{"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 Annie. Nona's card is shown to Annie. Mary's card is shown to Mary. Annie's card is shown to Nona. 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 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nona can now know whether Nona picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annie","Mary","Nona"],"index":1845,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8086408377,"difficulty":0.1913591623}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephanie's card is shown to Stephanie. Estella's card is shown to Stephanie. Samuel's card is shown to Samuel. Estella's card is shown to Estella. 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: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:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephanie can now know whether Estella can know whether Stephanie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephanie","Samuel","Estella"],"index":3393,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970097542,"difficulty":0.0029902458}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mavis's card is shown to Mavis. Velma's card is shown to Mavis. Kevin's card is shown to Kevin. Kevin's card is shown to Velma. Velma's card is shown to Velma. Kevin's card is shown to Marc. It is publicly announced that someone picked a red card. It is publicly announced that Mavis does not know whether Marc picked a red card. It is publicly announced that Velma 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 whether 3)","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":"Mavis can now know whether Velma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mavis","Kevin","Velma","Marc"],"index":41014,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5754438043,"difficulty":1.5754438043}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to George. George's card is shown to Gary. Gary's card is shown to Doris. It is publicly announced that someone picked a red card. It is publicly announced that George does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"George can now know whether Gary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Gary","Doris"],"index":52587,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.878172636,"difficulty":0.121827364}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Florida. Florida's card is shown to Lawrence. Marivel's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Lawrence knows whether Florida picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Lawrence can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Florida","Lawrence","Marivel"],"index":37267,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999769628,"difficulty":0.000230372}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jackie's card is shown to Jackie. Megan's card is shown to Jackie. Kris's card is shown to Jackie. Megan's card is shown to Megan. Megan's card is shown to Kris. It is publicly announced that someone picked a red card. It is publicly announced that Megan knows whether or not everyone picked a red card. It is publicly announced that Kris knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Megan can now know whether Jackie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","Megan","Kris"],"index":38467,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Miyoko. Miyoko's card is shown to Janet. Janet's card is shown to Janet. Maurice's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janet can now know that Maurice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Miyoko","Janet","Maurice"],"index":15606,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982677698,"difficulty":0.0017322302}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terrence's card is shown to Ruth. Ruth's card is shown to Terrence. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dena can now know that Ruth can know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruth","Dena","Terrence"],"index":12902,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.93458426,"difficulty":1.93458426}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daryl's card is shown to Anna. Anna's card is shown to Rachel. 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 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know that Rachel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Rachel","Daryl","Matthew"],"index":22874,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984657764,"difficulty":0.0015342236}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Anja. Willie's card is shown to Grace. Robert'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:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 1)","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":"Willie can now know whether Anja can know whether Anja picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anja","Grace","Willie","Robert"],"index":35251,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9917164445,"difficulty":0.0082835555}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pei's card is shown to Gary. Danielle's card is shown to Gary. Ignacio's card is shown to Ignacio. Danielle's card is shown to Pei. Gary's card is shown to Danielle. Danielle's card is shown to Danielle. 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 Agentd:1,4 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:3,4 Agentb:2 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pei can now know that Danielle can know whether Pei picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Ignacio","Pei","Danielle"],"index":5414,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6739808917,"difficulty":0.3260191083}
{"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. Wilfred's card is shown to Wilfred. It is publicly announced that someone picked a red card. It is publicly announced that Wilfred knows whether Wilfred 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:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Wilfred can now know that Robert can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Wilfred"],"index":35452,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9809651971,"difficulty":0.0190348029}
{"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 Melissa. Darlene's card is shown to Melissa. Roy's card is shown to Melissa. Darlene's card is shown to Michael. Darlene's card is shown to Darlene. Darlene's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that Melissa does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentd knows whether 2)","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":"Melissa can now know that Roy can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melissa","Michael","Darlene","Roy"],"index":9610,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9392580986,"difficulty":0.0607419014}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Shannon. Shirley's card is shown to Shirley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stacy can now know that Shannon can know that Stacy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shannon","Stacy","Shirley"],"index":4284,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980587363,"difficulty":0.0019412637}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacey's card is shown to Robert. Robert's card is shown to Rachael. Stacey's card is shown to Rachael. Rachael's card is shown to Stacey. Stacey's card is shown to Stacey. It is publicly announced that someone picked a red card. It is publicly announced that Rachael does not know whether Rachael 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) ] (Agentb knows that 3)","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":"Rachael can now know that Stacey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Rachael","Stacey"],"index":3298,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9888734818,"difficulty":0.0111265182}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Kimberly. Kimberly's card is shown to Patricia. Donna'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 Donna 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 that (Agentb knows that 2)","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":"Kimberly can now know that Donna can know that Donna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kimberly","Donna","Patricia"],"index":67521,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946419001,"difficulty":0.0053580999}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Janet. Carrie's card is shown to Janet. Janet's card is shown to Suzanne. Janet's card is shown to Carrie. Carrie's card is shown to Carrie. 