":0.0025378466}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Ruby. Betty's card is shown to Ruby. Ruby's card is shown to Betty. Betty's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Betty knows whether someone picked a red card. It is publicly announced that Betty knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Betty can now know whether Ruby can know whether Ruby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ruby","Betty"],"index":20240,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9942494631,"difficulty":0.0057505369}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Anthony's card is shown to Mark. Susie's card is shown to Mark. Susie's card is shown to Susie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know that Mark can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Mark","Susie"],"index":43582,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973657727,"difficulty":0.0026342273}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Timothy. Winifred's card is shown to Timothy. Timothy's card is shown to Issac. Issac's card is shown to Issac. Winifred's card is shown to Winifred. Winifred's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether Timothy picked a red card. It is publicly announced that Timothy knows whether or not nobody picked a red card. It is publicly announced that Winifred does not know whether Jason picked a red card. It is publicly announced that Issac knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Winifred can now know whether Timothy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Issac","Winifred","Jason"],"index":5045,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997076392,"difficulty":0.0002923608}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Stacy. Stacy's card is shown to Mark. Evelyn's card is shown to Mark. Patricia's card is shown to Evelyn. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,4 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:2 Agentb:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stacy","Patricia","Mark","Evelyn"],"index":10312,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985166192,"difficulty":0.0014833808}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Maureen. Kasey's card is shown to Christopher. Christopher's card is shown to Christopher. Maureen's card is shown to Thomas. Christopher's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kasey can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kasey","Maureen","Christopher","Thomas"],"index":20086,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6049044132,"difficulty":0.3950955868}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felix's card is shown to Felix. Debbie's card is shown to Felix. Louis's card is shown to Felix. Debbie's card is shown to Debbie. Louis's card is shown to Debbie. Felix's card is shown to Louis. Victor's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that Debbie does not know whether Victor picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1 Agentd: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 Agentb:2,3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Debbie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Felix","Debbie","Louis","Victor"],"index":57750,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984540939,"difficulty":0.0015459061}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Roy. Catherine's card is shown to Freddy. Denita's card is shown to Catherine. Freddy's card is shown to Catherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Freddy can now know whether Denita can know that Catherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Denita","Roy","Freddy","Catherine"],"index":38567,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9268438816,"difficulty":1.9268438816}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Whitney's card is shown to Thomas. Shirley's card is shown to Whitney. Jodie's card is shown to Whitney. Thomas's card is shown to Shirley. Whitney's card is shown to Jodie. Shirley's card is shown to Jodie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shirley can now know that Jodie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Whitney","Shirley","Jodie"],"index":52990,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999714911,"difficulty":0.000285089}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felicitas's card is shown to Monica. Steve's card is shown to Felicitas. Delmar's card is shown to Felicitas. Monica's card is shown to Steve. Felicitas's card is shown to Steve. Felicitas's card is shown to Delmar. Steve's card is shown to Delmar. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Delmar can now know whether Monica can know whether Steve picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monica","Felicitas","Steve","Delmar"],"index":15503,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981880784,"difficulty":0.0018119216}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Deanna. Christopher's card is shown to Christopher. John's card is shown to Christopher. Harold's card is shown to Christopher. John's card is shown to John. Harold's card is shown to Harold. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that John can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deanna","Christopher","John","Harold"],"index":32553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9900394082,"difficulty":0.0099605918}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Gary. David's card is shown to Gary. Gary's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Gary knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Gary can now know that David can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gary","David"],"index":3950,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6536402702,"difficulty":1.6536402702}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Juanita. Noah's card is shown to Juanita. Juanita's card is shown to Noah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Noah can now know that Juanita can know that Noah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juanita","Noah","Carolyn"],"index":54080,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972617626,"difficulty":0.0027382374}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Garrett's card is shown to Garrett. Mimi's card is shown to Mimi. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Phyllis can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Phyllis","Lavonna","Garrett","Mimi"],"index":41657,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999768436,"difficulty":0.000231564}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tony's card is shown to Tony. Tuan's card is shown to Tony. Tony's card is shown to Charles. Betty's card is shown to Charles. Tuan's card is shown to Charles. Betty's card is shown to Betty. Tuan's card is shown to Betty. Tony's card is shown to Tuan. Tuan's card is shown to Tuan. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 Agentc:3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 Agentc:3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tuan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tony","Charles","Betty","Tuan"],"index":59271,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983782768,"difficulty":0.0016217232}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Jefferson's card is shown to Jefferson. Mary's card is shown to Stephen. Jefferson's card is shown to Dorris. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Jefferson picked a red card. It is publicly announced that Dorris knows whether Jefferson picked a red card. It is publicly announced that Mary does not know whether Stephen picked a red card. It is publicly announced that Jefferson knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Dorris can now know whether Jefferson can know whether Stephen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Jefferson","Stephen","Dorris"],"index":17158,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978547692,"difficulty":0.0021452308}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Patricia. Marie's card is shown to Sandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Marie","Sandra"],"index":22638,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985376596,"difficulty":0.0014623404}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Susan. Susan's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that Susan knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Randy can now know that Susan can know that Susan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Susan","Randy"],"index":8746,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9515817761,"difficulty":0.0484182239}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marjorie's card is shown to Marjorie. Mildred's card is shown to Gary. Gary's card is shown to Mildred. Mildred's card is shown to Mildred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gary can now know whether Mildred can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marjorie","Gary","Mildred"],"index":47508,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997057319,"difficulty":0.0002942681}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Victor's card is shown to Christopher. Yvonne's card is shown to Yvonne. Christopher's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that Yvonne does not know whether Christopher picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb 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:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Victor can now know whether Christopher can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Yvonne","Victor"],"index":36053,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994655252,"difficulty":0.0005344748}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Austin. Tamar's card is shown to Austin. Arthur's card is shown to Austin. Tamar's card is shown to Robert. Tamar's card is shown to Arthur. Arthur's card is shown to Arthur. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tamar can now know that Robert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Austin","Robert","Tamar","Arthur"],"index":65793,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997140765,"difficulty":0.0002859235}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Blanch. Martha's card is shown to Marcelino. Raymond's card is shown to Marcelino. Raymond's card is shown to Martha. Martha's card is shown to Raymond. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marcelino can now know that Raymond picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Blanch","Marcelino","Martha","Raymond"],"index":51072,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978573918,"difficulty":0.0021426082}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Oscar. Tara's card is shown to Oscar. Blanche's card is shown to Blanche. Gregory's card is shown to Tara. It is publicly announced that someone picked a red card. It is publicly announced that Gregory does not know whether Tara picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Gregory can now know whether Blanche can know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Oscar","Blanche","Gregory","Tara"],"index":40862,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9626654387,"difficulty":0.0373345613}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Mary. Mary's card is shown to Ruth. Robert's card is shown to Ruth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clifford can now know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clifford","Mary","Robert","Ruth"],"index":59896,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983752966,"difficulty":0.0016247034}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Cynthia. Steven's card is shown to Steven. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether or not everyone picked a red card. It is publicly announced that Steven knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Cynthia can now know whether Steven can know that Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cynthia","Steven"],"index":10138,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9213355184,"difficulty":1.9213355184}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Kelly. William's card is shown to Kelly. Kelly's card is shown to Bonnie. Bonnie's card is shown to Bonnie. William's card is shown to William. Kelly's card is shown to Melanie. Bonnie's card is shown to Melanie. It is publicly announced that someone picked a red card. It is publicly announced that Kelly does not know whether Melanie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Kelly can now know that Melanie can know whether Melanie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Bonnie","William","Melanie"],"index":51708,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6372243166,"difficulty":0.3627756834}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Michael's card is shown to Eddie. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card. It is publicly announced that Michael knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Eddie can now know that Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Eddie"],"index":61221,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9109556675,"difficulty":0.0890443325}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Latonya. Clarence's card is shown to Latonya. George's card is shown to George. Latonya's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Latonya does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Latonya can now know that George can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Latonya","George","Clarence"],"index":5960,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9886277318,"difficulty":0.0113722682}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Etta's card is shown to Etta. Rowena's card is shown to Etta. Donald's card is shown to Rowena. Etta's card is shown to Rowena. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know whether Rowena picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Etta","Rowena"],"index":58769,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.842869401,"difficulty":0.157130599}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Fredrick's card is shown to James. Fredrick's card is shown to Vernita. James's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Nancy does not know whether Fredrick picked a red card. It is publicly announced that Vernita does not know whether Nancy picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Vernita can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Vernita","Nancy","Fredrick"],"index":44089,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Sheila. Fred's card is shown to Sheila. Sheila's card is shown to David. David's card is shown to David. Fred's card is shown to David. Sheila's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Sheila does not know whether Sheila picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Fred can now know that Fred picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sheila","David","Fred"],"index":34547,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9638840556,"difficulty":0.0361159444}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Richard. Efrain's card is shown to Richard. Richard's card is shown to Ruth. Rosa's card is shown to Rosa. It is publicly announced that someone picked a red card. It is publicly announced that Ruth picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Ruth can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Ruth","Rosa","Efrain"],"index":7823,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Pamela. Pamela's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"John can now know that Pamela can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pamela","John"],"index":321,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984429479,"difficulty":0.0015570521}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Todd. Yolanda's card is shown to William. Todd's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Todd picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Todd can now know that William can know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Todd","William","Kevin","Yolanda"],"index":6478,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9848970175,"difficulty":1.9848970175}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeff's card is shown to Cecil. Eldon's card is shown to Joy. Joy's card is shown to Joy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Cecil does not know whether Jeff picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Eldon can now know that Cecil can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eldon","Cecil","Jeff","Joy"],"index":60763,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997164607,"difficulty":0.0002835393}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Kenneth's card is shown to Doris. It is publicly announced that someone picked a red card. It is publicly announced that Doris does not know whether Doris picked a red card. It is publicly announced that Kenneth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Doris can now know that Kenneth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenneth","Doris"],"index":28250,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mercedes's card is shown to Angela. Angela's card is shown to Chester. Mercedes's card is shown to Chester. Angela's card is shown to Mercedes. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mercedes can now know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Angela","Chester","Mercedes"],"index":66803,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6854445934,"difficulty":1.6854445934}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Karri. Karri's card is shown to Regina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lucy can now know whether Karri can know that Karri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karri","Lucy","Regina"],"index":6121,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6235328317,"difficulty":0.3764671683}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norma's card is shown to Stanley. Mark's card is shown to Mark. Norma's card is shown to Norma. It is publicly announced that someone picked a red card. It is publicly announced that Norma does not know whether Mark picked a red card. It is publicly announced that Mark does not know whether Norma picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Norma can now know that Stanley can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stanley","Mark","Norma"],"index":37129,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997841716,"difficulty":0.0002158284}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to Victoria. Lawrence's card is shown to Victoria. Deanna's card is shown to Gregory. Victoria's card is shown to Deanna. It is publicly announced that someone picked a red card. It is publicly announced that Lawrence does not know whether Lawrence picked a red card. It is publicly announced that Victoria does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Gregory can now know that Deanna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Lawrence","Gregory","Deanna"],"index":26481,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7216499448,"difficulty":0.2783500552}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Megan's card is shown to Jackie. Edward's card is shown to Megan. Elsa's card is shown to Megan. Megan's card is shown to Edward. Elsa's card is shown to Elsa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Megan can now know whether Jackie can know that Elsa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jackie","Megan","Edward","Elsa"],"index":65445,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9024967551,"difficulty":0.0975032449}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heather's card is shown to Joe. Joe's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that Joe knows whether someone picked a red card. It is publicly announced that Joe does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Heather can now know that Joe can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joe","Heather"],"index":57802,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997773767,"difficulty":0.0002226233}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Charles. Charles's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that William picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"William can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Charles","Donna"],"index":17035,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5931307077,"difficulty":1.5931307077}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Terrell's card is shown to Olivia. Olivia's card is shown to Terrell. Michael's card is shown to George. Olivia's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether George can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Olivia","Terrell","George"],"index":32856,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elisa's card is shown to Brian. Brian's card is shown to Karen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know that Karen can know that Elva picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Karen","Elisa","Elva"],"index":67036,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984871149,"difficulty":0.0015128851}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Paul. Vida's card is shown to Vida. Eric's card is shown to Vida. Paul's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Vida does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know that Vida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Joseph","Vida","Eric"],"index":10145,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7694762349,"difficulty":0.2305237651}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Preston's card is shown to Catherine. Marian's card is shown to Catherine. Marian's card is shown to Preston. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Preston can now know that Catherine can know that Preston picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Catherine","Preston","Marian"],"index":61154,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960401058,"difficulty":0.0039598942}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Mark's card is shown to Aaron. Hugh's card is shown to Hugh. Aaron's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Benjamin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Hugh can now know that Aaron can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Aaron","Hugh","Benjamin"],"index":35665,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981752634,"difficulty":0.0018247366}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steve's card is shown to Walter. Steve's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Steve knows whether Walter picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Steve can now know that Steve picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Walter","Steve"],"index":5036,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9972555041,"difficulty":0.0027444959}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Jeffrey. Mary's card is shown to Jeffrey. Mark's card is shown to Jeffrey. Mary's card is shown to Mary. Mark's card is shown to Mary. Jeffrey's card is shown to Mark. Mary's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mark can now know whether Mary can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeffrey","Mary","Mark"],"index":4360,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999705255,"difficulty":0.000294745}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Gwen. Patricia's card is shown to Gwen. Laura's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Laura can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gwen","Laura","Patricia"],"index":50280,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953363538,"difficulty":0.0046636462}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Jose. Rosemary's card is shown to Holly. Rosemary's card is shown to Rosemary. Cynthia's card is shown to Cynthia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know whether Jose can know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","Holly","Rosemary","Cynthia"],"index":28260,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977204204,"difficulty":0.0022795796}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Horace's card is shown to Horace. Horace's card is shown to Yvonne. Yvonne's card is shown to Yvonne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Horace can now know that Andrew can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Horace","Andrew","Yvonne","Sharon"],"index":19749,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997217059,"difficulty":0.0002782941}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lindsay's card is shown to Lindsay. Anne's card is shown to Lindsay. Lindsay's card is shown to William. Anne's card is shown to William. Anne's card is shown to Anne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Anne can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lindsay","William","Anne"],"index":27065,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adrienne's card is shown to Thomas. Joanne's card is shown to Thomas. Joanne's card is shown to Adrienne. Thomas's card is shown to Joanne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joanne can now know whether Thomas can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Adrienne","Joanne"],"index":58847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yvette's card is shown to Yvette. David's card is shown to Yvette. William's card is shown to Yvette. William's card is shown to David. William's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card. It is publicly announced that David does not know whether David picked a red card. It is publicly announced that Yvette knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Yvette can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Yvette","David","William"],"index":40234,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8562533855,"difficulty":0.1437466145}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victor's card is shown to Victor. Mary's card is shown to Ruby. Victor's card is shown to Mary. Darrin's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruby can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","Darrin","Ruby","Mary"],"index":18748,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982403517,"difficulty":0.0017596483}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Ronald. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that George knows whether someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (~(1&2)) ] 0","hypothesis":"George can now know whether Ronald can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronald","George"],"index":4958,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996987581,"difficulty":0.0003012419}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marissa's card is shown to Marissa. Jeremy's card is shown to Marissa. Marissa's card is shown to Jeremy. Jeremy's card is shown to Gayla. Winford's card is shown to Gayla. Gayla's card is shown to Winford. It is publicly announced that someone picked a red card. It is publicly announced that Jeremy picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Jeremy can now know that Winford can know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marissa","Jeremy","Gayla","Winford"],"index":4651,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9344180226,"difficulty":0.0655819774}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yolanda's card is shown to Merle. Mattie's card is shown to Mattie. Merle's card is shown to Yolanda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know that Merle can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Merle","Mattie","Rita","Yolanda"],"index":42175,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99836725,"difficulty":0.00163275}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Betty. Donald's card is shown to Mildred. Betty's card is shown to James. Betty's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Mildred","James","Donald"],"index":48516,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983505011,"difficulty":0.0016494989}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jay's card is shown to Rick. Stephanie's card is shown to Rick. Rick's card is shown to Pierre. Rick's card is shown to Stephanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jay can now know whether Pierre picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jay","Rick","Pierre","Stephanie"],"index":47482,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9279618263,"difficulty":0.0720381737}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Trevor's card is shown to Trevor. Trevor's card is shown to Michael. Thomas's card is shown to Keith. Keith's card is shown to Keith. It is publicly announced that someone picked a red card. It is publicly announced that Thomas picked a black card. It is publicly announced that Trevor picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 1 ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Michael can now know that Trevor can know that Trevor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Trevor","Thomas","Michael","Keith"],"index":13297,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7471942902,"difficulty":0.2528057098}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Traci's card is shown to Traci. Clayton's card is shown to Clayton. It is publicly announced that someone picked a red card. It is publicly announced that Traci does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Traci can now know whether Clayton can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Traci","Clayton"],"index":10054,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997692704,"difficulty":0.0002307296}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Eva. Ronald's card is shown to Ronald. Eva's card is shown to Ilene. Ronald's card is shown to Ilene. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eva","Ronald","Ilene","Patricia"],"index":30479,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919546247,"difficulty":0.0080453753}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marian's card is shown to James. Marian's card is shown to Marian. James's card is shown to Olivia. Olivia's card is shown to Olivia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Marian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Marian","Olivia"],"index":57257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5800293088,"difficulty":0.4199706912}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allison's card is shown to Yvonne. Tracy's card is shown to Allison. Yvonne's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Allison does not know whether Allison picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Allison can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Yvonne","Allison","Tracy"],"index":61108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracey's card is shown to Jeffery. Jeffery's card is shown to Tracey. Concetta's card is shown to Tracey. Jeffery's card is shown to Concetta. Tracey's card is shown to Concetta. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Concetta can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffery","Tracey","Concetta"],"index":28803,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lahoma's card is shown to Justin. Nathaniel's card is shown to Matthew. Lahoma's card is shown to Nathaniel. Nathaniel's card is shown to Lahoma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know that Nathaniel can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Matthew","Nathaniel","Lahoma"],"index":14954,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997133613,"difficulty":0.0002866387}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arturo's card is shown to Arturo. Randy's card is shown to Sally. Phillip's card is shown to Randy. Randy's card is shown to Phillip. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Phillip can now know that Randy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arturo","Sally","Randy","Phillip"],"index":23650,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997772574,"difficulty":0.0002227426}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Joseph picked a red card. It is publicly announced that Joseph knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Joseph can now know whether Shannon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Shannon"],"index":6939,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6726197004,"difficulty":1.6726197004}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryne's card is shown to Kathryne. Willie's card is shown to Kathryne. Walter's card is shown to Kathryne. Willie's card is shown to Willie. Grace's card is shown to Willie. Walter's card is shown to Walter. Grace's card is shown to Walter. Willie's card is shown to Grace. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Walter can now know whether Willie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathryne","Willie","Walter","Grace"],"index":59576,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8038173914,"difficulty":1.8038173914}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melanie's card is shown to Melanie. Melanie's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Joseph can now know whether Melanie can know whether Melanie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melanie","Joseph"],"index":19261,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9964197874,"difficulty":0.0035802126}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Joseph. Steven's card is shown to Joseph. Steven's card is shown to Jennifer. Jennifer's card is shown to Steven. Steven's card is shown to Steven. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether Jennifer picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jennifer can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Jennifer","Steven"],"index":2865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999779284,"difficulty":0.000220716}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether someone picked a red card. It is publicly announced that Anthony knows whether someone picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! 2 ] (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! 2 ] 0","hypothesis":"Anthony can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anthony","Patricia"],"index":32557,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999783814,"difficulty":0.000216186}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Jeffrey. Jeffrey's card is shown to Joseph. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey picked a red card. It is publicly announced that Joseph picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] 0","hypothesis":"Jeffrey can now know whether Joseph can know whether Jeffrey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeffrey","Joseph"],"index":44060,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970641732,"difficulty":0.0029358268}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Karen. Charles's card is shown to Theodore. Theodore's card is shown to Michelle. Michelle's card is shown to Michelle. Karen's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Charles picked a red card. It is publicly announced that Theodore picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(2) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Charles can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Theodore","Michelle","Charles"],"index":46422,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984351993,"difficulty":0.0015648007}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Florence's card is shown to Florence. Andrew's card is shown to Florence. Andrew's card is shown to Andrew. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Florence can now know that Andrew can know whether Florence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","Andrew","Daniel"],"index":9785,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7570416927,"difficulty":0.2429583073}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Richard. Richard's card is shown to Nicole. Rita's card is shown to Nicole. Richard's card is shown to Rita. Nicole's card is shown to Rita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nicole can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Nicole","Rita"],"index":29207,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997729659,"difficulty":0.0002270341}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Sally. Sally's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether or not everyone picked a red card. It is publicly announced that Sally knows whether Sally picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Sally can now know that Deborah can know that Deborah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sally","Deborah"],"index":22645,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5625312924,"difficulty":0.4374687076}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Andrew. Andrew's card is shown to Esther. Esther's card is shown to Dean. Dean's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dean can now know that Andrew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Esther","Dean","John"],"index":12557,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982642531,"difficulty":0.0017357469}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wendy's card is shown to Wendy. Ali's card is shown to Wendy. Wendy's card is shown to Ali. Ali's card is shown to Ali. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Wendy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Wendy","Ali"],"index":36319,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6185434461,"difficulty":0.3814565539}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francisco's card is shown to Patricia. Mary's card is shown to Francisco. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Francisco knows whether Mary picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Francisco can now know whether Mary can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Francisco","Mary"],"index":27487,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999481976,"difficulty":0.000518024}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hillary's card is shown to Walter. Karen's card is shown to Karen. Walter's card is shown to Hillary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Hillary can now know that Karen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Walter","Karen","Hillary"],"index":45982,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984278679,"difficulty":0.0015721321}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Carol. Carol's card is shown to Carol. Latoya's card is shown to Carol. Jean's card is shown to Latoya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 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:1,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Chester can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jean","Chester","Carol","Latoya"],"index":25229,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997715354,"difficulty":0.0002284646}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Teresa. Teresa's card is shown to Melissa. Teresa's card is shown to Mark. Melissa's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Teresa can now know that Melissa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Teresa","Melissa","Mark"],"index":27335,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Charles. Roland's card is shown to Eric. Charles's card is shown to Roland. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Michael can know whether Roland picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Eric","Roland","Michael"],"index":32453,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7374662757,"difficulty":0.2625337243}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Michelle. Anna's card is shown to Michelle. Michelle's card is shown to Amanda. Amanda's card is shown to Amanda. Amanda's card is shown to Anna. Anna's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Anna does not know whether Michelle picked a red card. It is publicly announced that Amanda does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Amanda can now know whether Michelle can know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Amanda","Anna"],"index":51536,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9229752421,"difficulty":0.0770247579}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Peter. Kris's card is shown to Gina. Gina's card is shown to Kris. Peter's card is shown to Karen. Gina's card is shown to Karen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gina can now know that Karen can know that Gina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Peter","Gina","Kris","Karen"],"index":58389,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968403578,"difficulty":0.0031596422}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Jason. Jason's card is shown to Beulah. Beulah's card is shown to Beulah. Jason's card is shown to Maria. Beulah's card is shown to Maria. Maria's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Beulah can now know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jason","Beulah","Maria"],"index":45585,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7766760588,"difficulty":0.2233239412}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurice's card is shown to Maureen. Bonnie's card is shown to Maureen. It is publicly announced that someone picked a red card. It is publicly announced that Maurice does not know whether Maureen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Maurice can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maurice","Bonnie","Maureen"],"index":53479,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997197986,"difficulty":0.0002802014}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Raymond. Earl's card is shown to Raymond. Donald's card is shown to Raymond. Raymond's card is shown to Earl. Donald's card is shown to Earl. Raymond's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymond can now know that Earl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Donna","Earl","Donald"],"index":40747,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979903698,"difficulty":0.0020096302}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Stacy. Philip's card is shown to Stacy. Stacy's card is shown to Brenda. Stacy's card is shown to Jennifer. Brenda's card is shown to Philip. Jennifer's card is shown to Philip. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Philip can now know whether Brenda can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stacy","Brenda","Jennifer","Philip"],"index":16549,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Mary can now know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Kevin","Linda"],"index":6520,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9972015619,"difficulty":0.0027984381}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Lisa. Lisa's card is shown to Lisa. Steven's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know whether Rosemary can know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosemary","Lisa","Steven"],"index":52119,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6996873617,"difficulty":1.6996873617}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to William. Ela's card is shown to Harold. Gertrude's card is shown to Harold. William's card is shown to Ela. Gertrude's card is shown to Ela. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether Gertrude picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"William can now know whether Harold can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Harold","Ela","Gertrude"],"index":56224,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Bruce. Christina's card is shown to Bruce. Jake's card is shown to Christina. Bruce's card is shown to Jake. Jake's card is shown to Jake. It is publicly announced that someone picked a red card. It is publicly announced that Jake does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bruce can now know whether Jake can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bruce","Christina","Jake"],"index":60120,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996808767,"difficulty":0.0003191233}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. Todd's card is shown to Paul. Paul's card is shown to Todd. Todd's card is shown to Todd. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether Todd picked a red card. It is publicly announced that Paul picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 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 2) ] [ ! 1 ] 0","hypothesis":"Paul can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Paul","Todd"],"index":21485,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Gustavo. Natasha's card is shown to Gustavo. Gustavo's card is shown to Natasha. Natasha's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Natasha picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Natasha can now know whether William can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Gustavo","Natasha","Shannon"],"index":43116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995318651,"difficulty":0.0004681349}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Bertha. Jennifer's card is shown to Bertha. Alan's card is shown to Alan. Geoffrey's card is shown to Jennifer. Bertha's card is shown to Jennifer. Alan's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Geoffrey picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Geoffrey can now know that Alan can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geoffrey","Bertha","Alan","Jennifer"],"index":59101,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997833371,"difficulty":0.0002166629}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to John. James's card is shown to James. James's card is shown to Molly. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Molly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","John","James","Molly"],"index":8187,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978778362,"difficulty":0.0021221638}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glenn's card is shown to Glenn. Donald's card is shown to Glenn. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb 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:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Glenn can now know whether Donald can know that Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Glenn","Donald"],"index":17378,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9679307938,"difficulty":0.0320692062}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. Charles's card is shown to Troy. Kristen's card is shown to Troy. Paul's card is shown to Kristen. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether Paul picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Paul can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Troy","Charles","Kristen"],"index":2371,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986152649,"difficulty":0.0013847351}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathy's card is shown to Kathy. Kathryn's card is shown to Kathy. Kathy's card is shown to Terry. Terry's card is shown to Terry. Kathryn's card is shown to Terry. Kathy's card is shown to Kathryn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathryn can now know that Kathy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathy","Terry","Kathryn"],"index":67607,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981870055,"difficulty":0.0018129945}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myrna's card is shown to Jimmie. Jimmie's card is shown to Myrna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jimmie can now know whether Myrna can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmie","Myrna","Anthony"],"index":31910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999769628,"difficulty":0.000230372}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Brandon. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Brandon knows whether someone picked a red card. It is publicly announced that Brandon does not know whether or not everyone picked a red card. It is publicly announced that Brandon picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(1) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(1) ] 0","hypothesis":"Larry can now know that Brandon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brandon","Larry"],"index":35687,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.639018178,"difficulty":1.639018178}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Steven. Gloria's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that Gloria does not know whether Steven picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Gloria can now know that Steven can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Gloria"],"index":29037,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997801185,"difficulty":0.0002198815}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leo's card is shown to Leo. Alva's card is shown to Leo. Susann's card is shown to Alva. Susann's card is shown to Susann. Melissa's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melissa can now know that Alva picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leo","Alva","Susann","Melissa"],"index":60202,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980788231,"difficulty":0.0019211769}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Pauline. Elizabeth's card is shown to Pauline. Pauline's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Pauline picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Elizabeth can now know that Pauline can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pauline","Elizabeth"],"index":3997,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997105002,"difficulty":0.0002894998}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aaron's card is shown to Francis. Susan's card is shown to Susan. Susan's card is shown to James. Aaron's card is shown to James. Francis's card is shown to Aaron. Susan's card is shown to Aaron. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francis","Susan","James","Aaron"],"index":48167,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9916439652,"difficulty":0.0083560348}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jill's card is shown to Jill. Jill's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that James knows whether James picked a red card. It is publicly announced that Jill knows whether Jill picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jill","James"],"index":47943,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9928432703,"difficulty":0.0071567297}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Donald. Brian's card is shown to Brian. Paula's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Brian can now know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Brian","David","Paula"],"index":27702,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5697490573,"difficulty":1.5697490573}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to Wayne. Kimberlee's card is shown to Wayne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Erin can now know whether Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erin","Wayne","Kimberlee"],"index":52055,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9433723092,"difficulty":0.0566276908}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rolando's card is shown to Rolando. James's card is shown to Rolando. Rolando's card is shown to Peter. Kyle's card is shown to Peter. Rolando's card is shown to Kyle. James's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that Kyle picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1,4 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:1,4 Agentb:1,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Kyle can now know that Rolando can know that Rolando picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rolando","Peter","Kyle","James"],"index":23265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9304373264,"difficulty":0.0695626736}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Lucy. Jim's card is shown to Lucy. Tuyet's card is shown to Jim. Jim's card is shown to Tuyet. It is publicly announced that someone picked a red card. It is publicly announced that Tuyet does not know whether Tuyet picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lucy can now know that Jim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lucy","Jim","Tuyet"],"index":22118,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9800134301,"difficulty":0.0199865699}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sergio's card is shown to Lorenza. Jason's card is shown to Sergio. Sergio's card is shown to Michele. Jason's card is shown to Michele. Lorenza's card is shown to Jason. Michele's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sergio can now know that Lorenza picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorenza","Sergio","Michele","Jason"],"index":56704,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973312616,"difficulty":0.0026687384}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Jimmie. Joan's card is shown to Tom. Tom's card is shown to Joan. Joan's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Tom can now know that Joan can know that Tom picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmie","Tom","Joan"],"index":491,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7127860188,"difficulty":1.7127860188}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Leon. Gary's card is shown to Gary. George's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Leon knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Leon can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leon","Gary","George"],"index":5447,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985812902,"difficulty":0.0014187098}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jeremy. Susan's card is shown to Jessica. Susan's card is shown to Susan. Hilda's card is shown to Susan. Susan's card is shown to Hilda. Hilda's card is shown to Hilda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeremy can now know whether Hilda can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeremy","Jessica","Susan","Hilda"],"index":22758,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999424696,"difficulty":0.000575304}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phuong's card is shown to Keith. Keith's card is shown to Phuong. Phuong's card is shown to Phuong. It is publicly announced that someone picked a red card. It is publicly announced that Phuong knows whether someone picked a red card. It is publicly announced that Keith knows whether someone picked a red card. It is publicly announced that Phuong knows whether Keith picked a red card. It is publicly announced that Phuong knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Phuong can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Keith","Phuong"],"index":33700,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Forrest's card is shown to Forrest. Deborah's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Forrest does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Deborah can now know that Forrest can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Forrest","Deborah"],"index":58759,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989147186,"difficulty":0.0010852814}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kate's card is shown to Kate. Penelope's card is shown to Kate. Penelope's card is shown to Katherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kate can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kate","Penelope","Katherine"],"index":32217,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994261265,"difficulty":0.0005738735}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Danny. Danny's card is shown to Thomas. Thomas's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Danny","Thomas","John"],"index":7853,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993051291,"difficulty":0.0006948709}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. James's card is shown to Michael. Michael's card is shown to James. James's card is shown to James. Joseph's card is shown to James. James's card is shown to Joseph. Joseph's card is shown to Martin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Martin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","James","Joseph","Martin"],"index":65632,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983926415,"difficulty":0.0016073585}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Dianne. Al's card is shown to Dianne. Dianne's card is shown to Lisa. Al's card is shown to Lisa. Kathryn's card is shown to Kathryn. Lisa's card is shown to Al. It is publicly announced that someone picked a red card. It is publicly announced that Dianne knows whether or not nobody picked a red card. It is publicly announced that Dianne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 1 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 1 ] 0","hypothesis":"Kathryn can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dianne","Lisa","Kathryn","Al"],"index":37117,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990420938,"difficulty":0.0009579062}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to James. James's card is shown to Edward. Ericka's card is shown to Ericka. Ericka's card is shown to Keith. It is publicly announced that someone picked a red card. It is publicly announced that Keith does not know whether Edward picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Edward can now know that James can know whether Keith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Edward","Ericka","Keith"],"index":12589,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952581525,"difficulty":0.0047418475}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Cheryl. Kathryn's card is shown to Cheryl. Kathryn's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Cheryl does not know whether Cheryl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Cheryl can now know that Amanda can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amanda","Cheryl","Kathryn","Linda"],"index":1049,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990441203,"difficulty":0.0009558797}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jane's card is shown to Jane. Robyn's card is shown to Jane. Ashley's card is shown to Ashley. Jane's card is shown to Robyn. Robyn's card is shown to Robyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ashley can now know whether Ashley picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jane","Ashley","Robyn"],"index":7396,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5084484816,"difficulty":0.4915515184}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Donna. Donna's card is shown to Brent. Brenda's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Brenda does not know whether Donna picked a red card. It is publicly announced that Brenda does not know whether Donna picked a red card. It is publicly announced that Brenda does not know whether Donna picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3)) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Donna can now know whether Brenda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","Brent","Brenda"],"index":63059,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9871698618,"difficulty":0.0128301382}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlotte's card is shown to Charlotte. Susan's card is shown to Charlotte. Brenda's card is shown to Brenda. Charlotte's card is shown to Susan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charlotte can now know whether Susan can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charlotte","Brenda","Susan"],"index":18923,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993456006,"difficulty":0.0006543994}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Louise. Michael's card is shown to Louise. Joyce's card is shown to Karen. Louise's card is shown to Michael. Michael's card is shown to Michael. Michael's card is shown to Joyce. Joyce's card is shown to Joyce. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1,3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1,3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louise can now know that Karen can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louise","Karen","Michael","Joyce"],"index":41480,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993558526,"difficulty":0.0006441474}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louis's card is shown to Louis. Neil's card is shown to Louis. Louis's card is shown to Stacey. Stacey's card is shown to Neil. Neil's card is shown to Neil. It is publicly announced that someone picked a red card. It is publicly announced that Louis picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Louis can now know whether Stacey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Louis","Stacey","Neil"],"index":9049,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8532918692,"difficulty":1.8532918692}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Milan's card is shown to Milan. Nina's card is shown to Milan. Justin's card is shown to Justin. Nina's card is shown to Justin. Milan's card is shown to Karen. Nina's card is shown to Karen. Nina's card is shown to Nina. It is publicly announced that someone picked a red card. It is publicly announced that Nina does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nina can now know whether Karen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Milan","Justin","Karen","Nina"],"index":5299,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9868761301,"difficulty":0.0131238699}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Heather. Stephen's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Heather picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Stephen can now know whether Stephen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Heather","Stephen"],"index":941,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9852446914,"difficulty":0.0147553086}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. Everett's card is shown to Daniel. Mark's card is shown to Mark. Mark's card is shown to Johnathan. It is publicly announced that someone picked a red card. It is publicly announced that Mark picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Daniel can now know that Everett can know that Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Mark","Everett","Johnathan"],"index":12156,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9804602265,"difficulty":0.0195397735}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Joseph. Alysia's card is shown to Alysia. Leslie's card is shown to Alysia. Leslie's card is shown to Robert. Alysia's card is shown to Leslie. Robert's card is shown to Leslie. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether Alysia can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Alysia","Robert","Leslie"],"index":40174,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9697844386,"difficulty":0.0302155614}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Justin. Justin's card is shown to Robert. Carter's card is shown to Robert. Robert's card is shown to Carter. Shane's card is shown to Carter. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether Shane picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Carter can now know that Shane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Robert","Carter","Shane"],"index":60483,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956160784,"difficulty":0.0043839216}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lee's card is shown to Gwen. Thelma's card is shown to Gwen. Lee's card is shown to Lee. Thelma's card is shown to Thelma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lee can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gwen","Lee","Thelma"],"index":40871,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989535809,"difficulty":0.0010464191}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marla's card is shown to Karl. Karl's card is shown to Willie. Marla's card is shown to Willie. Willie's card is shown to Marla. Marla's card is shown to Marla. It is publicly announced that someone picked a red card. It is publicly announced that Willie does not know whether Willie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Marla can now know whether Willie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karl","Willie","Marla"],"index":47899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5936346054,"difficulty":0.4063653946}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Juliet. Stephen's card is shown to Juliet. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Aaron picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Susan can now know that Juliet picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Aaron","Stephen","Juliet"],"index":35052,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997887671,"difficulty":0.002112329}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Irene. Elizabeth's card is shown to Irene. Elizabeth's card is shown to Rhonda. Irene's card is shown to Elizabeth. Jean's card is shown to Elizabeth. Jean's card is shown to Jean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Irene","Rhonda","Elizabeth","Jean"],"index":9489,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8300721645,"difficulty":1.8300721645}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruben's card is shown to Jason. Leo's card is shown to Ruben. Leo's card is shown to Leo. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Jason can now know that Leo can know that Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Ruben","Leo"],"index":63732,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9824202061,"difficulty":0.0175797939}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Peter. Roy's card is shown to Kevin. Kevin's card is shown to Robert. Robert's card is shown to Robert. Roy's card is shown to Robert. Kevin's card is shown to Roy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Peter can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Peter","Kevin","Robert","Roy"],"index":66888,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993879795,"difficulty":0.0006120205}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ella's card is shown to Brenda. Karen's card is shown to Brenda. Brenda's card is shown to Jose. Ella's card is shown to Jose. Karen's card is shown to Jose. Brenda's card is shown to Ella. Brenda's card is shown to Karen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ella can now know whether Karen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brenda","Jose","Ella","Karen"],"index":31853,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6353532076,"difficulty":0.3646467924}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geneva's card is shown to Geneva. Kerrie's card is shown to Kerrie. Helen's card is shown to Kerrie. Helen's card is shown to Helen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kerrie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Geneva","Kerrie","Helen"],"index":25676,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9914719462,"difficulty":0.0085280538}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Newton. Eli's card is shown to Eli. Edward's card is shown to Eli. Newton's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Newton can now know that Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Newton","Eli","Edward"],"index":46570,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9809897542,"difficulty":0.0190102458}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Kenneth's card is shown to Michael. Kenneth's card is shown to Sheila. Sheila's card is shown to Sheila. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb: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 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that Kenneth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Kenneth","Sheila"],"index":28188,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994257689,"difficulty":0.0005742311}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to Victoria. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Victoria can now know whether Benjamin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Benjamin","Victoria","Mark"],"index":47199,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993641973,"difficulty":0.0006358027}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Violet's card is shown to Sharon. Sharon's card is shown to Judy. Violet's card is shown to Judy. Judy's card is shown to Violet. Violet's card is shown to Violet. It is publicly announced that someone picked a red card. It is publicly announced that Judy knows whether or not everyone picked a red card. It is publicly announced that Judy knows whether Violet picked a red card. It is publicly announced that Judy knows whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Judy can now know whether Sharon can know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Judy","Violet"],"index":54878,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8131505847,"difficulty":0.1868494153}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracy's card is shown to Tracy. Matthew's card is shown to Tracy. Keith's card is shown to Tracy. Marsha's card is shown to Matthew. Marsha's card is shown to Keith. Keith's card is shown to Keith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc: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:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Matthew can now know that Tracy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tracy","Matthew","Marsha","Keith"],"index":40754,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973166585,"difficulty":0.0026833415}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Richard. Richard's card is shown to Randy. Richard's card is shown to Gene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Randy can now know whether Richard can know that Gene picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Randy","Gene"],"index":5026,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.887509644,"difficulty":0.112490356}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessie's card is shown to Jessie. Jessie's card is shown to Bridget. Ervin's card is shown to Bridget. Ervin's card is shown to Andrew. Andrew's card is shown to Ervin. Ervin's card is shown to Ervin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrew can now know whether Jessie can know that Andrew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessie","Bridget","Andrew","Ervin"],"index":18337,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.647980392,"difficulty":0.352019608}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pennie's card is shown to Pennie. Matt's card is shown to Matt. Jennifer's card is shown to Jennifer. Pennie's card is shown to Ebony. Jennifer's card is shown to Ebony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ebony can now know that Jennifer can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pennie","Matt","Jennifer","Ebony"],"index":27292,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9692741036,"difficulty":0.0307258964}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Ryan. Michael's card is shown to Michael. Ryan's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 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:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Melissa can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ryan","Michael","Melissa","Neil"],"index":22288,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9772166014,"difficulty":0.0227833986}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmy's card is shown to Sara. Rhonda's card is shown to Sara. Rhonda's card is shown to Jimmy. Rhonda's card is shown to Star. It is publicly announced that someone picked a red card. It is publicly announced that Star does not know whether Sara picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Sara can now know that Star can know whether Sara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sara","Jimmy","Star","Rhonda"],"index":24206,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6030892134,"difficulty":0.3969107866}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Byron. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Byron does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Kevin can now know that Byron can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Byron","Kevin"],"index":30495,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988942742,"difficulty":0.0011057258}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Alice. Alice's card is shown to Eugene. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Eugene knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Eugene can now know that Eugene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alice","Eugene"],"index":44361,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9895964265,"difficulty":0.0104035735}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Roxanne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christine","Roxanne","James","George"],"index":41326,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989697933,"difficulty":0.0010302067}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norma's card is shown to Norma. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Norma picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Wanda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Norma","Wanda","David"],"index":54611,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9314910769,"difficulty":0.0685089231}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leigh's card is shown to Leigh. Leigh's card is shown to Chelsea. Chelsea's card is shown to Chelsea. It is publicly announced that someone picked a red card. It is publicly announced that Chelsea knows whether or not nobody picked a red card. It is publicly announced that Chelsea knows whether Leigh picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Chelsea can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Leigh","Chelsea"],"index":24580,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987180233,"difficulty":0.0012819767}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Lloyd. Mary's card is shown to Christopher. Christopher's card is shown to Christopher. Eric's card is shown to Christopher. Lloyd's card is shown to Eric. Eric's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Christopher picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Christopher can now know that Lloyd can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Lloyd","Christopher","Eric"],"index":54696,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.711356461,"difficulty":0.288643539}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Mary. Michael's card is shown to Richard. Mary's card is shown to Michael. Richard's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Richard","Michael"],"index":26256,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990051389,"difficulty":0.0009948611}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julia's card is shown to Julia. Lyndsey's card is shown to Julia. Julia's card is shown to Denise. Michael's card is shown to Michael. Denise's card is shown to Lyndsey. Michael's card is shown to Lyndsey. Lyndsey's card is shown to Lyndsey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lyndsey can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julia","Denise","Michael","Lyndsey"],"index":49833,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994131327,"difficulty":0.0005868673}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Jennifer. Ronald's card is shown to Jennifer. Jennifer's card is shown to Linda. Jennifer's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Jennifer","Linda","Ronald"],"index":18760,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989462495,"difficulty":0.0010537505}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Mi. Mi's card is shown to Virginia. Virginia's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mi can now know whether Virginia can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Mi","Virginia","Kimberly"],"index":31298,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9443525076,"difficulty":0.0556474924}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Kevin. Kevin's card is shown to Ana. Ana's card is shown to Ana. Ana's card is shown to Walter. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Walter can now know that Kevin can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Ana","Walter"],"index":33320,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993739724,"difficulty":0.0006260276}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Demetrius. Demetrius's card is shown to Demetrius. Leroy's card is shown to Demetrius. Leroy's card is shown to Leroy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Demetrius can now know whether James can know whether Demetrius picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Demetrius","Leroy"],"index":18071,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973570704,"difficulty":0.0026429296}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Jesse. Katie's card is shown to Frank. Jesse's card is shown to Katie. Katie's card is shown to Katie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jesse can now know whether Jesse picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jesse","Frank","Katie"],"index":17864,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9103828669,"difficulty":0.0896171331}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Heath. Kristopher's card is shown to Andrew. Heath's card is shown to Kristopher. Andrew's card is shown to Kristopher. Kristopher's card is shown to Kristopher. It is publicly announced that someone picked a red card. It is publicly announced that Andrew knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Andrew can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Heath","Andrew","Kristopher"],"index":55949,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993946552,"difficulty":0.0006053448}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Avril's card is shown to Sandra. David's card is shown to Sandra. Marie's card is shown to Sandra. Sandra's card is shown to David. David's card is shown to David. David's card is shown to Marie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sandra","Avril","David","Marie"],"index":17900,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9430911541,"difficulty":0.0569088459}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Audrey's card is shown to Judy. Audrey's card is shown to Audrey. Robert's card is shown to Audrey. Judy's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether Judy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Judy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judy","Audrey","Robert"],"index":10179,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9316136241,"difficulty":0.0683863759}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joe's card is shown to Joe. Joe's card is shown to Joseph. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Grant can now know whether Joe can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Grant","Joe","Joseph"],"index":53834,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994334579,"difficulty":0.0005665421}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mitchell's card is shown to Mitchell. Bruce's card is shown to Mitchell. Edward's card is shown to George. Bruce's card is shown to Edward. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edward can now know that George can know that George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mitchell","George","Edward","Bruce"],"index":2433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981922507,"difficulty":0.0018077493}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Sharon. Sharon's card is shown to Roy. Sharon's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Sharon knows whether or not everyone picked a red card. It is publicly announced that Sylvia does not know whether Roy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sharon can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sharon","Roy","Sylvia","Jason"],"index":64864,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994775653,"difficulty":0.0005224347}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Todd. Wendy's card is shown to Todd. Todd's card is shown to Wendy. Wendy's card is shown to Wendy. Michael's card is shown to Wendy. Wendy's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Todd can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roberta","Todd","Wendy","Michael"],"index":32859,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994143248,"difficulty":0.0005856752}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Debra. Debra's card is shown to Rosa. Rosa's card is shown to Rosa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Rosa can now know that Debra can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Debra","Rosa"],"index":21113,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993891716,"difficulty":0.0006108284}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. David's card is shown to Robert. Robert's card is shown to Robert. Robert's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether Robert can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Robert","Mary"],"index":18030,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5817809105,"difficulty":1.5817809105}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Vivian. Vivian's card is shown to Claire. It is publicly announced that someone picked a red card. It is publicly announced that Claire does not know whether Claire picked a red card. It is publicly announced that Vivian does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Claire can now know whether Vivian can know whether Claire picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vivian","Claire"],"index":12231,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9967783093,"difficulty":0.0032216907}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Sharon's card is shown to Robert. Robert's card is shown to Sharon. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Sharon can now know whether Robert can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Sharon"],"index":13291,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979819059,"difficulty":0.0020180941}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Bryan. Frank's card is shown to Garth. Frank's card is shown to Frank. Frank's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bryan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bryan","Garth","Frank","Barbara"],"index":15759,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993964434,"difficulty":0.0006035566}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denise's card is shown to Denise. Scott's card is shown to Denise. Ray's card is shown to Denise. Rose's card is shown to Ray. Ray's card is shown to Rose. Rose's card is shown to Rose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Denise can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Denise","Scott","Ray","Rose"],"index":13434,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994155169,"difficulty":0.0005844831}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Albert. Vicky's card is shown to Albert. Maxine's card is shown to Albert. Albert's card is shown to Vicky. Maxine's card is shown to Vicky. Albert's card is shown to Maxine. Maxine's card is shown to Maxine. It is publicly announced that someone picked a red card. It is publicly announced that Vicky knows whether or not nobody picked a red card. It is publicly announced that Albert knows whether Susan picked a red card. It is publicly announced that Vicky knows whether or not nobody picked a red card. It is publicly announced that Vicky picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Albert can now know whether Vicky can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Susan","Vicky","Maxine"],"index":12737,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9781746864,"difficulty":0.0218253136}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Sherry. Sherry's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Sherry does not know whether or not everyone picked a red card. It is publicly announced that Angela knows whether Angela picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sherry can now know that Angela can know that Angela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sherry","Angela"],"index":60130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5541439056,"difficulty":0.4458560944}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Susan. David's card is shown to Susan. Susan's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether someone picked a red card. It is publicly announced that David knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"David can now know that Susan can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Susan","David"],"index":51853,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990647435,"difficulty":0.0009352565}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marjorie's card is shown to Dora. Brian's card is shown to Dora. Dora's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marjorie can now know whether Dora can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dora","Marjorie","Brian"],"index":48144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992685914,"difficulty":0.0007314086}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lula's card is shown to Lula. Lula's card is shown to Blanca. Donna's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Lula knows whether or not nobody picked a red card. It is publicly announced that Lula does not know whether Donna picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Blanca can now know whether Donna can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lula","Blanca","Donna"],"index":43257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994298816,"difficulty":0.0005701184}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larue's card is shown to Larue. Larue's card is shown to Roberta. It is publicly announced that someone picked a red card. It is publicly announced that Larue does not know whether Roberta picked a red card. It is publicly announced that Larue knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Larue can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Larue","Roberta"],"index":60735,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994578958,"difficulty":0.0005421042}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Joseph's card is shown to Robert. Joseph's card is shown to Joseph. Janet's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Joseph","Janet"],"index":51953,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999062717,"difficulty":0.000937283}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Roger. Randall's card is shown to Randall. Roger's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether Roger picked a red card. It is publicly announced that Randall does not know whether Roger picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roger","Randall","Mary"],"index":11205,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994327426,"difficulty":0.0005672574}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kent's card is shown to Felisa. George's card is shown to Felisa. Felisa's card is shown to Kent. George's card is shown to George. Earnest's card is shown to George. Earnest's card is shown to Earnest. It is publicly announced that someone picked a red card. It is publicly announced that Earnest does not know whether Kent picked a red card. It is publicly announced that Felisa knows whether George picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (Agenta knows whether 3) ] Agentd knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Earnest can now know whether Felisa can know that George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Felisa","Kent","George","Earnest"],"index":61670,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9577646852,"difficulty":1.9577646852}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Bruce. Bruce's card is shown to Mitchel. Frank's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Bruce knows whether or not nobody picked a red card. It is publicly announced that Bruce does not know whether Frank picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Frank can now know whether Bruce can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bruce","Mitchel","Frank"],"index":16877,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9769206047,"difficulty":0.0230793953}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amber's card is shown to Sandra. Katherine's card is shown to Amber. Katherine's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Katherine knows whether or not nobody picked a red card. It is publicly announced that Amber picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 2 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 2 ] 0","hypothesis":"Amber can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Amber","Katherine","Benjamin"],"index":37907,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990398288,"difficulty":0.0009601712}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Karen. Lee's card is shown to Karen. Karen's card is shown to Rita. Rita's card is shown to Rita. Jaclyn's card is shown to Jaclyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lee can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Rita","Lee","Jaclyn"],"index":6275,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989159107,"difficulty":0.0010840893}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Otha's card is shown to Otha. Jacqueline's card is shown to Lori. Ginger's card is shown to Lori. Otha's card is shown to Jacqueline. Otha's card is shown to Ginger. It is publicly announced that someone picked a red card. It is publicly announced that Ginger does not know whether Ginger picked a red card. It is publicly announced that Jacqueline knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Ginger can now know whether Jacqueline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Otha","Lori","Jacqueline","Ginger"],"index":47509,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9176466465,"difficulty":0.0823533535}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Wade. Margaret's card is shown to Shirley. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Margaret knows whether Margaret picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Wade can now know whether Margaret can know whether Shirley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Wade","Shirley"],"index":64607,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987549782,"difficulty":0.0012450218}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tanja's card is shown to Christine. Christine's card is shown to Tanja. Rosa's card is shown to Tanja. Rosa's card is shown to Rosa. It is publicly announced that someone picked a red card. It is publicly announced that Rosa does not know whether Christine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Rosa can now know whether Christine can know whether Rosa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christine","Tanja","Rosa"],"index":61803,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980408549,"difficulty":0.0019591451}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Ashley's card is shown to Christopher. Alexander's card is shown to Alexander. Robert's card is shown to Alexander. Alexander's card is shown to Ashley. Ashley's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Alexander","Ashley","Robert"],"index":58859,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5617179871,"difficulty":1.5617179871}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jamie's card is shown to Jamie. Jamie's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Jamie does not know whether Jane picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Nora can now know that Jamie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nora","Jamie","Jane"],"index":7471,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999047935,"difficulty":0.000952065}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Carmen's card is shown to John. Michael's card is shown to John. Carmen's card is shown to Rick. Carmen's card is shown to Carmen. Carmen's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Rick picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"John can now know whether Carmen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Rick","Carmen","Michael"],"index":3220,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9592522383,"difficulty":0.0407477617}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Gloria. James's card is shown to Gloria. Teresa's card is shown to Teresa. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Gloria picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"James can now know whether Gloria can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gloria","Teresa","James"],"index":52426,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981437922,"difficulty":0.0018562078}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Xiomara's card is shown to Sharon. Richard's card is shown to Sharon. Sharon's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Xiomara does not know whether Kathy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Xiomara can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Xiomara","Kathy","Sharon","Richard"],"index":51743,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994235039,"difficulty":0.0005764961}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Charles. Charles's card is shown to Mildred. Mildred's card is shown to Mildred. Rita's card is shown to Mildred. William's card is shown to Mildred. Mildred's card is shown to Rita. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Mildred","Rita","William"],"index":4511,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989874959,"difficulty":0.0010125041}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronnie's card is shown to Ronnie. Edward's card is shown to Ronnie. Ronnie's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Ronnie knows whether Ronnie picked a red card. It is publicly announced that Edward does not know whether or not everyone picked a red card. It is publicly announced that Edward does not know whether Edward picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Edward can now know that Ronnie can know whether Edward picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronnie","Edward"],"index":6588,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8688269854,"difficulty":0.1311730146}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresia's card is shown to Carolyn. Carolyn's card is shown to Julie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 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 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Theresia can now know that Carolyn can know whether Julie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Theresia","Carolyn","Julie"],"index":31570,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973345995,"difficulty":0.0026654005}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Roger. Russell's card is shown to Roger. Roger's card is shown to John. John's card is shown to John. Roger's card is shown to Russell. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Russell knows whether Russell picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] [ ! (1&2&3) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] [ ! (1&2&3) ] 0","hypothesis":"John can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roger","John","Russell"],"index":61391,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9955436587,"difficulty":0.0044563413}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Twila's card is shown to Twila. Harry's card is shown to Twila. Harry's card is shown to Harry. Twila's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Harry does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Twila can now know that Twila picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Twila","Harry","Matthew"],"index":62323,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9397266507,"difficulty":0.0602733493}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virgil's card is shown to Lauren. Virgil's card is shown to Theodore. Lauren's card is shown to Clara. Clara's card is shown to Clara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lauren can now know that Virgil can know whether Clara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lauren","Theodore","Virgil","Clara"],"index":7277,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6438952684,"difficulty":1.6438952684}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derek's card is shown to Derek. Ronald's card is shown to Derek. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Ronald picked a red card. It is publicly announced that Ronald does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Derek can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Derek","Ronald"],"index":38097,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968915582,"difficulty":0.0031084418}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. William's card is shown to Michael. William's card is shown to Kristina. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Michael can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Michael","Kristina"],"index":48718,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9878150225,"difficulty":0.0121849775}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Mike. John's card is shown to John. Linda's card is shown to John. John's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Mike picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mike","Theodore","John","Linda"],"index":4466,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982514977,"difficulty":0.0017485023}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Carl's card is shown to Kenneth. Carl's card is shown to Carl. Michael's card is shown to Carl. Kenneth's card is shown to Michael. Carl's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether Carl picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Carl can now know that Carl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Carl","Michael"],"index":35793,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9639113545,"difficulty":0.0360886455}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to Tamar. John's card is shown to Tamar. Connie's card is shown to Connie. Tamar's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Tamar does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Tamar can now know whether John can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tamar","Connie","John"],"index":50248,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9915573597,"difficulty":1.9915573597}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Robin. Mark's card is shown to Robin. Mark's card is shown to Melanie. Robin's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Robin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Melanie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Robin","Melanie","Mark"],"index":24748,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9806975126,"difficulty":0.0193024874}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Oscar's card is shown to Andrew. Mildred's card is shown to Oscar. Andrew's card is shown to Mildred. Oscar's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Oscar knows whether or not nobody picked a red card. It is publicly announced that Oscar does not know whether Andrew picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Andrew can now know that Andrew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrew","Oscar","Mildred"],"index":32272,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9891659617,"difficulty":0.0108340383}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Damon's card is shown to Terrance. Terrance's card is shown to Damon. Stacy's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terrance can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stacy","Terrance","Damon","Robert"],"index":29724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993370175,"difficulty":0.0006629825}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josephine's card is shown to Josephine. Josephine's card is shown to Stacy. Jonathan's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc: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 Agentb:1 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stacy can now know whether Jonathan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josephine","Stacy","Jonathan","John"],"index":26293,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993927479,"difficulty":0.0006072521}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Davis's card is shown to Sharon. Walter's card is shown to Sharon. Sharon's card is shown to Davis. Davis's card is shown to Davis. Sharon's card is shown to Donald. Walter's card is shown to Donald. Sharon's card is shown to Walter. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Davis can now know whether Walter can know whether Davis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Davis","Donald","Walter"],"index":53670,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9969735146,"difficulty":0.0030264854}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Janet. Janet's card is shown to James. James's card is shown to Stephanie. Ilse's card is shown to Stephanie. Ilse's card is shown to Ilse. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether or not nobody picked a red card. It is publicly announced that Stephanie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Janet can now know whether Stephanie can know that Janet picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","James","Stephanie","Ilse"],"index":45950,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9699876904,"difficulty":1.9699876904}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Abigail. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Abigail"],"index":7732,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994168282,"difficulty":0.0005831718}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harry's card is shown to Harry. Mary's card is shown to Harry. Harry's card is shown to Mary. Harry's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey does not know whether Jeffrey picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jeffrey can now know whether Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harry","Mary","Jeffrey"],"index":24227,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9137242436,"difficulty":0.0862757564}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Joann. Joann's card is shown to Maria. Maria's card is shown to Maria. Maria's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know whether Joann can know that Joann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joann","Maria","Robert"],"index":36470,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6048618555,"difficulty":0.3951381445}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ellen's card is shown to Ellen. Ellen's card is shown to Roy. Betty's card is shown to Roy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Betty can now know that Ellen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ellen","Betty","Roy"],"index":43977,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956015348,"difficulty":0.0043984652}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Daniell. Stephen's card is shown to Daniell. Stephen's card is shown to Raymond. Daniell's card is shown to Stephen. Stephen's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Daniell does not know whether Daniell picked a red card. It is publicly announced that Raymond does not know whether or not everyone picked a red card. It is publicly announced that Stephen picked a red card. It is publicly announced that Raymond does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Stephen can now know whether Daniell can know whether Raymond picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniell","Raymond","Stephen"],"index":54831,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985386133,"difficulty":0.0014613867}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. David's card is shown to Charles. Daniel's card is shown to Charles. Daniel's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that David can know that Daniel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","David","Daniel"],"index":2526,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979006052,"difficulty":0.0020993948}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annette's card is shown to Glen. Maurice's card is shown to Annette. Maurice's card is shown to Maurice. It is publicly announced that someone picked a red card. It is publicly announced that Maurice knows whether or not everyone picked a red card. It is publicly announced that Annette does not know whether Glen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Glen can now know whether Maurice can know that Glen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Glen","Annette","Maurice"],"index":21904,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.559333086,"difficulty":1.559333086}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Phillip. Stephanie's card is shown to Stephanie. It is publicly announced that someone picked a red card. It is publicly announced that Stephanie does not know whether Phillip picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Phillip can now know whether Stephanie can know whether Phillip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Phillip","Stephanie"],"index":46565,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979248047,"difficulty":0.0020751953}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Jessica. Constance's card is shown to Jessica. Richard's card is shown to Richard. Constance's card is shown to Richard. Jessica's card is shown to Constance. Richard's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Jessica does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Constance can know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Richard","Constance","Daniel"],"index":52654,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982861876,"difficulty":0.0017138124}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to David. Peter's card is shown to David. Charles's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Peter picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card. It is publicly announced that Charles does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"David can now know that Charles can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","David","Richard","Peter"],"index":35657,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6399667859,"difficulty":1.6399667859}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Freda's card is shown to Freda. Richard's card is shown to Freda. Freda's card is shown to Richard. Freda's card is shown to Jesse. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Freda picked a red card. It is publicly announced that Freda picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Jesse can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Freda","Richard","Jesse"],"index":57284,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994190931,"difficulty":0.0005809069}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dena's card is shown to Patrick. Renee's card is shown to Renee. Dena's card is shown to Dena. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that Patrick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Patrick","Renee","Dena"],"index":26371,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974089265,"difficulty":0.0025910735}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gwendolyn's card is shown to Jon. Robert's card is shown to Robert. Gwendolyn's card is shown to Robert. Gwendolyn's card is shown to Gwendolyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gwendolyn can now know whether Robert can know that Jon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jon","Robert","Gwendolyn"],"index":22057,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9120473266,"difficulty":1.9120473266}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Philip. Cherrie's card is shown to Philip. Anthony's card is shown to Lisa. Philip's card is shown to Cherrie. Cherrie's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cherrie can now know whether Lisa can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Philip","Lisa","Cherrie","Anthony"],"index":9696,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9921938181,"difficulty":0.0078061819}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donn's card is shown to Donn. Donn's card is shown to Avis. Donn's card is shown to Frances. Frances's card is shown to Frances. Freddy's card is shown to Frances. Frances's card is shown to Freddy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Avis can now know whether Donn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donn","Avis","Frances","Freddy"],"index":52272,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5641435981,"difficulty":0.4358564019}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katie's card is shown to Jimmy. Jimmy's card is shown to Katie. It is publicly announced that someone picked a red card. It is publicly announced that Jimmy does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jimmy can now know whether David can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Jimmy","Katie"],"index":8988,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992142916,"difficulty":0.0007857084}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antoinette's card is shown to Antoinette. Antoinette's card is shown to Carl. Carl's card is shown to Carl. It is publicly announced that someone picked a red card. It is publicly announced that Carl knows whether Carl picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Carl can now know that Antoinette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Antoinette","Carl"],"index":10751,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9341638088,"difficulty":0.0658361912}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to David. Ryan's card is shown to Stephen. David's card is shown to Stephen. Stephen's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Ryan knows whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Ryan can now know that David can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ryan","David","Stephen","John"],"index":19877,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8748211861,"difficulty":0.1251788139}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Frederick. Frederick's card is shown to Lisa. Jane's card is shown to David. Frederick's card is shown to Jane. Lisa's card is shown to Jane. Jane's card is shown to Jane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frederick","Lisa","David","Jane"],"index":2462,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958429933,"difficulty":0.0041570067}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alma's card is shown to Alexandria. Alma's card is shown to Alma. Alexandria's card is shown to Shakia. Shakia's card is shown to Shakia. It is publicly announced that someone picked a red card. It is publicly announced that Alma does not know whether Alexandria picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alma can now know whether Alexandria can know that Alma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alexandria","Alma","Shakia"],"index":54749,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8075041175,"difficulty":0.1924958825}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Rebecca. Rebecca's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Jennifer knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jennifer can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rebecca","Jennifer"],"index":34484,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5692154765,"difficulty":0.4307845235}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Genevieve's card is shown to Genevieve. Genevieve's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Genevieve does not know whether Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Patricia can now know that Genevieve can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Genevieve","Patricia"],"index":18793,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989087582,"difficulty":0.0010912418}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether Robert picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Christine"],"index":34442,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994559884,"difficulty":0.0005440116}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Pamela. Pamela's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Andrea does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Pamela can now know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrea","Pamela","Denise"],"index":48108,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9774466157,"difficulty":0.0225533843}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henrietta's card is shown to Ruth. Michael's card is shown to Ruth. Ruth's card is shown to Henrietta. Brenda's card is shown to Henrietta. Michael's card is shown to Henrietta. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,3,4 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:2,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Henrietta can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Henrietta","Brenda","Michael"],"index":51522,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989602566,"difficulty":0.0010397434}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herman's card is shown to Herman. Gerald's card is shown to Herman. Timothy's card is shown to Herman. Timothy's card is shown to Gerald. Herman's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 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:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gerald can now know that Timothy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herman","Gerald","Timothy"],"index":53267,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993755221,"difficulty":0.0006244779}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Clinton. Paul's card is shown to Paul. Rebecca's card is shown to Rebecca. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether Paul picked a red card. It is publicly announced that Paul does not know whether Rebecca picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rebecca can now know whether Clinton can know whether Clinton picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clinton","Paul","Rebecca"],"index":16238,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7985431552,"difficulty":0.2014568448}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that Teresa knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Teresa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Teresa","Sue"],"index":38640,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990686774,"difficulty":0.0009313226}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Evelyn. Fred's card is shown to Evelyn. David's card is shown to David. Evelyn's card is shown to Fred. Fred's card is shown to Fred. Fred's card is shown to Francis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Evelyn can now know whether Evelyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","David","Fred","Francis"],"index":44301,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7078278661,"difficulty":1.7078278661}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keith's card is shown to Charles. Angela's card is shown to Charles. Charles's card is shown to Angela. Keith's card is shown to Angela. Angela's card is shown to Angela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Keith can now know whether Charles can know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Keith","Angela"],"index":63804,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989088774,"difficulty":0.0010911226}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adrienne's card is shown to Barbara. Forrest's card is shown to Adrienne. Barbara's card is shown to Forrest. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Adrienne can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Adrienne","Forrest"],"index":26957,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940689802,"difficulty":0.0059310198}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mike's card is shown to Mike. Mike's card is shown to Michael. Linda's card is shown to Michael. Michael's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mike can now know that Linda can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mike","Michael","Linda"],"index":7205,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988960028,"difficulty":0.0011039972}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alex's card is shown to Alex. Josue's card is shown to Josue. Tony's card is shown to Josue. Alex's card is shown to Tony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alex can now know that Josue can know that Alex picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alex","Josue","Tony"],"index":21794,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960838556,"difficulty":0.0039161444}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Isabel's card is shown to Steven. Stephen's card is shown to Isabel. Angelina's card is shown to Angelina. Stephen's card is shown to Angelina. Angelina's card is shown to Stephen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Isabel","Angelina","Stephen"],"index":67039,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994040728,"difficulty":0.0005959272}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leonard's card is shown to Richard. Leonard's card is shown to Julian. Richard's card is shown to Leonard. Lawrence's card is shown to Lawrence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lawrence can now know that Julian can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Julian","Leonard","Lawrence"],"index":59639,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986822009,"difficulty":0.0013177991}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derek's card is shown to Phyllis. Phyllis's card is shown to Phyllis. Cathy's card is shown to Phyllis. Phyllis's card is shown to Cathy. Cathy's card is shown to Cathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Phyllis can now know that Cathy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Derek","Phyllis","Cathy"],"index":40142,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.98662287,"difficulty":0.01337713}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Brett. Brett's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Ashley picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Ashley can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ashley","Brett","Matthew","Leonard"],"index":16916,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990505576,"difficulty":0.0009494424}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Betty. Mary's card is shown to Betty. Kenneth's card is shown to Kenneth. Robert's card is shown to Kenneth. Kenneth's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know that Betty can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Kenneth","Robert","Mary"],"index":20394,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993824959,"difficulty":0.0006175041}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dana's card is shown to Jason. Dana's card is shown to Dana. Dana's card is shown to Raymond. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jason can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Dana","Raymond"],"index":55081,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998985827,"difficulty":0.001014173}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Clarence. Tameka's card is shown to Clarence. Sharon's card is shown to Sharon. Clarence's card is shown to Tameka. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tameka can now know whether Clarence can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clarence","Sharon","Tameka"],"index":58464,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994046688,"difficulty":0.0005953312}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandra's card is shown to Sandra. Jay's card is shown to Sandra. Jay's card is shown to Brock. Sandra's card is shown to Apryl. Brock's card is shown to Jay. Jay's card is shown to Jay. It is publicly announced that someone picked a red card. It is publicly announced that Brock does not know whether Sandra picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Brock can now know whether Apryl can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Brock","Apryl","Jay"],"index":11031,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994109869,"difficulty":0.0005890131}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ellen's card is shown to Ellen. William's card is shown to Ellen. Martha's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Martha knows whether Ellen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ellen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ellen","Martha","William"],"index":26574,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989848733,"difficulty":0.0010151267}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Steven. Steven's card is shown to Larry. Steven's card is shown to Sharon. Larry's card is shown to Sharon. Sharon's card is shown to Sharon. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc: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:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sharon can now know that Larry can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Larry","Sharon"],"index":66377,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994266033,"difficulty":0.0005733967}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Nicole. Charlene's card is shown to Charlene. John's card is shown to Charlene. Charlene's card is shown to Peter. Peter's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nicole","Charlene","Peter","John"],"index":50544,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993025064,"difficulty":0.0006974936}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nikki's card is shown to Walter. Nikki's card is shown to Nikki. Christine's card is shown to Nikki. Nikki's card is shown to Christine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Walter can now know whether Walter picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Walter","Nikki","Christine"],"index":24802,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9614754319,"difficulty":0.0385245681}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gordon's card is shown to Gordon. Gordon's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Gordon knows whether someone picked a red card. It is publicly announced that Edward does not know whether or not everyone picked a red card. It is publicly announced that Gordon does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Edward can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gordon","Edward"],"index":57329,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988453388,"difficulty":0.0011546612}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Kari. Linda's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Kari knows whether Kari picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kari can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kari","Linda"],"index":18479,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994583726,"difficulty":0.0005416274}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Stephanie. Stephanie's card is shown to Thomas. Thomas's card is shown to Thomas. Thomas's card is shown to Edna. Edna's card is shown to Edna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know whether Thomas can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Stephanie","Thomas","Edna"],"index":60153,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982510209,"difficulty":0.0017489791}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Deanna's card is shown to Deanna. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Deanna picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Deanna can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jennifer","Deanna"],"index":54793,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994075298,"difficulty":0.0005924702}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. James's card is shown to Patricia. Patricia's card is shown to Jimmy. Chris's card is shown to Jimmy. Chris's card is shown to Chris. It is publicly announced that someone picked a red card. It is publicly announced that Jimmy does not know whether Jimmy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Jimmy","James","Chris"],"index":48845,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9807588458,"difficulty":0.0192411542}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlotte's card is shown to Jessica. Doris's card is shown to Jessica. Charlotte's card is shown to Charlotte. Jessica's card is shown to Doris. Charlotte's card is shown to Doris. Doris's card is shown to Doris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Doris can now know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jessica","Charlotte","Doris"],"index":23732,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7263852954,"difficulty":1.7263852954}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. Paul's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Virginia does not know whether Virginia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Paul can now know that Virginia can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Virginia"],"index":39854,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9745355248,"difficulty":1.9745355248}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vera's card is shown to Vera. Alphonso's card is shown to Vera. Vera's card is shown to Eric. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eric can now know whether Vera can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Vera","Eric","Alphonso"],"index":50714,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8297035098,"difficulty":0.1702964902}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Herbert's card is shown to Jennifer. Ellen's card is shown to Jennifer. Jennifer's card is shown to Ellen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Herbert can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Herbert","Ellen"],"index":19161,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993969202,"difficulty":0.0006030798}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ariel's card is shown to Ariel. Valerie's card is shown to Ariel. Valerie's card is shown to Jessica. Ariel's card is shown to Valerie. Ariel's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Gary does not know whether Jessica picked a red card. It is publicly announced that Gary does not know whether Gary picked a red card. It is publicly announced that Jessica does not know whether Gary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentb knows whether 4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Gary can now know whether Jessica can know that Jessica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ariel","Jessica","Valerie","Gary"],"index":971,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7542353272,"difficulty":0.2457646728}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daphne's card is shown to Christopher. Christopher's card is shown to Cornelius. Christopher's card is shown to Daphne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Cornelius","Daphne","Manuel"],"index":46928,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9384733438,"difficulty":1.9384733438}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Edward. Alice's card is shown to Nona. Edward's card is shown to Alice. Nona's card is shown to Alice. Alice's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Nona picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb: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 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Edward can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edward","Nona","Alice"],"index":40067,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990413785,"difficulty":0.0009586215}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Anthony. Lydia's card is shown to Maurice. Anthony's card is shown to Maurice. Mildred's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Lydia does not know whether Lydia picked a red card. It is publicly announced that Anthony knows whether or not everyone picked a red card. It is publicly announced that Anthony does not know whether Maurice picked a red card. It is publicly announced that Anthony picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] (Agentb knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Anthony can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lydia","Anthony","Maurice","Mildred"],"index":33178,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994613528,"difficulty":0.0005386472}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Jessie. Agnes's card is shown to Charles. Charles's card is shown to Agnes. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that Agnes can know whether Jessie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jessie","Charles","Agnes"],"index":51194,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965862036,"difficulty":0.0034137964}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to John. Thomas's card is shown to Elizabeth. Tammy's card is shown to Elizabeth. Elizabeth's card is shown to Thomas. Tammy's card is shown to Tammy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Elizabeth can know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Elizabeth","Thomas","Tammy"],"index":59208,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9274653792,"difficulty":1.9274653792}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeanne's card is shown to Norma. Patricia's card is shown to Patricia. Norma's card is shown to Carmen. Norma's card is shown to Jeanne. Patricia's card is shown to Jeanne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Norma can now know that Carmen can know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Norma","Patricia","Carmen","Jeanne"],"index":7881,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982995391,"difficulty":0.0017004609}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to John. Amanda's card is shown to William. John's card is shown to Michael. Amanda's card is shown to Michael. Amanda's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"John can now know that William can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","William","Michael","Amanda"],"index":58868,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990417361,"difficulty":0.0009582639}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Jennifer's card is shown to Fred. Kyle's card is shown to Jessica. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Kyle picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kyle can now know that Fred can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Fred","Kyle","Jessica"],"index":50885,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935469031,"difficulty":0.0064530969}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Lucy. Larry's card is shown to Lucy. Carolyn's card is shown to Lucy. Carolyn's card is shown to Larry. Larry's card is shown to Carolyn. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn does not know whether or not everyone picked a red card. It is publicly announced that Carolyn does not know whether Carolyn picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&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:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Larry can now know whether Carolyn can know whether Larry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucy","Larry","Carolyn"],"index":47483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9954081178,"difficulty":0.0045918822}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Royce's card is shown to Alice. Alice's card is shown to James. Alice's card is shown to Royce. James's card is shown to Royce. Royce's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan does not know whether Alice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 Agentd:3 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:3 Agentb:1 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Alice can now know that Jonathan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alice","James","Royce","Jonathan"],"index":13021,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973145127,"difficulty":0.0026854873}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Suzanne's card is shown to Trevor. Priscilla's card is shown to Priscilla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Suzanne can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Suzanne","Trevor","Priscilla","Herb"],"index":45938,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989756346,"difficulty":0.0010243654}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phyllis's card is shown to Phyllis. Sarah's card is shown to Ruth. Sarah's card is shown to David. Phyllis's card is shown to Sarah. Sarah's card is shown to Sarah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Phyllis","Ruth","David","Sarah"],"index":8645,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994049072,"difficulty":0.0005950928}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kent's card is shown to Kent. Jay's card is shown to Kent. Myrtle's card is shown to Kent. Jay's card is shown to Williams. Myrtle's card is shown to Williams. Williams's card is shown to Jay. Kent's card is shown to Myrtle. Myrtle's card is shown to Myrtle. It is publicly announced that someone picked a red card. It is publicly announced that Jay does not know whether Jay picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jay can now know whether Williams picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kent","Williams","Jay","Myrtle"],"index":42443,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9428710938,"difficulty":1.9428710938}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carlos's card is shown to Micheal. Micheal's card is shown to Carlos. Mona's card is shown to Carlos. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mona can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Micheal","Mona","Carlos"],"index":30081,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989852309,"difficulty":0.0010147691}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stanley's card is shown to Jill. Jill's card is shown to Stanley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Jill can now know whether Stanley can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jill","Stanley"],"index":31334,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8844514489,"difficulty":0.1155485511}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nu's card is shown to Alton. Nu's card is shown to Christopher. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alton","Christopher","Nu"],"index":7035,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6747925878,"difficulty":0.3252074122}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emma's card is shown to Mary. Mary's card is shown to Emma. Walter's card is shown to Emma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emma can now know whether Mary can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Emma","Lauri","Walter"],"index":10010,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9899142981,"difficulty":0.0100857019}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Jerome. Jerome's card is shown to Stacey. Stacey's card is shown to Stacey. Alice's card is shown to Stacey. Stacey's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Alice knows whether Stacey picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Alice can now know that Stacey can know that Stacey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerome","Stacey","Alice"],"index":29639,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9144585133,"difficulty":0.0855414867}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Ron. Ron's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 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 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Ron can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Ron","John","David"],"index":2763,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9888021946,"difficulty":0.0111978054}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Michael. Jessica's card is shown to Linda. Linda's card is shown to Linda. Linda's card is shown to Barbra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Jessica","Linda","Barbra"],"index":40169,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7628654838,"difficulty":1.7628654838}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Jack. Paul's card is shown to Jack. Jack's card is shown to David. Jack's card is shown to Paul. Paul's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jack can now know whether Paul can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jack","David","Paul"],"index":61597,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992727637,"difficulty":0.0007272363}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Esther's card is shown to Esther. Marie's card is shown to John. Esther's card is shown to Marie. John's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Marie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Esther can now know whether Marie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Esther","John","Marie"],"index":37751,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9932761192,"difficulty":1.9932761192}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Ruthie's card is shown to Mark. Andrew's card is shown to Mark. Ruthie's card is shown to Ruthie. Andrew's card is shown to Ruthie. Ruthie's card is shown to Jessica. Mark's card is shown to Andrew. Ruthie's card is shown to Andrew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruthie can now know that Andrew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Ruthie","Jessica","Andrew"],"index":25384,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978510141,"difficulty":0.0021489859}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leah's card is shown to Leah. Raymond's card is shown to Leah. Brittney's card is shown to Leah. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leah can now know that Raymond can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leah","Raymond","Brittney"],"index":42220,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993243217,"difficulty":0.0006756783}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Justin. Justin's card is shown to Bryan. Bryan's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Justin picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Justin can now know that Bryan can know that Justin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Justin","Bryan"],"index":61143,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.907800436,"difficulty":0.092199564}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnold's card is shown to Arnold. Dwight's card is shown to Arnold. Omar's card is shown to Arnold. Edwin's card is shown to Dwight. Arnold's card is shown to Omar. Arnold's card is shown to Edwin. Dwight's card is shown to Edwin. Omar's card is shown to Edwin. Edwin's card is shown to Edwin. It is publicly announced that someone picked a red card. It is publicly announced that Dwight does not know whether Omar picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:1 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:1 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Arnold can now know whether Dwight can know that Omar picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arnold","Dwight","Omar","Edwin"],"index":24903,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.954169631,"difficulty":0.045830369}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerome's card is shown to Jerome. Steve's card is shown to Jerome. Jerome's card is shown to Christa. Barbara's card is shown to Steve. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Jerome","Christa","Steve"],"index":3242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989666939,"difficulty":0.0010333061}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allan's card is shown to Daniel. Daniel's card is shown to Jefferson. Jefferson's card is shown to Allan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Allan can now know that Jefferson can know whether Jefferson picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Jefferson","Allan"],"index":4294,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8645808697,"difficulty":0.1354191303}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Tracy. Tracy's card is shown to Jose. Faith's card is shown to Jose. Tracy's card is shown to Faith. Jose's card is shown to Faith. It is publicly announced that someone picked a red card. It is publicly announced that Tracy does not know whether Francis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Tracy can now know that Faith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tracy","Jose","Francis","Faith"],"index":16950,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948878884,"difficulty":0.0051121116}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Gregory. Eric's card is shown to Gregory. Andrea's card is shown to Andrea. Gregory's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Gregory does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Andrea can now know that Eric can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gregory","Andrea","Eric"],"index":57753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989418387,"difficulty":0.0010581613}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Jeffrey. Bridget's card is shown to Bridget. James's card is shown to Bridget. Jeffrey's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeffrey can now know that Bridget can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Bridget","James"],"index":17599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990547299,"difficulty":0.0009452701}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Judy. Alicia's card is shown to Judy. John's card is shown to Alicia. John's card is shown to John. Eugene's card is shown to Eugene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alicia can now know whether Eugene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Judy","Alicia","John","Eugene"],"index":15879,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9254385233,"difficulty":0.0745614767}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Michelle. Michelle's card is shown to Edna. It is publicly announced that someone picked a red card. It is publicly announced that Janice picked a black card. It is publicly announced that Janice picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(1) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(1) ] 0","hypothesis":"Michelle can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Michelle","Edna","Kenneth"],"index":59458,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985086322,"difficulty":0.0014913678}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephanie's card is shown to Rosemary. Stephanie's card is shown to Ray. Patricia's card is shown to Stephanie. Ray's card is shown to Stephanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rosemary can now know that Ray can know that Rosemary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Rosemary","Ray","Stephanie"],"index":22731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981939197,"difficulty":0.0018060803}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to William. William's card is shown to Sarah. Sarah's card is shown to Sarah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Sarah","Janette"],"index":52171,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7634845376,"difficulty":0.2365154624}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauletta's card is shown to Pauletta. Pauletta's card is shown to Kimberly. Kimberly's card is shown to Kimberly. It is publicly announced that someone picked a red card. It is publicly announced that Pauletta knows whether Pauletta picked a red card. It is publicly announced that Pauletta does not know whether Kimberly picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Pauletta can now know that Kimberly can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pauletta","Kimberly"],"index":5387,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994530082,"difficulty":0.0005469918}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Celia's card is shown to Celia. Celia's card is shown to Herbert. Luann's card is shown to Herbert. Herbert's card is shown to Luann. It is publicly announced that someone picked a red card. It is publicly announced that Herbert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Celia can now know whether Herbert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Celia","Herbert","Luann"],"index":33150,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.867991209,"difficulty":1.867991209}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martin's card is shown to Martin. Martin's card is shown to Charles. Frankie's card is shown to Charles. Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Martin picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb: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 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Frankie can now know that Frankie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Martin","Frankie","Charles"],"index":23227,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.957262516,"difficulty":0.042737484}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lydia's card is shown to Lydia. Lydia's card is shown to Gloria. Gloria's card is shown to Gloria. Lydia's card is shown to Lamar. Gloria's card is shown to Lamar. Lamar's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lydia can now know that Lamar picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lydia","Gloria","Lamar","Carol"],"index":35353,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970549345,"difficulty":0.0029450655}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victor's card is shown to Victor. Jeremy's card is shown to Victor. Abigail's card is shown to Victor. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Victor can now know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","Jeremy","Abigail","Nina"],"index":16914,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977900982,"difficulty":0.0022099018}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. David's card is shown to Ruth. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Ruth knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Ruth can now know that David can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Ruth"],"index":10061,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993962049,"difficulty":0.0006037951}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fiona's card is shown to Joyce. Marcus's card is shown to Joyce. Chester's card is shown to Fiona. Marcus's card is shown to Marcus. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Chester can now know whether Joyce can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","Chester","Fiona","Marcus"],"index":16890,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994035959,"difficulty":0.0005964041}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Samuel. Vanesa's card is shown to Inez. Inez's card is shown to Inez. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Vanesa can now know whether Samuel can know that Inez picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Vanesa","Samuel","Inez"],"index":8329,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9166252613,"difficulty":1.9166252613}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Charles's card is shown to Amy. Charles's card is shown to Charles. Amy's card is shown to Peter. Charles's card is shown to Peter. Peter's card is shown to Peter. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Peter can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amy","Charles","Peter"],"index":52267,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989997745,"difficulty":0.0010002255}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lavette's card is shown to Lavette. Lavette's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether someone picked a red card. It is publicly announced that William does not know whether William picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lavette can now know that William can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lavette","William","Becky"],"index":3018,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994422793,"difficulty":0.0005577207}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Kevin. Antonio's card is shown to Kevin. David's card is shown to Antonio. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kevin","David","Antonio"],"index":24387,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993879795,"difficulty":0.0006120205}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyrone's card is shown to Tyrone. Tyrone's card is shown to Ada. Ada's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tyrone can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tyrone","Ada","Michael"],"index":12926,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981422424,"difficulty":0.0018577576}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricardo's card is shown to Walter. Walter's card is shown to Ricardo. It is publicly announced that someone picked a red card. It is publicly announced that Ricardo does not know whether Ricardo picked a red card. It is publicly announced that Ricardo does not know whether Ricardo picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ricardo can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Walter","Ricardo"],"index":12331,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988293052,"difficulty":0.0011706948}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alexander's card is shown to Sam. Scott's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Alexander does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Sam can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alexander","Sam","Scott"],"index":67483,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9673376679,"difficulty":0.0326623321}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Steven. Steven's card is shown to Barbara. Steven's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Julie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Barbara can now know that Earl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Steven","Barbara","Earl"],"index":12149,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967679977,"difficulty":0.0032320023}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Kathy. Michael's card is shown to Michael. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Kathy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathy","Michael","Linda","Barbara"],"index":27146,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994485974,"difficulty":0.0005514026}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Shirley. April's card is shown to Shirley. Emmitt's card is shown to April. Emmitt's card is shown to Missy. Shirley's card is shown to Missy. It is publicly announced that someone picked a red card. It is publicly announced that April does not know whether or not everyone picked a red card. It is publicly announced that April does not know whether or not everyone picked a red card. It is publicly announced that Shirley knows whether Shirley picked a red card. It is publicly announced that April does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Emmitt can now know whether April picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emmitt","Shirley","April","Missy"],"index":20807,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6417216063,"difficulty":0.3582783937}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to Bertha. Kimberly's card is shown to Bertha. Bertha's card is shown to Kimberly. Bertha's card is shown to Elizabeth. Monica's card is shown to Elizabeth. Kimberly's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Bertha does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Monica can now know whether Monica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bertha","Monica","Kimberly","Elizabeth"],"index":52375,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6304323077,"difficulty":0.3695676923}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Jason. Jason's card is shown to Renee. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether Renee picked a red card. It is publicly announced that Jason does not know whether Renee picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Renee can now know whether Jason can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jason","Renee"],"index":58095,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5311011076,"difficulty":1.5311011076}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beatrice's card is shown to James. James's card is shown to Beatrice. Beatrice's card is shown to Beatrice. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card. It is publicly announced that Stefan does not know whether Stefan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stefan","James","Beatrice"],"index":33827,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7740748525,"difficulty":1.7740748525}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luz's card is shown to Luz. Edward's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Luz can now know that Edward can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Luz","Edward"],"index":66493,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994341731,"difficulty":0.0005658269}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to William. Patricia's card is shown to William. Patricia's card is shown to Charles. Matthew's card is shown to Matthew. Charles's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Matthew knows whether someone picked a red card. It is publicly announced that William picked a red card. It is publicly announced that Charles does not know whether Matthew picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"William can now know whether Charles can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Charles","Matthew","Patricia"],"index":58457,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5668174624,"difficulty":1.5668174624}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kaitlyn's card is shown to Kaitlyn. Amy's card is shown to Kaitlyn. Daniel's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Daniel picked a red card. It is publicly announced that Kellie does not know whether or not everyone picked a red card. It is publicly announced that Amy picked a red card. It is publicly announced that Kaitlyn does not know whether Kellie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Kellie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kaitlyn","Kellie","Daniel","Amy"],"index":54057,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978755713,"difficulty":0.0021244287}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charissa's card is shown to Charissa. Marissa's card is shown to Charissa. Charissa's card is shown to Marissa. Charissa's card is shown to Mildred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charissa","Marissa","Mildred","Ivan"],"index":26997,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993541837,"difficulty":0.0006458163}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Jessica. Carolyn's card is shown to Daniel. Carolyn's card is shown to Harry. Daniel's card is shown to Harry. Harry's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn does not know whether Jessica picked a red card. It is publicly announced that Jessica does not know whether or not everyone picked a red card. It is publicly announced that Carolyn does not know whether Jessica picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jessica can now know whether Daniel can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Carolyn","Daniel","Harry"],"index":22081,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994508624,"difficulty":0.0005491376}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Eric. Shawnta's card is shown to Michael. Eric's card is shown to Beulah. Shawnta's card is shown to Beulah. Michael's card is shown to Shawnta. Shawnta's card is shown to Shawnta. It is publicly announced that someone picked a red card. It is publicly announced that Shawnta picked a red card. It is publicly announced that Eric does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Shawnta can now know whether Eric can know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Michael","Beulah","Shawnta"],"index":43932,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.987868607,"difficulty":0.012131393}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Gary. Mildred's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Gary knows whether someone picked a red card. It is publicly announced that Gary does not know whether or not everyone picked a red card. It is publicly announced that Gary picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(1) ] 0","hypothesis":"Mildred can now know whether Mildred picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gary","Mildred"],"index":8178,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9551489353,"difficulty":0.0448510647}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Philip. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Philip can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Philip","James"],"index":38887,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990112782,"difficulty":0.0009887218}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dewey's card is shown to Dewey. Ruth's card is shown to Dewey. Ruth's card is shown to Ruth. Verna's card is shown to Ella. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know that Verna can know whether Dewey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dewey","Ruth","Verna","Ella"],"index":61589,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8869317174,"difficulty":0.1130682826}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathan's card is shown to Nathan. Benjamin's card is shown to Nathan. Betty's card is shown to Betty. Benjamin's card is shown to Betty. Nathan's card is shown to Benjamin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nathan can now know whether Benjamin can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nathan","Betty","Benjamin"],"index":44127,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993956089,"difficulty":0.0006043911}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Thelma. John's card is shown to Thelma. Kenneth's card is shown to Kenneth. Thelma's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Thelma picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"John can now know whether Thelma can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thelma","Kenneth","John"],"index":59081,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9251947999,"difficulty":0.0748052001}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Orville. John's card is shown to Joseph. Joseph's card is shown to Michael. Michael's card is shown to Michael. Joseph's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Orville can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Orville","Joseph","Michael","John"],"index":9120,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982415438,"difficulty":0.0017584562}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Troy's card is shown to Troy. Wanda's card is shown to Wanda. Troy's card is shown to Eldridge. Troy's card is shown to Mei. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Troy can now know whether Wanda can know that Eldridge picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Troy","Wanda","Eldridge","Mei"],"index":39546,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8297435641,"difficulty":0.1702564359}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Philip's card is shown to Ilona. Ilona's card is shown to Yvonne. Yvonne's card is shown to James. Philip's card is shown to James. James's card is shown to Philip. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Philip can now know whether Yvonne can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ilona","Yvonne","James","Philip"],"index":39201,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9406256676,"difficulty":0.0593743324}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Diana. Diana's card is shown to Teresa. Teresa's card is shown to Teresa. Diana's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Diana knows whether Teresa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Richard can now know that Diana can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diana","Teresa","Richard","Mavis"],"index":51489,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989056587,"difficulty":0.0010943413}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yvonne's card is shown to Lawrence. Connie's card is shown to Connie. Franklin's card is shown to Yvonne. Lawrence's card is shown to Yvonne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2 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:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Connie can now know whether Lawrence can know that Yvonne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Franklin","Lawrence","Connie","Yvonne"],"index":56547,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9038661122,"difficulty":0.0961338878}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Nancy. Augusta's card is shown to Nancy. Nancy's card is shown to Kelly. Nancy's card is shown to Augusta. Kelly's card is shown to Augusta. It is publicly announced that someone picked a red card. It is publicly announced that Nancy does not know whether Kelly picked a red card. It is publicly announced that Kelly knows whether or not everyone picked a red card. It is publicly announced that Augusta knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kelly can now know that Augusta can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Kelly","Augusta"],"index":37273,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8961539865,"difficulty":0.1038460135}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Carole. James's card is shown to Carole. James's card is shown to Jeffrey. Carole's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carole","Jeffrey","James"],"index":28944,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993696809,"difficulty":0.0006303191}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Emily. Edith's card is shown to Edith. Emily's card is shown to Tina. William's card is shown to Tina. Emily's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edith can now know that Emily picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Emily","Edith","Tina","William"],"index":5702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973237514,"difficulty":0.0026762486}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Richard. Richard's card is shown to Amy. Manuel's card is shown to Marie. Amy's card is shown to Marie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Manuel","Amy","Marie"],"index":57538,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969393015,"difficulty":0.0030606985}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Darrell. Emily's card is shown to Darrell. Matthew's card is shown to Darrell. Matthew's card is shown to Deanna. Darrell's card is shown to Emily. Darrell's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Deanna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Emily can now know that Deanna can know that Deanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darrell","Deanna","Emily","Matthew"],"index":3699,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8355800509,"difficulty":0.1644199491}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kara's card is shown to Kara. Leslie's card is shown to Kara. Anna's card is shown to Anna. Leslie's card is shown to Daniel. Kara's card is shown to Leslie. Anna's card is shown to Leslie. Leslie's card is shown to Leslie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know that Kara can know whether Leslie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kara","Anna","Daniel","Leslie"],"index":55647,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8260161877,"difficulty":0.1739838123}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Linda. Dollie's card is shown to Linda. Miriam's card is shown to Richard. Dollie's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Miriam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Richard","Miriam","Dollie"],"index":50471,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977706671,"difficulty":0.0022293329}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Oscar's card is shown to Oscar. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Leon knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Leon can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Leon","Oscar"],"index":32915,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990487695,"difficulty":0.0009512305}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Margret's card is shown to Margret. Roberto's card is shown to Margret. Margret's card is shown to Roberto. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know that Margret can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Margret","Roberto"],"index":31239,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9841992855,"difficulty":0.0158007145}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Mercedes. Mary's card is shown to Mercedes. Mercedes's card is shown to Richard. Mercedes's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know that Richard can know whether Helen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Mercedes","Richard","Mary"],"index":28417,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.788916111,"difficulty":1.788916111}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Leslie. Christy's card is shown to Leslie. Gertrude's card is shown to Leslie. Christy's card is shown to Christy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christy can now know whether Leslie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leslie","Christy","Gertrude"],"index":19850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992516637,"difficulty":0.0007483363}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sue's card is shown to Jacob. Lois's card is shown to Lois. Jacob's card is shown to Sue. It is publicly announced that someone picked a red card. It is publicly announced that Sue picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Lois can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jacob","Lois","Sue"],"index":32743,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994694591,"difficulty":0.0005305409}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Donald's card is shown to Donald. Larry's card is shown to Donald. Larry's card is shown to Larry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Donald","Larry"],"index":53280,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990020394,"difficulty":0.0009979606}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Tawana. Shelley's card is shown to Thelma. Shelley's card is shown to Shelley. Tawana's card is shown to Melissa. Thelma's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Shelley does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Tawana can now know whether Melissa can know whether Shelley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tawana","Thelma","Shelley","Melissa"],"index":66632,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9971362352,"difficulty":0.0028637648}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Andrew. Regina's card is shown to Andrew. Andrew's card is shown to Melanie. It is publicly announced that someone picked a red card. It is publicly announced that Andrew knows whether someone picked a red card. It is publicly announced that Andrew does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Andrew can now know whether Regina can know that Regina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Regina","Melanie"],"index":61794,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6897882819,"difficulty":1.6897882819}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Francis. Lorita's card is shown to Francis. Francis's card is shown to Tonda. Tonda's card is shown to Jerry. Lorita's card is shown to Lorita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tonda can now know that Jerry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francis","Tonda","Jerry","Lorita"],"index":11752,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976161718,"difficulty":0.0023838282}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doug's card is shown to Travis. Travis's card is shown to Ada. William's card is shown to Ada. Travis's card is shown to Doug. Travis's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 Agentc:1 Agentd:1 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:3 Agentb:1,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doug can now know that Travis can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Travis","Ada","Doug","William"],"index":40171,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988677502,"difficulty":0.0011322498}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Mildred. Mildred's card is shown to Joesph. It is publicly announced that someone picked a red card. It is publicly announced that Mildred does not know whether Joesph picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mildred can now know that Joesph can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mildred","Joesph"],"index":13611,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994412065,"difficulty":0.0005587935}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to James. James's card is shown to Randy. Rhonda's card is shown to Randy. James's card is shown to Rhonda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rhonda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Randy","Rhonda"],"index":36014,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943957329,"difficulty":0.0056042671}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamela's card is shown to Pamela. Bettye's card is shown to Pamela. Lee's card is shown to Valarie. Pamela's card is shown to Lee. Valarie's card is shown to Lee. Bettye's card is shown to Bettye. It is publicly announced that someone picked a red card. It is publicly announced that Bettye does not know whether Pamela picked a red card. It is publicly announced that Lee knows whether someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Bettye can now know that Pamela can know whether Valarie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Valarie","Lee","Bettye"],"index":55652,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6908904314,"difficulty":1.6908904314}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Guadalupe. Melinda's card is shown to Guadalupe. Nellie's card is shown to Melinda. Melinda's card is shown to Nellie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Melinda can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Guadalupe","Melinda","Nellie"],"index":22001,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994139671,"difficulty":0.0005860329}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenny's card is shown to Edgar. Edgar's card is shown to Jenny. Thomas's card is shown to Jenny. Jenny's card is shown to Thomas. Willie's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2,4 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:2 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jenny can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edgar","Jenny","Thomas","Willie"],"index":19174,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988923669,"difficulty":0.0011076331}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elisa's card is shown to Lorna. Lorna's card is shown to Elisa. Elisa's card is shown to Elisa. Tom's card is shown to Elisa. Elisa's card is shown to Tom. Jeri's card is shown to Jeri. It is publicly announced that someone picked a red card. It is publicly announced that Jeri picked a red card. It is publicly announced that Lorna picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Elisa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorna","Elisa","Tom","Jeri"],"index":25046,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990480542,"difficulty":0.0009519458}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lowell's card is shown to Pamela. Lowell's card is shown to Sarah. Kevin's card is shown to Lowell. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pamela can now know that Sarah can know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Pamela","Sarah","Lowell"],"index":67074,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8659090996,"difficulty":0.1340909004}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenna's card is shown to Matthew. Matthew's card is shown to Jenna. Robert's card is shown to Robert. Matthew's card is shown to Bennett. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bennett can now know whether Jenna can know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Jenna","Robert","Bennett"],"index":62631,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8954231739,"difficulty":0.1045768261}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julian's card is shown to Holly. Maximina's card is shown to Holly. Julian's card is shown to Julian. Holly's card is shown to Maximina. Julian's card is shown to Maximina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maximina can now know that Julian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Holly","Julian","Maximina"],"index":46807,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995118022,"difficulty":0.004881978}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Marion. Joan's card is shown to Gregory. Mildred's card is shown to Gregory. Gregory's card is shown to Joan. Gregory's card is shown to Mildred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marion","Gregory","Joan","Mildred"],"index":57148,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8320430517,"difficulty":0.1679569483}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Denver. Aurora's card is shown to Denver. Denver's card is shown to Juan. Aurora's card is shown to Juan. Juan's card is shown to Michael. Aurora's card is shown to Michael. Denver's card is shown to Aurora. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Denver","Juan","Michael","Aurora"],"index":49235,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9931266308,"difficulty":0.0068733692}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Terry. Christopher's card is shown to Christopher. Beverly's card is shown to Christopher. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card. It is publicly announced that Beverly does not know whether Philomena picked a red card. It is publicly announced that Terry does not know whether Christopher picked a red card. It is publicly announced that Beverly does not know whether or not everyone picked a red card. It is publicly announced that Christopher does not know whether Philomena picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Christopher can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Terry","Christopher","Beverly","Philomena"],"index":58246,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994634986,"difficulty":0.0005365014}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Stephanie. Stephanie's card is shown to Maureen. Maureen's card is shown to Maureen. Joyce's card is shown to Maureen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephanie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephanie","Maureen","Joyce"],"index":14512,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993203878,"difficulty":0.0006796122}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jocelyn's card is shown to John. John's card is shown to Brain. Jocelyn's card is shown to Brain. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether Jocelyn picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"John can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Brain","Jocelyn"],"index":45932,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990418553,"difficulty":0.0009581447}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Forest's card is shown to Forest. Rose's card is shown to Forest. Anthony's card is shown to Rose. Forest's card is shown to Rose. It is publicly announced that someone picked a red card. It is publicly announced that Forest picked a black card. It is publicly announced that Anthony knows whether Anthony picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Forest can now know that Forest picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Forest","Rose"],"index":844,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.965988338,"difficulty":0.034011662}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Rose. Fernando's card is shown to Rose. Fernando's card is shown to Sarah. Rose's card is shown to Fernando. Fernando's card is shown to Fernando. It is publicly announced that someone picked a red card. It is publicly announced that Rose does not know whether Rose picked a red card. It is publicly announced that Sarah does not know whether or not everyone picked a red card. It is publicly announced that Fernando picked a red card. It is publicly announced that Sarah does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Fernando can now know whether Rose can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rose","Sarah","Fernando"],"index":9960,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992280006,"difficulty":0.0007719994}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erika's card is shown to Evelyn. Rowena's card is shown to Rowena. Evelyn's card is shown to Erika. Roman's card is shown to Erika. Rowena's card is shown to Erika. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn does not know whether Rowena picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Rowena can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Roman","Rowena","Erika"],"index":4728,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99896276,"difficulty":0.00103724}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Deloris. Camille's card is shown to Elizabeth. Elizabeth's card is shown to Richard. Camille's card is shown to Richard. Deloris's card is shown to Camille. Elizabeth's card is shown to Camille. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Elizabeth can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deloris","Elizabeth","Richard","Camille"],"index":10819,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992978573,"difficulty":0.0007021427}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Brian. John's card is shown to Brian. John's card is shown to John. Brian's card is shown to Kelli. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"John can now know that Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","John","Kelli"],"index":16931,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9301191568,"difficulty":0.0698808432}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Prince's card is shown to Prince. Walter's card is shown to Walter. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Prince picked a red card. It is publicly announced that Walter picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Prince can now know that Michael can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Prince","Walter","Michael","Charles"],"index":20657,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989815354,"difficulty":0.0010184646}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Francis. Brian's card is shown to Francis. Francis's card is shown to Brian. Linda's card is shown to Brian. Paul's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paul can now know that Francis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Francis","Brian","Linda"],"index":28148,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964026213,"difficulty":0.0035973787}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roger's card is shown to Paula. Eboni's card is shown to Eboni. Roger's card is shown to Eboni. Phillis's card is shown to Eboni. Phillis's card is shown to Roger. Roger's card is shown to Phillis. It is publicly announced that someone picked a red card. It is publicly announced that Roger does not know whether Roger picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Phillis can now know that Paula can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Eboni","Roger","Phillis"],"index":9940,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994294047,"difficulty":0.0005705953}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Florida. Marvin's card is shown to Marvin. It is publicly announced that someone picked a red card. It is publicly announced that Florida knows whether someone picked a red card. It is publicly announced that Dan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Florida can now know whether Dan can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dan","Florida","Marvin"],"index":20471,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.646851778,"difficulty":0.353148222}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marian's card is shown to Kelly. Kelly's card is shown to Billy. Billy's card is shown to Billy. Marian's card is shown to Billy. Kelly's card is shown to Marian. It is publicly announced that someone picked a red card. It is publicly announced that Marian does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marian can now know that Kelly can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelly","Billy","Marian"],"index":58270,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998929441,"difficulty":0.001070559}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to George. Michelle's card is shown to Michelle. Michelle's card is shown to Judith. Judith's card is shown to Judith. Judith's card is shown to Claudia. It is publicly announced that someone picked a red card. It is publicly announced that George knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Claudia can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Michelle","Judith","Claudia"],"index":4424,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990465045,"difficulty":0.0009534955}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Robert's card is shown to Jennifer. Joel's card is shown to Gloria. Jennifer's card is shown to Robert. Joel's card is shown to Robert. Gloria's card is shown to Joel. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Jennifer picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jennifer can now know that Joel can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Gloria","Robert","Joel"],"index":41743,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935488105,"difficulty":0.0064511895}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathy's card is shown to Tad. Billy's card is shown to Cathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amy can now know that Billy can know whether Billy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Billy","Amy","Tad","Cathy"],"index":19086,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.867321074,"difficulty":0.132678926}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roxanne's card is shown to Roxanne. Roxanne's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Mark can now know that Roxanne can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Roxanne","Mark"],"index":4793,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988837838,"difficulty":0.0011162162}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Howard. Brian's card is shown to Howard. Howard's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Howard picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Howard can now know whether Brian can know that Howard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Howard","Brian"],"index":39222,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9524357319,"difficulty":0.0475642681}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jim's card is shown to Jerilyn. Michael's card is shown to Michael. Jim's card is shown to Michael. Jerilyn's card is shown to Jim. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Jim can now know that Jerilyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jerilyn","Michael","Jim"],"index":37369,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8900204897,"difficulty":0.1099795103}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bill's card is shown to Bill. Bill's card is shown to Clarence. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Clarence knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Bill does not know whether Clarence picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Bill can now know that Clarence can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bill","Clarence"],"index":58528,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994621873,"difficulty":0.0005378127}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Clyde. Clyde's card is shown to Heather. Heather's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clyde can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clyde","Heather","Janet"],"index":14399,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993312359,"difficulty":0.0006687641}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Burl's card is shown to Daniel. Burl's card is shown to Leticia. Leticia's card is shown to Leticia. It is publicly announced that someone picked a red card. It is publicly announced that Burl knows whether someone picked a red card. It is publicly announced that Burl does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Burl picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 2 ] (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 2 ] 0","hypothesis":"Burl can now know whether Leticia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daniel","Burl","Leticia"],"index":7930,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8617038727,"difficulty":0.1382961273}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raven's card is shown to Michael. Raven's card is shown to Raven. Lana's card is shown to Raven. Michael's card is shown to Jack. Jack's card is shown to Jack. Michael's card is shown to Lana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Raven","Jack","Lana"],"index":26973,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930816293,"difficulty":0.0069183707}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Richard. Susan's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Susan knows whether Richard picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Richard can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Richard","Susan"],"index":6426,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9964841604,"difficulty":0.0035158396}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Leroy. Leroy's card is shown to Martin. Joseph's card is shown to Martin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leroy can now know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leroy","Martin","Joseph"],"index":57519,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8165162802,"difficulty":0.1834837198}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. David's card is shown to Charles. Charley's card is shown to Charles. Nathaniel's card is shown to Nathaniel. Charles's card is shown to Charley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nathaniel can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Charles","Nathaniel","Charley"],"index":42448,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6762297153,"difficulty":0.3237702847}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herbert's card is shown to Sharon. Sharon's card is shown to Herbert. Herbert's card is shown to Herbert. Angela's card is shown to Herbert. Herbert's card is shown to Angela. Angela's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Herbert knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Herbert can now know whether Sharon can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Herbert","Angela"],"index":61493,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994589686,"difficulty":0.0005410314}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amelia's card is shown to Amelia. John's card is shown to Amelia. Amelia's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Isabel does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Amelia can now know whether Isabel can know whether Isabel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amelia","Isabel","John"],"index":39571,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9117289186,"difficulty":0.0882710814}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ginger's card is shown to Christopher. Ginger's card is shown to Ginger. Mike's card is shown to Mike. It is publicly announced that someone picked a red card. It is publicly announced that Mike knows whether Mike picked a red card. It is publicly announced that Ginger picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 2 ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 2 ] 0","hypothesis":"Ginger can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Ginger","Mike"],"index":13928,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9230903983,"difficulty":1.9230903983}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to James. James's card is shown to Gerald. Gerald's card is shown to Gerald. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Raymond picked a red card. It is publicly announced that James does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Gerald","Raymond"],"index":61383,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986832738,"difficulty":0.0013167262}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jackie's card is shown to Luke. Jackie's card is shown to Linda. Linda's card is shown to Fabian. Linda's card is shown to Jackie. Jackie's card is shown to Jackie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Luke can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Luke","Linda","Fabian","Jackie"],"index":46332,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989625216,"difficulty":0.0010374784}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Russel's card is shown to Michael. Russel's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Timothy does not know whether Ruby picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Michael can now know that Ruby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Timothy","Ruby","Russel"],"index":33039,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948815107,"difficulty":0.0051184893}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lillian's card is shown to Helen. Rhonda's card is shown to Helen. Helen's card is shown to Helen. Maria's card is shown to Helen. Helen's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lillian can now know that Rhonda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lillian","Rhonda","Helen","Maria"],"index":4810,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998296082,"difficulty":0.001703918}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Eva. Eva's card is shown to Joann. Joann's card is shown to Joann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Joann can now know that Eva can know whether Eva picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eva","Joann"],"index":40617,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8318006396,"difficulty":0.1681993604}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allen's card is shown to Lisa. Emily's card is shown to Emily. Allen's card is shown to Emily. Emily's card is shown to Allen. Allen's card is shown to Allen. It is publicly announced that someone picked a red card. It is publicly announced that Allen picked a red card. It is publicly announced that Allen does not know whether Lisa picked a red card. It is publicly announced that Allen knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Emily","Allen"],"index":1798,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994764924,"difficulty":0.0005235076}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Judith. Judith's card is shown to Rosemary. Rosemary's card is shown to Rosemary. It is publicly announced that someone picked a red card. It is publicly announced that Judith picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Rosemary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Judith","Rosemary"],"index":14612,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994731545,"difficulty":0.0005268455}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tina's card is shown to Meta. Henrietta's card is shown to Tina. Henrietta's card is shown to Henrietta. It is publicly announced that someone picked a red card. It is publicly announced that Henrietta knows whether someone picked a red card. It is publicly announced that Tina does not know whether Meta picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Tina can now know that Meta can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Meta","Tina","Henrietta"],"index":49498,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9903038144,"difficulty":0.0096961856}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Edward. Rosa's card is shown to Rosa. Edward's card is shown to Alfonso. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alfonso can now know whether Edward can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Rosa","Alfonso"],"index":34202,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8572249413,"difficulty":1.8572249413}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlene's card is shown to Marlene. Don's card is shown to Marlene. Marlene's card is shown to Don. It is publicly announced that someone picked a red card. It is publicly announced that Thomas knows whether or not everyone picked a red card. It is publicly announced that Marlene knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Thomas can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Marlene","Don"],"index":49913,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994804263,"difficulty":0.0005195737}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Basil's card is shown to Michael. Basil's card is shown to Basil. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Basil does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb 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:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Michael can now know that Basil can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Basil"],"index":59651,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.542273581,"difficulty":1.542273581}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francisco's card is shown to Harry. Harry's card is shown to Ginger. Francisco's card is shown to Ginger. Harry's card is shown to Francisco. It is publicly announced that someone picked a red card. It is publicly announced that Harry does not know whether Colleen picked a red card. It is publicly announced that Colleen does not know whether Ginger picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Colleen can now know whether Ginger can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harry","Colleen","Ginger","Francisco"],"index":35416,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9862653613,"difficulty":0.0137346387}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Freda's card is shown to Freda. Freda's card is shown to Thomas. Clarence's card is shown to Thomas. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clarence can now know whether Thomas can know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Freda","Thomas","Clarence"],"index":29144,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6643324494,"difficulty":0.3356675506}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Todd. Ricky's card is shown to Kenneth. Catherine's card is shown to Kenneth. Ricky's card is shown to Ricky. Catherine's card is shown to Ricky. Kenneth's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Ricky does not know whether Kenneth picked a red card. It is publicly announced that Ricky does not know whether Kenneth picked a red card. It is publicly announced that Catherine does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Kenneth can now know that Ricky can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Todd","Kenneth","Ricky","Catherine"],"index":55860,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994284511,"difficulty":0.0005715489}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leonard's card is shown to Susan. Alex's card is shown to Susan. Leonard's card is shown to Leonard. Susan's card is shown to Alex. Leonard's card is shown to Alex. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leonard can now know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Leonard","Alex"],"index":42105,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6993653774,"difficulty":1.6993653774}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiesha's card is shown to Tiesha. Sharon's card is shown to Tiesha. Tiesha's card is shown to Sharon. Sharon's card is shown to Sharon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Tiesha can now know whether Sharon can know whether Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tiesha","Sharon"],"index":26790,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99704355,"difficulty":0.00295645}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresa's card is shown to Mario. Mario's card is shown to Theresa. It is publicly announced that someone picked a red card. It is publicly announced that Mario picked a red card. It is publicly announced that Theresa does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mario can now know whether Theresa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mario","Theresa"],"index":6735,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9492769837,"difficulty":0.0507230163}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Betsy. Betsy's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Gloria knows whether or not nobody picked a red card. It is publicly announced that Betsy knows whether Gloria picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Gloria can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Betsy","Gloria"],"index":29973,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994513392,"difficulty":0.0005486608}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacy's card is shown to Stacy. Stacy's card is shown to Matthew. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Stacy picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Stacy can now know whether Matthew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stacy","Matthew"],"index":1527,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994520545,"difficulty":0.0005479455}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Kyle. Gustavo's card is shown to Kyle. Kyle's card is shown to Gustavo. It is publicly announced that someone picked a red card. It is publicly announced that Kyle knows whether or not everyone picked a red card. It is publicly announced that Gustavo knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Gustavo can now know that Gustavo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kyle","Gustavo"],"index":56319,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8929852843,"difficulty":0.1070147157}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregg's card is shown to Regina. John's card is shown to John. Craig's card is shown to Gregg. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether Gregg picked a red card. It is publicly announced that John does not know whether Gregg picked a red card. It is publicly announced that John does not know whether Craig picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"John can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Regina","John","Craig","Gregg"],"index":45775,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.988806963,"difficulty":0.011193037}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lonnie's card is shown to Anthony. Betty's card is shown to Lonnie. Anthony's card is shown to Betty. Betty's card is shown to Betty. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know that Lonnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Lonnie","Betty"],"index":54466,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982661605,"difficulty":0.0017338395}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to James. Justin's card is shown to Andrew. Andrew's card is shown to Harold. Harold's card is shown to Harold. Andrew's card is shown to Justin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrew can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Andrew","Harold","Justin"],"index":39751,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989076853,"difficulty":0.0010923147}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristina's card is shown to David. Alana's card is shown to David. David's card is shown to Cristina. David's card is shown to Alana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cristina can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Cristina","Alana"],"index":14561,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963155389,"difficulty":0.0036844611}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Shawn. Shawn's card is shown to Jimmie. Lawrence's card is shown to Jimmie. Jimmie's card is shown to Lawrence. Lawrence's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Shawn does not know whether or not everyone picked a red card. It is publicly announced that Lawrence picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Jimmie can now know whether Shawn can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shawn","Leonila","Jimmie","Lawrence"],"index":11535,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994356036,"difficulty":0.0005643964}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joshua's card is shown to Ilda. Ilda's card is shown to Joshua. Joshua's card is shown to Joshua. Ilda's card is shown to Michael. Joshua's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joshua can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ilda","Joshua","Floyd","Michael"],"index":39706,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917125702,"difficulty":0.0082874298}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Teresa's card is shown to William. Delphine's card is shown to Teresa. Kevin's card is shown to Delphine. Teresa's card is shown to Delphine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Teresa can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Kevin","Teresa","Delphine"],"index":15511,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958491325,"difficulty":0.0041508675}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Timmy. Delores's card is shown to Timmy. Delores's card is shown to Delores. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juanita can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Timmy","Abigail","Delores"],"index":66970,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994161129,"difficulty":0.0005838871}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Melissa. Christina's card is shown to Amy. Melissa's card is shown to Christina. Christina's card is shown to Christina. It is publicly announced that someone picked a red card. It is publicly announced that Christina does not know whether Amy picked a red card. It is publicly announced that Melissa does not know whether Christina picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Christina can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melissa","Amy","Christina"],"index":37351,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963920712,"difficulty":0.0036079288}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernestina's card is shown to Ernestina. Anthony's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Daniel does not know whether Daniel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ernestina can now know that Daniel can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ernestina","Daniel","Anthony"],"index":26906,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948621392,"difficulty":0.0051378608}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Clyde. Clyde's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Clyde knows whether Clyde picked a red card. It is publicly announced that Clyde knows whether William picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Clyde","William"],"index":14826,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.95094347,"difficulty":1.95094347}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Jerry. Penny's card is shown to Jerry. Jerry's card is shown to Annette. Penny's card is shown to Annette. Jerry's card is shown to Linda. Annette's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Jerry can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Annette","Linda","Penny"],"index":3071,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993718266,"difficulty":0.0006281734}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Sharon. Donald's card is shown to Sharon. Sharon's card is shown to Donald. Dorothy's card is shown to Donald. Donald's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Dorothy","Donald"],"index":40261,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990001321,"difficulty":0.0009998679}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Warren's card is shown to Dorothy. Dorothy's card is shown to Yolanda. Warren's card is shown to Yolanda. Yolanda's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Brian can now know that Warren picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Yolanda","Brian","Warren"],"index":40974,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9812672138,"difficulty":0.0187327862}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steve's card is shown to Steve. Jessica's card is shown to Steve. Steve's card is shown to Harriet. Harriet's card is shown to Harriet. Jessica's card is shown to Harriet. Steve's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know whether Harriet can know that Harriet picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steve","Harriet","Jessica"],"index":33794,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5609778166,"difficulty":0.4390221834}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Edward. Edward's card is shown to Michael. William's card is shown to Barbara. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Edward does not know whether Edward picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that William can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","William","Michael","Barbara"],"index":17091,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988553524,"difficulty":0.0011446476}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Deborah. James's card is shown to Deborah. Deborah's card is shown to Margaret. James's card is shown to Margaret. Margaret's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Deborah picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Deborah can now know whether James can know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deborah","Margaret","James"],"index":41338,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998898387,"difficulty":0.001101613}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josephine's card is shown to Josephine. David's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Josephine can now know that Josephine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Josephine","David","Patricia"],"index":31310,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9937847853,"difficulty":0.0062152147}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ross's card is shown to Arletta. Arletta's card is shown to Ross. Ross's card is shown to Ross. It is publicly announced that someone picked a red card. It is publicly announced that Ross picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Ross can now know that Arletta can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arletta","Ross"],"index":23301,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994539618,"difficulty":0.0005460382}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Etta's card is shown to Etta. Jack's card is shown to Jack. Jack's card is shown to Christopher. Etta's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know whether Jack picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Etta","Jack","Christopher","Joseph"],"index":55662,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7712291479,"difficulty":1.7712291479}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Guadalupe. Ronald's card is shown to Guadalupe. Michael's card is shown to Guadalupe. Michael's card is shown to Arthur. Guadalupe's card is shown to Ronald. Arthur's card is shown to Michael. Ronald's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Ronald picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Arthur can now know whether Michael can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Guadalupe","Arthur","Ronald","Michael"],"index":25770,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9914225936,"difficulty":0.0085774064}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tony's card is shown to Chris. Susana's card is shown to Susana. Tony's card is shown to Susana. Tony's card is shown to Tony. It is publicly announced that someone picked a red card. It is publicly announced that Tony does not know whether Susana picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc 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:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Chris can now know that Tony can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chris","Susana","Tony"],"index":67032,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994202852,"difficulty":0.0005797148}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. Herbert's card is shown to Betty. Alex's card is shown to William. Betty's card is shown to Herbert. William's card is shown to Alex. Herbert's card is shown to Alex. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alex can now know that Herbert can know that Betty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","William","Herbert","Alex"],"index":7652,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983776808,"difficulty":0.0016223192}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carlos's card is shown to Carlos. John's card is shown to Margery. Carlos's card is shown to Margery. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Carlos does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc: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:2 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Carlos","Margery","Margaret"],"index":66550,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998570919,"difficulty":0.001429081}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Carl. Carl's card is shown to Carl. Edith's card is shown to Carl. Frances's card is shown to Edith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 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:1,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bill can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frances","Bill","Carl","Edith"],"index":54618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989988208,"difficulty":0.0010011792}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandra's card is shown to Sandra. Josephine's card is shown to Edith. It is publicly announced that someone picked a red card. It is publicly announced that Josephine does not know whether Edith picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Sandra can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Josephine","Edith"],"index":48084,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949765205,"difficulty":0.0050234795}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Cherly's card is shown to Patrick. Patrick's card is shown to Cherly. It is publicly announced that someone picked a red card. It is publicly announced that Patrick does not know whether Timothy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Patrick can now know whether Maria can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Patrick","Timothy","Cherly"],"index":24539,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9863134623,"difficulty":0.0136865377}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Jennifer. Lance's card is shown to Thomas. Jennifer's card is shown to Victoria. Lance's card is shown to Victoria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether Thomas can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Thomas","Lance","Victoria"],"index":44825,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993767142,"difficulty":0.0006232858}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Ebony. Ebony's card is shown to John. John's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Ebony picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Joseph picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Ebony can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Ebony","John","Joseph"],"index":8837,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9907485843,"difficulty":0.0092514157}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Anna. Anna's card is shown to Roberta. Vennie's card is shown to Roberta. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marlene can now know whether Roberta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Marlene","Vennie","Roberta"],"index":27736,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9522659779,"difficulty":0.0477340221}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zelma's card is shown to Zelma. Tammy's card is shown to Zelma. Lynn's card is shown to Zelma. Zelma's card is shown to Tammy. Tammy's card is shown to Tammy. Bill's card is shown to Tammy. Lynn's card is shown to Tammy. Zelma's card is shown to Bill. Lynn's card is shown to Bill. Zelma's card is shown to Lynn. It is publicly announced that someone picked a red card. It is publicly announced that Lynn does not know whether Tammy picked a red card. It is publicly announced that Lynn does not know whether Bill picked a red card. It is publicly announced that Zelma does not know whether Bill picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentd knows that (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lynn can now know that Bill can know whether Lynn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Zelma","Tammy","Bill","Lynn"],"index":55039,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6278433204,"difficulty":0.3721566796}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Lorraine. Lorraine's card is shown to Robert. Robert's card is shown to Robert. Lorraine's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Nancy picked a red card. It is publicly announced that Robert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Nancy can now know that Lorraine can know that Lorraine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lorraine","Robert","Nancy"],"index":34303,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8919941187,"difficulty":0.1080058813}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Brad. Vivian's card is shown to Vivian. It is publicly announced that someone picked a red card. It is publicly announced that Brad knows whether Vivian picked a red card. It is publicly announced that Brad does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Vivian can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brad","Vivian"],"index":9383,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973022938,"difficulty":0.0026977062}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachel's card is shown to David. David's card is shown to Rachel. Frank's card is shown to Rachel. Rachel's card is shown to Frank. John's card is shown to Frank. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rachel can now know whether Frank picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Rachel","Frank","John"],"index":30635,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8417631984,"difficulty":1.8417631984}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to James. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card. It is publicly announced that James knows whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mildred can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Mildred","Elizabeth"],"index":5975,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990386963,"difficulty":0.0009613037}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlie's card is shown to Charlie. Charlie's card is shown to Virginia. Virginia's card is shown to Virginia. Darin's card is shown to Virginia. Charlie's card is shown to Darin. Darin's card is shown to Darin. Charlie's card is shown to Norman. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darin can now know that Virginia can know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlie","Virginia","Darin","Norman"],"index":35201,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979192615,"difficulty":0.0020807385}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delores's card is shown to Charles. Priscilla's card is shown to Alta. Charles's card is shown to Priscilla. Priscilla's card is shown to Priscilla. It is publicly announced that someone picked a red card. It is publicly announced that Priscilla does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Alta can now know whether Priscilla can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Alta","Priscilla","Delores"],"index":11766,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994354844,"difficulty":0.0005645156}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Howard. Kyle's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Kyle can now know that Howard can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Howard","Kyle"],"index":53286,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993982315,"difficulty":0.0006017685}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chester's card is shown to John. Chester's card is shown to Chester. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Chester can now know whether John can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Chester"],"index":45250,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999378562,"difficulty":0.000621438}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Maria. Dennis's card is shown to Maria. Christine's card is shown to Christine. Christine's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Christine knows whether Christine picked a red card. It is publicly announced that Christine does not know whether or not everyone picked a red card. It is publicly announced that Maria does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Christine can now know whether Dennis can know whether Christine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Christine","Dennis"],"index":37954,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980667233,"difficulty":0.0019332767}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. Paul's card is shown to Michael. Michael's card is shown to Ardith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Ardith can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Michael","Ardith"],"index":57936,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999404788,"difficulty":0.000595212}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Georgina. Jose's card is shown to Tom. Tom's card is shown to Tom. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jose can now know that Georgina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Georgina","Jose","Tom"],"index":64912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998467505,"difficulty":0.001532495}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Velma's card is shown to Richard. Richard's card is shown to Robin. Richard's card is shown to Velma. Velma's card is shown to Velma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Robin","Velma"],"index":55487,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989365935,"difficulty":0.0010634065}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carol. Joyce's card is shown to Carol. Carol's card is shown to Donnette. Donnette's card is shown to Donnette. Carol's card is shown to Joyce. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joyce can now know whether Joyce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carol","Donnette","Joyce"],"index":25946,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5031784177,"difficulty":0.4968215823}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tara's card is shown to James. James's card is shown to Tara. Albert's card is shown to Tara. Tara's card is shown to Albert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Tara","Albert"],"index":6123,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996009469,"difficulty":0.003990531}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Rose. Brandon's card is shown to Jean. Erick's card is shown to Jean. Rose's card is shown to Brandon. Jean's card is shown to Brandon. Jean's card is shown to Erick. Brandon's card is shown to Erick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandon can now know that Rose can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Jean","Brandon","Erick"],"index":13130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999309659,"difficulty":0.000690341}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carole's card is shown to James. James's card is shown to Carole. It is publicly announced that someone picked a red card. It is publicly announced that Carole does not know whether Carole picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know whether Carole can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Carole"],"index":63497,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8417441845,"difficulty":1.8417441845}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Kevin. Todd's card is shown to Kevin. Kevin's card is shown to Todd. Todd's card is shown to Todd. Douglas's card is shown to Todd. Todd's card is shown to Douglas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Kevin","Todd","Douglas"],"index":39515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990081191,"difficulty":0.0009918809}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Liz's card is shown to Karen. Karen's card is shown to Liz. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Karen can now know whether Liz picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Karen","Liz"],"index":37310,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5833329558,"difficulty":1.5833329558}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Gary. Irene's card is shown to Gary. Gary's card is shown to Lisa. Lisa's card is shown to Irene. It is publicly announced that someone picked a red card. It is publicly announced that Gary does not know whether Gary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gary can now know whether Irene can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Lisa","Irene"],"index":43949,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993962049,"difficulty":0.0006037951}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Andrew. Jeffrey's card is shown to Andrew. Sharda's card is shown to Sharda. Sharda's card is shown to Jeffrey. Jeffrey's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey does not know whether or not everyone picked a red card. It is publicly announced that Jeffrey does not know whether Jeffrey picked a red card. It is publicly announced that Andrew knows whether Jeffrey picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Sharda can now know whether Jeffrey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","Sharda","Jeffrey","Stephen"],"index":54963,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8514096141,"difficulty":0.1485903859}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Sara. Olga's card is shown to Sara. Robert's card is shown to Sara. Olga's card is shown to Louisa. Olga's card is shown to Olga. Olga's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Sara does not know whether Louisa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Sara can now know that Robert can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sara","Louisa","Olga","Robert"],"index":41758,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960946441,"difficulty":0.0039053559}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ward's card is shown to Lillian. Lillian's card is shown to Ward. Ward's card is shown to Ward. Lillian's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Ward does not know whether William picked a red card. It is publicly announced that Ward picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] Agentc knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"William can now know whether Ward can know whether Ward picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lillian","Ward","William"],"index":1402,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979806542,"difficulty":0.0020193458}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamela's card is shown to Corene. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Corene knows whether Pamela picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Corene can now know whether Pamela can know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Corene","Pamela"],"index":67354,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9882655144,"difficulty":0.0117344856}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Elizabeth. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Robert","Thomas"],"index":1231,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9871789217,"difficulty":0.0128210783}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beth's card is shown to Beth. Theresa's card is shown to Beth. Tammi's card is shown to Theresa. Beth's card is shown to Tammi. Tammi's card is shown to Tammi. It is publicly announced that someone picked a red card. It is publicly announced that Theresa picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 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 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Tammi can now know that Theresa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Beth","Theresa","Tammi"],"index":57711,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990039468,"difficulty":0.0009960532}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Timothy. Timothy's card is shown to Christopher. Christopher's card is shown to Christopher. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 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 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Timothy can now know that Christopher can know whether Joanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Timothy","Christopher","Joanne"],"index":62442,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995693922,"difficulty":0.004306078}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Jonathan. Ella's card is shown to Jonathan. Jonathan's card is shown to Barbara. Ella's card is shown to Barbara. Jonathan's card is shown to Ella. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Ella picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jonathan","Barbara","Ella"],"index":392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945561886,"difficulty":0.0054438114}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Pauline. Jerry's card is shown to Pauline. Joyce's card is shown to Joyce. Joyce's card is shown to Jean. Jerry's card is shown to Jerry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd: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:2,4 Agentb:2 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jean can now know whether Jerry can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pauline","Joyce","Jean","Jerry"],"index":45150,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993616939,"difficulty":0.0006383061}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sally's card is shown to Sally. Viola's card is shown to Sally. Gertrude's card is shown to Stella. Stella's card is shown to Stella. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Viola can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sally","Viola","Gertrude","Stella"],"index":48398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993335605,"difficulty":0.0006664395}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. David's card is shown to Marjorie. David's card is shown to Benjamin. Marjorie's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Marjorie","Benjamin"],"index":13228,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990192652,"difficulty":0.0009807348}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emilio's card is shown to James. Emilio's card is shown to Emilio. It is publicly announced that someone picked a red card. It is publicly announced that Emilio does not know whether James picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Emilio can now know that James can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Emilio"],"index":34989,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994215965,"difficulty":0.0005784035}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sophie's card is shown to Sophie. Wilmer's card is shown to Sophie. Sophie's card is shown to Charles. Sophie's card is shown to Wilmer. Wilmer's card is shown to Wilmer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sophie","Charles","Wilmer"],"index":61884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942427278,"difficulty":0.0057572722}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristy's card is shown to Marjorie. Marjorie's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Kristy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Kristy can now know whether Kristy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kristy","Marjorie"],"index":41880,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6116583347,"difficulty":1.6116583347}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Joshua's card is shown to Donald. Donald's card is shown to Denise. Joshua's card is shown to Denise. Denise's card is shown to Billy. Billy's card is shown to Billy. Denise's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Denise knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Donald can now know whether Billy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Denise","Billy","Joshua"],"index":907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992832541,"difficulty":0.0007167459}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Anna. Christopher's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher knows whether Anna picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Anna can now know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anna","Christopher"],"index":27453,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.90768677,"difficulty":0.09231323}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Grace. Kelly's card is shown to Julie. Randy's card is shown to Julie. Grace's card is shown to Randy. Julie's card is shown to Randy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kelly can now know whether Julie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Grace","Kelly","Julie","Randy"],"index":53032,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8063346148,"difficulty":0.1936653852}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Marisa. David's card is shown to Bessie. Lionel's card is shown to David. Marisa's card is shown to Lionel. David's card is shown to Lionel. It is publicly announced that someone picked a red card. It is publicly announced that Bessie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know whether Lionel can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marisa","Bessie","David","Lionel"],"index":19520,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983024597,"difficulty":0.0016975403}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronnie's card is shown to Laurie. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Laurie does not know whether Laurie picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Laurie can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laurie","Ronnie","Mary"],"index":60678,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964829683,"difficulty":0.0035170317}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maricela's card is shown to Maricela. Ray's card is shown to Maricela. Dave's card is shown to Maricela. Dave's card is shown to Ray. Dave's card is shown to Dave. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ray can now know that Maricela can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maricela","Ray","Dave"],"index":27054,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994152784,"difficulty":0.0005847216}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonette's card is shown to Louise. Marva's card is shown to Louise. Paula's card is shown to Antonette. Paula's card is shown to Marva. Antonette's card is shown to Marva. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Antonette can now know whether Louise can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Louise","Antonette","Marva"],"index":57092,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9932821989,"difficulty":0.0067178011}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalyn's card is shown to Rosalyn. Priscilla's card is shown to Rosalyn. Priscilla's card is shown to Priscilla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Rosalyn can now know that Rosalyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rosalyn","Priscilla"],"index":60949,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9903772473,"difficulty":0.0096227527}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Malcolm. Juliette's card is shown to Juliette. Manuel's card is shown to Juliette. Manuel's card is shown to Ralph. Malcolm's card is shown to Manuel. Juliette's card is shown to Manuel. Ralph's card is shown to Manuel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Manuel can now know whether Malcolm can know that Juliette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Malcolm","Juliette","Ralph","Manuel"],"index":5777,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9358462095,"difficulty":0.0641537905}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rae's card is shown to Rae. Naomi's card is shown to Rae. Naomi's card is shown to Dana. Anderson's card is shown to Anderson. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rae can now know whether Dana can know that Dana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rae","Naomi","Dana","Anderson"],"index":57988,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9848756194,"difficulty":1.9848756194}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Kathryn. Kathryn's card is shown to Mark. Mark's card is shown to Mark. James's card is shown to Mark. Kathryn's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card. It is publicly announced that Mark knows whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kathryn can now know whether Mark can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathryn","Mark","James"],"index":8501,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9692941308,"difficulty":1.9692941308}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Agnes's card is shown to Darlene. Bryan's card is shown to Darlene. Darlene's card is shown to Carlos. Agnes's card is shown to Carlos. Agnes's card is shown to Agnes. Agnes's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Agnes does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Carlos can now know that Darlene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darlene","Carlos","Agnes","Bryan"],"index":46317,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.968334496,"difficulty":0.031665504}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Doris. Johnny's card is shown to Johnny. Mark's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Christopher picked a red card. It is publicly announced that Johnny does not know whether Christopher picked a red card. It is publicly announced that Johnny does not know whether Mark picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Mark can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doris","Johnny","Mark","Christopher"],"index":3008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.966920197,"difficulty":0.033079803}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodore's card is shown to Theodore. Alice's card is shown to Theodore. Keith's card is shown to Theodore. Theodore's card is shown to Alice. Keith's card is shown to Keith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Keith can now know that Theodore can know that Keith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Theodore","Alice","Keith"],"index":56074,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958181977,"difficulty":0.0041818023}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Randy. Steven's card is shown to Peter. Peter's card is shown to Peter. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know whether Randy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Steven","Peter","Geraldine"],"index":32185,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9867239594,"difficulty":0.0132760406}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Agnes's card is shown to William. Jaqueline's card is shown to Jaqueline. Agnes's card is shown to Jaqueline. Agnes's card is shown to Agnes. William's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Agnes can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Jaqueline","Agnes","Annie"],"index":53055,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7887471914,"difficulty":0.2112528086}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chester's card is shown to Chester. Gregory's card is shown to Gregory. Mercedes's card is shown to Mercedes. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Chester can know whether Mercedes picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Chester","Gregory","Mercedes"],"index":44168,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5496553779,"difficulty":1.5496553779}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danny's card is shown to Julius. Emily's card is shown to Danny. Marsha's card is shown to Marsha. Emily's card is shown to Marsha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Danny can now know whether Marsha can know that Julius picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julius","Danny","Marsha","Emily"],"index":65915,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8948574066,"difficulty":0.1051425934}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Paul. Sheila's card is shown to Paul. Nancy's card is shown to Nancy. Paul's card is shown to Sheila. Nancy's card is shown to Sheila. Sheila's card is shown to Sheila. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Nancy","Sheila"],"index":40560,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989956021,"difficulty":0.0010043979}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Emma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Emma can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Emma","Steven","Joyce"],"index":33440,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995582521,"difficulty":0.004417479}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Russel's card is shown to Wm. Wm's card is shown to Josefina. Justin's card is shown to Josefina. Russel's card is shown to Justin. Justin's card is shown to Justin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wm can now know that Russel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wm","Russel","Josefina","Justin"],"index":49495,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961793423,"difficulty":0.0038206577}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nichole's card is shown to Jerry. Jerry's card is shown to Jerry. Jennifer's card is shown to Jerry. Nichole's card is shown to Jennifer. Jerry's card is shown to Jennifer. Jennifer's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jerry can now know whether Nichole can know that Jerry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nichole","Jerry","Jennifer"],"index":21389,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7624345422,"difficulty":0.2375654578}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Tamra. Tamra's card is shown to Peter. Vera's card is shown to Peter. Michael's card is shown to Vera. Peter's card is shown to Vera. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tamra","Michael","Peter","Vera"],"index":41238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989621639,"difficulty":0.0010378361}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Walter. Donna's card is shown to Willis. Walter's card is shown to Willis. Samuel's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Walter can now know that Walter picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Walter","Willis","Samuel"],"index":54377,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7362667918,"difficulty":1.7362667918}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clement's card is shown to Clement. Clement's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Clement knows whether someone picked a red card. It is publicly announced that Eric knows whether Eric picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Eric can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Clement","Eric"],"index":11276,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7937288284,"difficulty":0.2062711716}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Debra. Marla's card is shown to Debra. Marla's card is shown to Ashley. Paul's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Debra can now know whether Ashley can know whether Debra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Ashley","Paul","Marla"],"index":595,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984771609,"difficulty":0.0015228391}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francine's card is shown to Daniel. Daniel's card is shown to Francine. Francine's card is shown to Francine. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Daniel picked a red card. It is publicly announced that Francine picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] 0","hypothesis":"Daniel can now know that Francine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daniel","Francine"],"index":53957,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989652634,"difficulty":0.0010347366}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Kim. Dorothy's card is shown to Dorothy. Lucille's card is shown to Lucille. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Dorothy does not know whether Kim picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kim can now know whether Lucille can know that Kim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","Dorothy","Lucille"],"index":23902,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7321740389,"difficulty":1.7321740389}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aaron's card is shown to Pearlie. Edith's card is shown to Pearlie. Pearlie's card is shown to Aaron. Edith's card is shown to Aaron. Benjamin's card is shown to Benjamin. Aaron's card is shown to Edith. It is publicly announced that someone picked a red card. It is publicly announced that Pearlie knows whether or not nobody picked a red card. It is publicly announced that Pearlie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 1 ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 1 ] 0","hypothesis":"Pearlie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Pearlie","Aaron","Benjamin","Edith"],"index":34039,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994468093,"difficulty":0.0005531907}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gertrude's card is shown to Gertrude. Elmer's card is shown to Gertrude. Billy's card is shown to Elmer. Billy's card is shown to Billy. Billy's card is shown to Sonia. It is publicly announced that someone picked a red card. It is publicly announced that Billy picked a red card. It is publicly announced that Gertrude picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(1) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(1) ] 0","hypothesis":"Gertrude can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gertrude","Elmer","Billy","Sonia"],"index":2032,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994546771,"difficulty":0.0005453229}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to William. William's card is shown to Hector. Hector's card is shown to Hector. Michael's card is shown to Hector. Hector's card is shown to Michael. Hector's card is shown to Thomas. Michael's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that William picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Michael can now know that Hector can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Hector","Michael","Thomas"],"index":62354,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999011755,"difficulty":0.000988245}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Michelle. Rachel's card is shown to Michelle. Rachel's card is shown to Rachel. Michelle's card is shown to Heidi. Heidi's card is shown to Heidi. Rachel's card is shown to Marie. Marie's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Rachel picked a red card. It is publicly announced that Rachel knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Heidi can now know whether Michelle can know whether Rachel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Rachel","Heidi","Marie"],"index":30117,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987333417,"difficulty":0.0012666583}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Mary. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Matthew does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Matthew can now know whether Mary can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Matthew"],"index":12306,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994180202,"difficulty":0.0005819798}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Amanda. Thomas's card is shown to Thomas. Amanda's card is shown to Margaret. Thomas's card is shown to Margaret. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Amanda does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta 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 Agentb:3 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know whether Amanda can know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","Mary","Thomas","Margaret"],"index":28187,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987246394,"difficulty":0.0012753606}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cassandra's card is shown to Walter. Cassandra's card is shown to Cassandra. Jenny's card is shown to Cassandra. Wayne's card is shown to Jenny. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether or not everyone picked a red card. It is publicly announced that Jenny does not know whether Walter picked a red card. It is publicly announced that Walter does not know whether Wayne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Walter can now know whether Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Cassandra","Jenny","Wayne"],"index":56991,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.971288085,"difficulty":0.028711915}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marjorie's card is shown to Marjorie. Larry's card is shown to Marjorie. Mildred's card is shown to Larry. Joseph's card is shown to Mildred. Mildred's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know whether Joseph can know whether Mildred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marjorie","Larry","Mildred","Joseph"],"index":52564,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985585809,"difficulty":0.0014414191}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Rose. Rose's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Rose can now know that Rose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rose","John"],"index":15060,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9353154898,"difficulty":0.0646845102}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sidney's card is shown to Jennifer. Whitney's card is shown to Jennifer. Jennifer's card is shown to Sidney. Jennifer's card is shown to Whitney. Sidney's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Sidney does not know whether Sidney picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jennifer can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Sidney","Whitney","Robert"],"index":26596,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989635944,"difficulty":0.0010364056}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Kenneth's card is shown to Abel. Abel's card is shown to Yvonne. Yvonne's card is shown to Yvonne. Yvonne's card is shown to Katheryn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Yvonne can now know whether Kenneth can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Abel","Yvonne","Katheryn"],"index":39753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8946009874,"difficulty":0.1053990126}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eldon's card is shown to Patricia. Ethel's card is shown to Ethel. Eldon's card is shown to Ethel. Ethel's card is shown to Eldon. Eldon's card is shown to Eldon. It is publicly announced that someone picked a red card. It is publicly announced that Eldon picked a red card. It is publicly announced that Eldon does not know whether Patricia picked a red card. It is publicly announced that Eldon knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Ethel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Ethel","Eldon"],"index":19846,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9479324818,"difficulty":0.0520675182}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eun's card is shown to Rachel. Sherry's card is shown to James. Rachel's card is shown to Eun. Rachel's card is shown to Sherry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Rachel can know whether Eun picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rachel","James","Eun","Sherry"],"index":64885,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6429770589,"difficulty":1.6429770589}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reginald's card is shown to Debra. Gretchen's card is shown to Debra. Debra's card is shown to Gretchen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Debra can now know whether Debra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debra","Reginald","Gretchen"],"index":13174,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8409997821,"difficulty":1.8409997821}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Ruby. Ruby's card is shown to Marie. Marie's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether Marie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ruby can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ruby","Marie"],"index":26153,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994449019,"difficulty":0.0005550981}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Earl. Earl's card is shown to Kerry. Earl's card is shown to Shirley. Shirley's card is shown to Shirley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kerry can now know whether Earl can know that Earl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Earl","Kerry","Shirley"],"index":17765,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8795042634,"difficulty":0.1204957366}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lakiesha's card is shown to Larry. Michael's card is shown to Larry. Lakiesha's card is shown to Lakiesha. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Larry picked a red card. It is publicly announced that Lakiesha knows whether Lakiesha picked a red card. It is publicly announced that Lakiesha does not know whether or not everyone picked a red card. It is publicly announced that Michael knows whether Lakiesha picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 2) ] (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Lakiesha","Michael"],"index":23439,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5789123774,"difficulty":0.4210876226}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelly's card is shown to Shelly. David's card is shown to Shelly. Shelly's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Shelly does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Shelly can now know whether Jewel can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jewel","Shelly","David"],"index":22447,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8008099794,"difficulty":0.1991900206}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joe's card is shown to Joe. Joe's card is shown to Hazel. It is publicly announced that someone picked a red card. It is publicly announced that Hazel does not know whether or not everyone picked a red card. It is publicly announced that Hazel does not know whether or not everyone picked a red card. It is publicly announced that Joe knows whether or not nobody picked a red card. It is publicly announced that Joe does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Hazel can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joe","Hazel"],"index":37121,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994503856,"difficulty":0.0005496144}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clara's card is shown to Nancy. Andrew's card is shown to Nancy. Clara's card is shown to Clara. Nancy's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Nancy knows whether Clara picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Clara can now know that Clara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Clara","Andrew"],"index":47591,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9850997329,"difficulty":0.0149002671}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnulfo's card is shown to Ethel. Ethel's card is shown to David. David's card is shown to David. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Arnulfo can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ethel","David","Arnulfo","Richard"],"index":26254,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994058609,"difficulty":0.0005941391}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Martin. Martin's card is shown to Donna. Paul's card is shown to Donna. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Paul does not know whether Martin picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Donna can now know whether Paul can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martin","Donna","Paul"],"index":9392,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9670968652,"difficulty":0.0329031348}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sean's card is shown to James. Jason's card is shown to Sean. Jason's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Sean does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"James can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Sean","Jason"],"index":63459,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6852491498,"difficulty":0.3147508502}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geraldine's card is shown to Carolina. Emily's card is shown to Carolina. Israel's card is shown to Geraldine. Emily's card is shown to Geraldine. Carolina's card is shown to Israel. Israel's card is shown to Israel. Emily's card is shown to Emily. It is publicly announced that someone picked a red card. It is publicly announced that Emily does not know whether Geraldine picked a red card. It is publicly announced that Israel does not know whether Geraldine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Geraldine can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carolina","Geraldine","Israel","Emily"],"index":54568,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989507198,"difficulty":0.0010492802}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Deborah. Jack's card is shown to Deborah. Deborah's card is shown to Jack. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deborah can now know whether Jack picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deborah","Jonathan","Jack"],"index":55242,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9205588102,"difficulty":1.9205588102}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Elizabeth's card is shown to Helen. Elizabeth's card is shown to Sharon. Helen's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Sharon can now know that Helen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","Sharon","Elizabeth"],"index":19123,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985297918,"difficulty":0.0014702082}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Carl's card is shown to Linda. Mary's card is shown to Linda. Carl's card is shown to Elmer. Carl's card is shown to Carl. Carl's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Elmer picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Elmer can now know that Mary can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Elmer","Carl","Mary"],"index":45621,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972535968,"difficulty":0.0027464032}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Joyce. John's card is shown to Joyce. Joyce's card is shown to Emmanuel. John's card is shown to Emmanuel. Emmanuel's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joyce can now know whether Emmanuel can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Nicole","Emmanuel","John"],"index":41031,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9576574564,"difficulty":0.0423425436}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Elizabeth. Christine's card is shown to Nadia. Nadia's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Nadia can now know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Brian","Nadia","Christine"],"index":50276,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9686134458,"difficulty":0.0313865542}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Monica. Joyce's card is shown to Lori. Lori's card is shown to Lori. Kari's card is shown to Lori. Monica's card is shown to Kari. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Joyce picked a black card. It is publicly announced that Joyce picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] [ ! ~(2) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Joyce can now know whether Lori can know whether Kari picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monica","Joyce","Lori","Kari"],"index":63836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981927276,"difficulty":0.0018072724}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Constance's card is shown to Constance. Constance's card is shown to Michelle. Steven's card is shown to Matthew. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc: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 Agentb:1 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know that Steven can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Constance","Michelle","Steven","Matthew"],"index":21988,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990332127,"difficulty":0.0009667873}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Margaret. Margaret's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John picked a red card. It is publicly announced that John knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Margaret can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Margaret","John"],"index":47684,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994702935,"difficulty":0.0005297065}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rex's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Kenneth picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kenneth","Rex"],"index":63242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9899140596,"difficulty":0.0100859404}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Michael. Richard's card is shown to Darrell. Michael's card is shown to Richard. Darrell's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card. It is publicly announced that Michael knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Richard can now know whether Michael can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Darrell","Richard"],"index":34163,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9493461847,"difficulty":0.0506538153}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alec's card is shown to Alec. Alec's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Robert picked a red card. It is publicly announced that Alec does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Alec can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alec","Robert"],"index":35411,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988805652,"difficulty":0.0011194348}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darnell's card is shown to Darnell. Johnnie's card is shown to Darnell. Nicole's card is shown to Holly. Darnell's card is shown to Johnnie. Nicole's card is shown to Johnnie. Holly's card is shown to Nicole. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Darnell picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Johnnie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Darnell can now know that Johnnie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darnell","Holly","Johnnie","Nicole"],"index":31534,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993408322,"difficulty":0.0006591678}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carol. Colleen's card is shown to Carol. Erica's card is shown to Carol. Carol's card is shown to Delmar. Erica's card is shown to Delmar. Carol's card is shown to Erica. It is publicly announced that someone picked a red card. It is publicly announced that Delmar knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Colleen can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carol","Colleen","Delmar","Erica"],"index":5815,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994606376,"difficulty":0.0005393624}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alissa's card is shown to Alissa. Lisa's card is shown to Alissa. Alissa's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Alissa picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Lisa can now know that Alissa can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alissa","Lisa"],"index":34485,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978938699,"difficulty":0.0021061301}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Mavis's card is shown to John. George's card is shown to Mavis. Mavis's card is shown to Mavis. It is publicly announced that someone picked a red card. It is publicly announced that George knows whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"John can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","George","Mavis"],"index":17304,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.859649539,"difficulty":0.140350461}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Tracey. Thomas's card is shown to Thomas. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracey","Thomas","Michael"],"index":8946,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9924701452,"difficulty":0.0075298548}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mamie's card is shown to Mamie. Malka's card is shown to Leonora. Leonora's card is shown to Malka. It is publicly announced that someone picked a red card. It is publicly announced that Madeline does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Leonora can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mamie","Madeline","Leonora","Malka"],"index":66457,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994627833,"difficulty":0.0005372167}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Chris. Chris's card is shown to William. William's card is shown to Eva. Eva's card is shown to Eva. Eva's card is shown to Sherry. It is publicly announced that someone picked a red card. It is publicly announced that Sherry does not know whether Chris picked a red card. It is publicly announced that Chris does not know whether William picked a red card. It is publicly announced that Eva knows whether Eva picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Sherry can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Chris","William","Eva","Sherry"],"index":39104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994482398,"difficulty":0.0005517602}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Billy's card is shown to Christopher. Christopher's card is shown to Evelyn. Billy's card is shown to Evelyn. Kenneth's card is shown to Evelyn. Billy's card is shown to Billy. Billy's card is shown to Kenneth. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,3,4 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,3,4 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Evelyn can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Evelyn","Billy","Kenneth"],"index":66271,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8333765268,"difficulty":0.1666234732}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leonard's card is shown to Michael. Leonard's card is shown to Brian. Brian's card is shown to Brian. Brian's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know that Michael can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Leonard","Brian","Ronald"],"index":13054,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9934802055,"difficulty":0.0065197945}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Selena's card is shown to Robert. Robert's card is shown to Richard. Robert's card is shown to Selena. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Richard can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Richard","Selena"],"index":44172,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9352275729,"difficulty":0.0647724271}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adrian's card is shown to Adrian. James's card is shown to James. Armando's card is shown to Edgar. Edgar's card is shown to Edgar. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Adrian can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Armando","Adrian","James","Edgar"],"index":49277,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989097118,"difficulty":0.0010902882}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Carlos. Carlos's card is shown to Carlos. Lisa's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know whether Carlos can know that Carlos picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Carlos","Mark"],"index":3203,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5567389131,"difficulty":0.4432610869}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindi's card is shown to Cindi. Liana's card is shown to Cindi. Cindi's card is shown to Liana. Liana's card is shown to Liana. It is publicly announced that someone picked a red card. It is publicly announced that Cindi knows whether Liana picked a red card. It is publicly announced that Cindi picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 1 ] (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 2) ] [ ! 1 ] 0","hypothesis":"Liana can now know whether Cindi picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cindi","Liana"],"index":50228,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9821692109,"difficulty":0.0178307891}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to Janice. David's card is shown to Janice. Arthur's card is shown to Janice. David's card is shown to David. Arthur's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Arthur picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"David can now know whether Arthur can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Janice","David","Arthur"],"index":14018,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8393124938,"difficulty":0.1606875062}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Joshua. Joshua's card is shown to Anne. It is publicly announced that someone picked a red card. It is publicly announced that Joshua does not know whether or not everyone picked a red card. It is publicly announced that Anne knows whether Anne picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joshua can now know that Anne can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joshua","Anne"],"index":17325,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975824356,"difficulty":0.0024175644}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Carl. Emily's card is shown to Joyce. Jennie's card is shown to Joyce. Carl's card is shown to Emily. Jennie's card is shown to Emily. It is publicly announced that someone picked a red card. It is publicly announced that Carl does not know whether Jennie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Carl can now know whether Emily can know that Jennie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carl","Joyce","Emily","Jennie"],"index":51186,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8844183087,"difficulty":1.8844183087}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Michael. Lisa's card is shown to Michael. Michael's card is shown to Angel. Donald's card is shown to Angel. Lisa's card is shown to Angel. Michael's card is shown to Donald. Angel's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether Michael can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Angel","Donald","Lisa"],"index":50891,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9976410866,"difficulty":0.0023589134}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Beverly. Emilio's card is shown to Beverly. Tammy's card is shown to Beverly. Tammy's card is shown to Emilio. Emilio's card is shown to Tammy. Tammy's card is shown to Tammy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emilio can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Beverly","Emilio","Tammy"],"index":60618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978690147,"difficulty":0.0021309853}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daphine's card is shown to Daphine. William's card is shown to Daphine. Ellen's card is shown to Ellen. William's card is shown to Ellen. Daphine's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Daphine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daphine","Ellen","William"],"index":23795,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9811378717,"difficulty":0.0188621283}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandra's card is shown to Sandra. Travis's card is shown to Sandra. Travis's card is shown to Travis. Sandra's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Travis does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Sandra can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sandra","Travis","Anna"],"index":15376,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9501934648,"difficulty":0.0498065352}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kylie's card is shown to Kylie. Deanna's card is shown to Norman. Norman's card is shown to James. Kylie's card is shown to Deanna. Norman's card is shown to Deanna. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc 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 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Norman can now know whether Norman picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kylie","Norman","James","Deanna"],"index":19411,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5784884095,"difficulty":0.4215115905}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vincenzo's card is shown to Cody. David's card is shown to David. David's card is shown to Jared. It is publicly announced that someone picked a red card. It is publicly announced that David picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Vincenzo can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cody","Vincenzo","David","Jared"],"index":12436,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994451404,"difficulty":0.0005548596}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonio's card is shown to Antonio. James's card is shown to Antonio. Antonio's card is shown to Michael. James's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Antonio knows whether or not nobody picked a red card. It is publicly announced that James knows whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Antonio can now know that Antonio picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Antonio","James","Michael"],"index":29513,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.994361639,"difficulty":0.005638361}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Susannah. Tessa's card is shown to Tessa. Susannah's card is shown to Dorothy. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Tessa does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Susannah can now know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Susannah","Tessa","Dorothy"],"index":22121,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8732469082,"difficulty":0.1267530918}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Charlotte. Charlotte's card is shown to Patsy. Patsy's card is shown to Patsy. Jared's card is shown to Patsy. Charlotte's card is shown to Jared. It is publicly announced that someone picked a red card. It is publicly announced that Jared does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jared can now know that Charlotte can know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charlotte","Patsy","Jared"],"index":620,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6509642005,"difficulty":1.6509642005}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Lewis's card is shown to John. Annie's card is shown to John. John's card is shown to Lewis. Lewis's card is shown to Paula. Annie's card is shown to Paula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paula can now know whether Lewis can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Lewis","Paula","Annie"],"index":60102,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994044304,"difficulty":0.0005955696}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sidney's card is shown to Matthew. Matthew's card is shown to Sidney. Dawn's card is shown to Sidney. Sidney's card is shown to Dawn. It is publicly announced that someone picked a red card. It is publicly announced that Sidney knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Matthew can now know that Sidney can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Sidney","Dawn"],"index":25082,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994006157,"difficulty":0.0005993843}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nydia's card is shown to Bill. Nydia's card is shown to Nydia. It is publicly announced that someone picked a red card. It is publicly announced that Bill knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Nydia can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bill","Nydia"],"index":53371,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994243383,"difficulty":0.0005756617}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcia's card is shown to Ramona. Ramona's card is shown to Marcia. Jeanne's card is shown to Jeanne. It is publicly announced that someone picked a red card. It is publicly announced that Jeanne knows whether Jeanne picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Marcia can now know that Ramona picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ramona","Marcia","Jeanne"],"index":22803,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9898472428,"difficulty":0.0101527572}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Aurora. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Aurora picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Richard can now know whether Aurora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Aurora","Richard"],"index":51170,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.925537467,"difficulty":0.074462533}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erica's card is shown to Erica. Estela's card is shown to Marc. Estela's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marc can now know whether Erica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erica","Marc","Estela","Jason"],"index":33533,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7053470612,"difficulty":0.2946529388}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Eddie. Eddie's card is shown to Jennifer. Eddie's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know that Jennifer can know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eddie","Jennifer","Jessica"],"index":17655,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8383966684,"difficulty":1.8383966684}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Rosemary. Paula's card is shown to Doug. Doug's card is shown to Doug. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paula can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rosemary","Paula","Doug"],"index":3048,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994119406,"difficulty":0.0005880594}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Ruby. James's card is shown to Keith. Isaiah's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruby can now know whether Isaiah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Isaiah","Ruby","Keith","James"],"index":10113,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8450246453,"difficulty":0.1549753547}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Stephen's card is shown to Charles. Charles's card is shown to Charles. Erin's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether Fred picked a red card. It is publicly announced that Erin picked a red card. It is publicly announced that Charles does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Fred can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Charles","Fred","Erin"],"index":13302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9267155528,"difficulty":0.0732844472}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Charles's card is shown to Dorothy. Charles's card is shown to Charles. Bryan's card is shown to Charles. Dorothy's card is shown to Bryan. Charles's card is shown to Bryan. Bryan's card is shown to Bryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Charles","Bryan"],"index":40961,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9931045175,"difficulty":0.0068954825}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mathew's card is shown to Robert. Glenda's card is shown to Mathew. Robert's card is shown to Glenda. Mathew's card is shown to Glenda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Mathew","Glenda"],"index":4955,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993822575,"difficulty":0.0006177425}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ray's card is shown to Brandon. Brandon's card is shown to Ray. Ray's card is shown to Ray. It is publicly announced that someone picked a red card. It is publicly announced that Ray picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Ray can now know that Brandon can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brandon","Ray"],"index":30172,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989859462,"difficulty":0.0010140538}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edmund's card is shown to Edmund. Gwendolyn's card is shown to Timothy. Edmund's card is shown to Timothy. Timothy's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gwendolyn can now know that Edmund can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gwendolyn","Edmund","Timothy","Robert"],"index":884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980956912,"difficulty":0.0019043088}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Dale. Lori's card is shown to Dale. Lori's card is shown to Lori. Michael's card is shown to Lori. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Dale can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dale","Lori","Michael"],"index":17517,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994797111,"difficulty":0.0005202889}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gaylord's card is shown to Lois. Lois's card is shown to Gaylord. It is publicly announced that someone picked a red card. It is publicly announced that Gaylord knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Gaylord can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lois","Gaylord"],"index":14264,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994084835,"difficulty":0.0005915165}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luis's card is shown to Sue. Sue's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Sue does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Luis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sue","Luis"],"index":48877,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981595874,"difficulty":0.0018404126}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Yu's card is shown to Chris. Michael's card is shown to Yu. Chris's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Yu can now know that Michael can know whether Yu picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Chris","Yu","Michael"],"index":37578,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5018200278,"difficulty":0.4981799722}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Heather. Christine's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Christine does not know whether or not everyone picked a red card. It is publicly announced that Heather does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Heather can now know that Heather picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Heather","Christine"],"index":48476,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9148827195,"difficulty":0.0851172805}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremiah's card is shown to Jeremiah. William's card is shown to William. Jeremiah's card is shown to Manuel. It is publicly announced that someone picked a red card. It is publicly announced that Manuel does not know whether Manuel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"William can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeremiah","William","Manuel"],"index":65410,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990455508,"difficulty":0.0009544492}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Micaela. Micaela's card is shown to Brigette. James's card is shown to Brigette. Brigette's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Brigette knows whether or not everyone picked a red card. It is publicly announced that Brigette knows whether James picked a red card. It is publicly announced that Brigette knows whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Brigette can now know whether James can know that Brigette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Micaela","Brigette","James"],"index":59412,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9565897584,"difficulty":1.9565897584}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fae's card is shown to Cara. Cara's card is shown to Susan. Fae's card is shown to Susan. Cara's card is shown to Fae. Susan's card is shown to Fae. Fae's card is shown to Fae. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cara can now know that Fae can know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cara","Susan","Fae"],"index":40590,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6333019137,"difficulty":0.3666980863}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Olga. Norbert's card is shown to Lorraine. Margaret's card is shown to Norbert. Norbert's card is shown to Norbert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lorraine can now know that Norbert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Olga","Margaret","Lorraine","Norbert"],"index":44587,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957585931,"difficulty":0.0042414069}