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 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":"Janet can now know whether Carrie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janet","Suzanne","Carrie"],"index":2692,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6038895249,"difficulty":1.6038895249}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Kathryn. Emily's card is shown to Kathryn. Samuel's card is shown to Samuel. Emily's card is shown to Samuel. Kathryn's card is shown to Scott. Scott's card is shown to Emily. Emily's card is shown to Emily. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 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:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Samuel can now know whether Scott can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Samuel","Scott","Emily"],"index":50455,"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). Shellie's card is shown to Shellie. Willie's card is shown to Shellie. Shellie's card is shown to Willie. Willie's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Shellie knows whether or not everyone 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)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Willie can now know that Shellie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Shellie","Willie"],"index":28392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6069005728,"difficulty":0.3930994272}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Bart. Mildred's card is shown to James. James'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:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mildred can now know that Mildred picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bart","James","Mildred"],"index":47396,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943717718,"difficulty":0.0056282282}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Lisa. Monica's card is shown to Carol. Kyle's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Lisa does not know whether Carol 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:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(4) ] (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 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Monica can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Monica","Lisa","Carol","Kyle"],"index":59118,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982977509,"difficulty":0.0017022491}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Amber. Amber's card is shown to Brenda. Brenda's card is shown to Brenda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 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":"Brenda can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amber","Brenda","Patricia"],"index":67213,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
{"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 Richard. Richard's card is shown to Richard. Richard's card is shown to Susie. Catherine's card is shown to Susie. 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:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Catherine can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Richard","Catherine","Susie"],"index":27344,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978629947,"difficulty":0.0021370053}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cara's card is shown to Vasiliki. Cara's card is shown to Conrad. Jennifer's card is shown to Conrad. Vasiliki's card is shown to Cara. It is publicly announced that someone picked a red card. It is publicly announced that Vasiliki knows whether someone 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows whether 2)","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) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Cara can now know whether Conrad picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vasiliki","Conrad","Cara","Jennifer"],"index":40244,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9662374854,"difficulty":0.0337625146}
{"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 Lester. Lester's card is shown to Nathan. Robert's card is shown to Nathan. Nathan's card is shown to Karen. Lester's card is shown to Robert. Karen'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 Lester knows whether or not nobody picked a red card. It is publicly announced that Karen 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 (Agenta knows whether (1&2&3&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":"Karen can now know that Lester can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lester","Nathan","Karen","Robert"],"index":51097,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.66116786,"difficulty":1.66116786}
{"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 Rachel. Patrica's card is shown to Stephen. Rachel's card is shown to Larry. Stephen's card is shown to Patrica. It is publicly announced that someone picked a red card. It is publicly announced that Rachel does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Rachel can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rachel","Stephen","Larry","Patrica"],"index":53867,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997010231,"difficulty":0.0002989769}
{"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 Nathaniel. Robert's card is shown to Nathaniel. Nathaniel's card is shown to John. Nathaniel's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 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":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nathaniel","John","Robert"],"index":29032,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997261167,"difficulty":0.0002738833}
{"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. Salvatore's card is shown to Salvatore. 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 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Salvatore can now know whether Dorothy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Salvatore"],"index":2077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9689156413,"difficulty":0.0310843587}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angel's card is shown to Angel. Warren's card is shown to Angel. Warren's card is shown to Warren. Angel's card is shown to Alexandria. Warren's card is shown to Alexandria. Alexandria's card is shown to Alexandria. 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) ] (Agentb knows whether (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":"Warren can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angel","Warren","Alexandria"],"index":43096,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9879034162,"difficulty":0.0120965838}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Junior's card is shown to Junior. Sharon's card is shown to Junior. Jacqueline's card is shown to Junior. Junior's card is shown to Sharon. Sharon's card is shown to Sharon. Jacqueline's card is shown to Jacqueline. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc: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:2,3,4 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sharon can now know whether Junior can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Junior","Sharon","Jacqueline"],"index":12509,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997074008,"difficulty":0.0002925992}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Burton's card is shown to Ruth. Randall's card is shown to Burton. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Burton can now know whether Ruth can know that Burton picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Burton","Randall"],"index":35597,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9541877508,"difficulty":0.0458122492}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Angela. Craig's card is shown to Craig. Angela's card is shown to Clare. Clare's card is shown to Clare. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether Angela 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 (Agenta 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":"Clare can now know that Angela can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Craig","Clare"],"index":51142,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982016087,"difficulty":0.0017983913}
{"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. Kathy's card is shown to Robert. Monique's card is shown to Robert. Robert's card is shown to Kathy. Kathy's card is shown to Kathy. Monique's card is shown to Kathy. Kathy's card is shown to Monique. Monique's card is shown to Monique. 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 Agentc: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:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Kathy","Monique"],"index":62793,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997263551,"difficulty":0.0002736449}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aaron's card is shown to Cheryl. Cheryl's card is shown to Aaron. Todd's card is shown to Aaron. Todd's card is shown to Todd. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cheryl can now know that Todd can know that Todd picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cheryl","Aaron","Todd"],"index":43098,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9820482731,"difficulty":0.0179517269}
{"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 Elizabeth. Evan's card is shown to Evan. Evan's card is shown to Joy. It is publicly announced that someone picked a red card. It is publicly announced that Evan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Evan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Evan","Joy"],"index":9838,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997970283,"difficulty":0.002029717}
{"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 Herman. Charles's card is shown to Charles. Judith's card is shown to Judith. 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:2 Agentc: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:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Charles can now know whether Herman can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herman","Charles","Judith"],"index":21738,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
{"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 Jeffrey. Jessica's card is shown to Jeffrey. Jessica's card is shown to Spencer. Jessica's card is shown to Elizabeth. Elizabeth's card is shown to Jessica. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessica can now know whether Elizabeth can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Spencer","Elizabeth","Jessica"],"index":3054,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8386368155,"difficulty":1.8386368155}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffery's card is shown to Mary. Mary's card is shown to Jeffery. Jeffery's card is shown to Jeffery. Sheldon's card is shown to Jeffery. Mary's card is shown to Sheldon. It is publicly announced that someone 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) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Jeffery","Sheldon"],"index":19160,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
{"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 James. James'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 Maria knows whether or not nobody 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":"Maria can now know that James can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Maria"],"index":51269,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999697566,"difficulty":0.000302434}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Joshua. Joshua's card is shown to Joshua. Mitchell's card is shown to Mitchell. It is publicly announced that someone picked a red card. It is publicly announced that Joshua picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Joshua can now know that Joshua picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cindy","Joshua","Mitchell"],"index":15778,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9195466042,"difficulty":0.0804533958}
{"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 Shannon. Cody's card is shown to Shannon. Mariann's card is shown to Lisa. Shannon's card is shown to Cody. Cody's card is shown to Mariann. 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) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lisa can now know whether Shannon can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shannon","Lisa","Cody","Mariann"],"index":18373,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997108579,"difficulty":0.0002891421}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Krista's card is shown to Gene. Krista's card is shown to Anna. Thomas's card is shown to Krista. Gene's card is shown to Thomas. Krista's card is shown to Thomas. 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.","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)) ] Agentd knows that (Agenta 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":"Thomas can now know that Gene can know whether Krista picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gene","Anna","Krista","Thomas"],"index":17010,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8488942981,"difficulty":0.1511057019}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Sherry. Jonathan's card is shown to David. Alice's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jonathan","Alice","Sherry","David"],"index":10648,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7276941538,"difficulty":1.7276941538}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olive's card is shown to Olive. Jospeh's card is shown to Olive. Olive's card is shown to Mattie. Jospeh's card is shown to Mattie. Jospeh's card is shown to Jospeh. 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) ] Agentc knows that (Agentb 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":"Jospeh can now know that Mattie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Olive","Mattie","Jospeh"],"index":13581,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984343648,"difficulty":0.0015656352}
{"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. Stephen's card is shown to Rachel. Rachel's card is shown to Rachel. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether Rachel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Stephen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephen","Rachel","Carolyn"],"index":13603,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Yvonne. Yvonne's card is shown to Yvonne. Anthony's card is shown to Carl. Yvonne's card is shown to Carl. Yvonne's card is shown to Jim. 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 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know whether Jim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Yvonne","Carl","Jim"],"index":39282,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9043669105,"difficulty":0.0956330895}
{"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 James. Jerry's card is shown to Jerry. James's card is shown to Robert. Jerry'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:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Jerry can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Jerry","Robert","Charles"],"index":17980,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.843547523,"difficulty":0.156452477}
{"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 Russell. Russell's card is shown to Christine. Russell's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Christine knows whether someone picked a red card. It is publicly announced that Russell does not know whether Travis picked a red card. It is publicly announced that Russell does not know whether Travis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Christine can now know that Russell picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Russell","Christine","Amy","Travis"],"index":49108,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786994457,"difficulty":0.0213005543}
{"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 David. Daniel's card is shown to David. Lillie's card is shown to David. David's card is shown to Rodney. It is publicly announced that someone picked a red card. It is publicly announced that Rodney does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rodney can now know whether Lillie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Rodney","Daniel","Lillie"],"index":16350,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5317273736,"difficulty":0.4682726264}
{"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 Shelia. Shelia's card is shown to Brenda. Paul's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether someone picked a red card. It is publicly announced that Paul picked a red card. It is publicly announced that Shelia knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Shelia can now know that Paul can know that Shelia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shelia","Paul","Brenda"],"index":22856,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.644996047,"difficulty":1.644996047}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cameron's card is shown to Cameron. Cameron's card is shown to Eleanor. Eleanor's card is shown to Eleanor. Paula's card is shown to Paula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eleanor can now know that Cameron picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cameron","Eleanor","Paula"],"index":23368,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979032278,"difficulty":0.0020967722}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Enrique. Enrique's card is shown to Lois. It is publicly announced that someone picked a red card. It is publicly announced that Enrique does not know whether Enrique picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lois can now know whether Enrique can know whether Lois picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Enrique","Lois"],"index":35204,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970781803,"difficulty":0.0029218197}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Scott. Kevin's card is shown to Scott. Scott's card is shown to Kevin. 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) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Scott can now know whether Kevin can know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Scott","Kevin"],"index":31046,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9935907125,"difficulty":0.0064092875}
{"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 Carl. Madison's card is shown to Madison. Marie's card is shown to Marie. 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) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Madison can now know whether Carl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carl","Madison","Marie"],"index":37804,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9246406555,"difficulty":0.0753593445}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yolanda's card is shown to Yolanda. David's card is shown to Yolanda. Yolanda'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 Yolanda knows whether David 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) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"David can now know that Yolanda can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Yolanda","David"],"index":25997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935905933,"difficulty":0.0064094067}
{"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 Lynn. Lynn's card is shown to Lynn. William's card is shown to James. Lynn'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 Lynn knows whether or not nobody picked a red card. It is publicly announced that William knows whether Lynn 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 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":"Lynn can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Lynn","James"],"index":51271,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6756027341,"difficulty":1.6756027341}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Lonnie. Donald's card is shown to Lonnie. Danielle's card is shown to Donald. Jody's card is shown to Donald. Donald's card is shown to Jody. 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:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Danielle can now know whether Lonnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lonnie","Danielle","Donald","Jody"],"index":65646,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.854802072,"difficulty":0.145197928}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Estela's card is shown to Estela. Eugene's card is shown to Estela. Jennifer's card is shown to Jennifer. Estela's card is shown to Eugene. Jennifer's card is shown to Eugene. It is publicly announced that someone picked a red card. It is publicly announced that Eugene does not know whether Eugene picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jennifer can now know whether Eugene can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Estela","Jennifer","Eugene"],"index":1390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9461049438,"difficulty":0.0538950562}
{"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. Sharon's card is shown to Barbara. Janice's card is shown to Barbara. Sharon's card is shown to Sharon. Janice's card is shown to Sharon. Sharon's card is shown to Jeff. Barbara's card is shown to Janice. Sharon's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Sharon","Jeff","Janice"],"index":67156,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997418046,"difficulty":0.002581954}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Samuel. Esther's card is shown to Samuel. Samuel's card is shown to Madeline. Samuel's card is shown to Esther. Esther's card is shown to Esther. 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) ] Agentc knows that (Agenta knows whether 3)","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":"Madeline can now know that Cheryl can know whether Madeline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Samuel","Madeline","Esther"],"index":20449,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8949557543,"difficulty":0.1050442457}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Ramona's card is shown to Ramona. It is publicly announced that someone picked a red card. It is publicly announced that Ramona 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) ] [ ! 2 ] [ ! (1&2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Ramona can now know that Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mark","Ramona"],"index":45206,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9966121316,"difficulty":0.0033878684}
{"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 Helen. Karissa's card is shown to Karissa. Joseph's card is shown to Karissa. Earl's card is shown to Joseph. Earl's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether Earl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Karissa can now know that Joseph can know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Karissa","Joseph","Earl"],"index":8538,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7044989467,"difficulty":1.7044989467}
{"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. Raymond's card is shown to Bernice. It is publicly announced that someone picked a red card. It is publicly announced that Bernice does not know whether Bernice 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Raymond can now know whether Bernice can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Bernice"],"index":7590,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996874332,"difficulty":0.0003125668}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacelyn's card is shown to Linda. Janice's card is shown to Janice. Isaac's card is shown to Janice. Jacelyn's card is shown to Janice. Janice's card is shown to Isaac. Isaac's card is shown to Jacelyn. It is publicly announced that someone picked a red card. It is publicly announced that Jacelyn 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|2|3|4)))","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":"Janice can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Janice","Isaac","Jacelyn"],"index":35008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979861975,"difficulty":0.0020138025}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. Daniel's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Brian knows whether or not nobody picked a red card. It is publicly announced that Brian knows whether Daniel 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 whether 1)","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":"Brian can now know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Daniel","Brian"],"index":56949,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5293607712,"difficulty":0.4706392288}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marge's card is shown to Marge. Jana's card is shown to Marge. Marge's card is shown to Clara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marge can now know that Clara can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marge","Clara","Jana"],"index":28471,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9830523729,"difficulty":0.0169476271}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Marvin. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card. It is publicly announced that Carmen does not know whether Marvin picked a red card. It is publicly announced that Marvin picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] 0","hypothesis":"Marvin can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marvin","Carmen"],"index":1550,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985266924,"difficulty":0.0014733076}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clayton's card is shown to Gregg. Clayton's card is shown to Clayton. Brandon's card is shown to Clayton. 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:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Gregg can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregg","Clayton","Brandon"],"index":54570,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983995557,"difficulty":0.0016004443}
{"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. Martha's card is shown to Melissa. James's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that Martha can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martha","James","Melissa"],"index":21107,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983567595,"difficulty":0.0016432405}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laraine's card is shown to Beatrice. Thelma's card is shown to Beatrice. Sandra's card is shown to Laraine. Sandra's card is shown to Thelma. Laraine's card is shown to Thelma. 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) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know whether Laraine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Beatrice","Laraine","Thelma"],"index":62326,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9900177121,"difficulty":0.0099822879}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kacie's card is shown to Kacie. Alexander's card is shown to Kacie. Eric's card is shown to Anthony. Eric's card is shown to Alexander. It is publicly announced that someone picked a red card. It is publicly announced that Kacie does not know whether Kacie picked a red card. It is publicly announced that Kacie does not know whether Anthony picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Eric can now know that Anthony can know that Alexander picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Kacie","Anthony","Alexander"],"index":33608,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9850357771,"difficulty":0.0149642229}
{"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. Donald's card is shown to Victoria. Frankie's card is shown to Victoria. Donald's card is shown to Elizabeth. Elizabeth's card is shown to Donald. Donald's card is shown to Donald. Victoria's card is shown to Frankie. Elizabeth's card is shown to Frankie. Frankie's card is shown to Frankie. 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:3 Agentc:2,3 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:2,3 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Elizabeth","Donald","Frankie"],"index":293,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976988435,"difficulty":0.0023011565}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to Craig. Connie's card is shown to Dorothy. Woodrow's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Connie does not know whether Craig picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Connie can now know whether Craig can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Craig","Connie","Dorothy","Woodrow"],"index":48869,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997037053,"difficulty":0.0002962947}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samantha's card is shown to Carolyn. Patricia's card is shown to Carolyn. Carolyn's card is shown to Edna. Samantha'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:2,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edna can now know whether Carolyn can know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Samantha","Edna","Patricia"],"index":2558,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986384511,"difficulty":0.0013615489}
{"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 Barbara. Barbara's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether or not everyone picked a red card. 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 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":"Eric can now know that Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Barbara","Eric"],"index":47676,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6763072014,"difficulty":0.3236927986}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Alexis. Alexis's card is shown to Cheryl. Cheryl's card is shown to Cheryl. 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) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Alexis can now know whether Cheryl can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alexis","Cheryl"],"index":29246,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marilyn's card is shown to Marilyn. Marilyn's card is shown to Tanna. David's card is shown to Tanna. Tanna's card is shown to Tanna. It is publicly announced that someone picked a red card. It is publicly announced that Marilyn does not know whether or not everyone 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 (1&2&3)) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether Marilyn can know that Tanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marilyn","David","Tanna"],"index":2049,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9699155092,"difficulty":0.0300844908}
{"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. Michael's card is shown to Christopher. Christopher's card is shown to Michael. Michael's card is shown to Michael. Ian's card is shown to Michael. Michael's card is shown to Ian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether Michael can know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Michael","Ian"],"index":66881,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7614784241,"difficulty":0.2385215759}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalie's card is shown to Rosalie. Rosalie'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 Patricia knows whether Patricia 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 (Agentb knows whether 2)","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":"Rosalie can now know that Patricia can know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rosalie","Patricia"],"index":64561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7544292808,"difficulty":0.2455707192}
{"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. Liliana's card is shown to James. James's card is shown to Liliana. Liliana's card is shown to Liliana. Myron's card is shown to Liliana. Myron's card is shown to Lawrence. James's card is shown to Myron. Lawrence's card is shown to Myron. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Lawrence can know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Liliana","Lawrence","Myron"],"index":35118,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6065781116,"difficulty":0.3934218884}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cinda's card is shown to Cinda. Elizabeth's card is shown to Cinda. Thomas's card is shown to Cinda. Cinda's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Cinda'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:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cinda can now know that Elizabeth can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Cinda","Elizabeth","Thomas"],"index":38301,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pearl's card is shown to Pearl. Pearl's card is shown to Joshua. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Pearl knows whether someone picked a red card. It is publicly announced that Pearl does not know whether Joshua 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) ] (Agenta 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|2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Pearl can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Pearl","Joshua"],"index":901,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Franklin. Corey's card is shown to Bonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bonnie can now know that Corey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Franklin","Bonnie","Corey"],"index":28989,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984049201,"difficulty":0.0015950799}
{"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 Jeremy. Jeremy's card is shown to Darrell. Christina's card is shown to Darrell. Darrell's card is shown to Christina. Gonzalo's card is shown to Christina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2,4 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:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darrell can now know whether Gonzalo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeremy","Darrell","Christina","Gonzalo"],"index":7356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7722993493,"difficulty":0.2277006507}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Ora. Ora's card is shown to Cesar. Dorothy's card is shown to Cesar. Ora's card is shown to Dorothy. 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:1 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:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sherry can now know whether Cesar can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ora","Sherry","Cesar","Dorothy"],"index":33792,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8966835141,"difficulty":1.8966835141}
{"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 Sabina. Rene's card is shown to Rene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Sabina can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sabina","William","Rene"],"index":59264,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995469451,"difficulty":0.0004530549}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Marjorie. Marjorie's card is shown to Jean. Jean's card is shown to Jean. Marjorie's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jean can now know whether Marjorie can know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marjorie","Jean","Elizabeth"],"index":57917,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982964396,"difficulty":0.0017035604}
{"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 Wendy. Jennifer's card is shown to Wendy. Mary's card is shown to Christopher. Christopher's card is shown to Mary. Jennifer's card is shown to Mary. Christopher's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Mary picked a red card. It is publicly announced that Christopher knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Wendy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wendy","Christopher","Mary","Jennifer"],"index":21964,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998472631,"difficulty":0.001527369}
{"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. Yvonne's card is shown to Dorothy. Dorothy's card is shown to Yvonne. It is publicly announced that someone picked a red card. It is publicly announced that Yvonne 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 whether (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":"Yvonne can now know that Dorothy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Yvonne"],"index":41195,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
{"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. Clifton's card is shown to Craig. Suzi's card is shown to Craig. Timothy's card is shown to Clifton. Timothy's card is shown to Suzi. Suzi's card is shown to Suzi. 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|2|3|4))","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":"Clifton can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Craig","Clifton","Timothy","Suzi"],"index":65236,"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). Lillian's card is shown to Beatrice. Patsy's card is shown to Patsy. Beatrice's card is shown to Lillian. It is publicly announced that someone picked a red card. It is publicly announced that Lillian does not know whether Lillian 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 whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Beatrice can now know that Lillian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Beatrice","Patsy","Lillian"],"index":56825,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954571724,"difficulty":0.0045428276}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Benito's card is shown to Anita. Joshua's card is shown to John. Joshua's card is shown to Joshua. Anita's card is shown to Benito. John's card is shown to Benito. 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.","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)) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Benito can now know that Joshua can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anita","John","Joshua","Benito"],"index":49612,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997714162,"difficulty":0.0002285838}
{"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. Mary's card is shown to Robert. Robert's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Shannon can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Robert","Shannon","Cynthia"],"index":43579,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.973050952,"difficulty":0.026949048}
{"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 Donald. Raymond's card is shown to Raymond. 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 whether 3)","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":"Donald can now know whether Alexis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Raymond","Alexis"],"index":51945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8942732811,"difficulty":0.1057267189}
{"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 John. John's card is shown to Jeffrey. John's card is shown to Doris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 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:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Doris can now know that Jeffrey can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Jeffrey","Doris"],"index":4742,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984331727,"difficulty":0.0015668273}
{"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 Danny. Janice's card is shown to Danny. Danny's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Danny's card is shown to Mario. Danny's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mario can now know whether Danny can know whether Mario picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danny","Carolyn","Mario","Janice"],"index":9899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997721374,"difficulty":0.002278626}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samantha's card is shown to Dan. John's card is shown to Janet. Samantha's card is shown to Samantha. 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 that 4)","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":"Dan can now know that Samantha can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dan","Janet","Samantha","John"],"index":23424,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980911613,"difficulty":0.0019088387}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Imelda's card is shown to Jacques. Imelda's card is shown to Imelda. Jesus's card is shown to Imelda. Imelda's card is shown to Jesus. 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) ] (Agenta knows that (1|2|3|4))","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":"Jacques can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacques","Frank","Imelda","Jesus"],"index":18465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997710586,"difficulty":0.0002289414}
{"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 Juliette. Juliette's card is shown to Marie. Marie's card is shown to William. Joseph's card is shown to William. William's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Marie knows whether Juliette 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) ] (Agenta 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":"Juliette can now know that Marie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Juliette","Marie","William","Joseph"],"index":7452,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969305396,"difficulty":0.0030694604}
{"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 Connie. Barbara's card is shown to Connie. Connie'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 Connie knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 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:2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Irvin can now know that Connie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Irvin","Connie","Barbara"],"index":52109,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986114502,"difficulty":0.0013885498}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Kim. Renee's card is shown to Kim. Kim's card is shown to Renee. 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) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Renee can now know that Kim can know whether Renee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kim","Renee"],"index":16212,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8366023898,"difficulty":1.8366023898}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brooke's card is shown to Brooke. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Brooke picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that Brooke can know whether Brooke picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brooke","Robert"],"index":59646,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9927152991,"difficulty":0.0072847009}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sammie's card is shown to David. Tracy's card is shown to Sammie. John's card is shown to Sammie. Sammie's card is shown to Tracy. 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:2 Agentb:3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tracy can now know whether David can know whether Sammie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Sammie","Tracy","John"],"index":60874,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989142418,"difficulty":0.0010857582}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnetta's card is shown to Tammy. Lisa's card is shown to Tammy. Johnetta's card is shown to Johnetta. Lisa's card is shown to Johnetta. Lisa's card is shown to Lisa. Anna's card is shown to Lisa. Anna's card is shown to Anna. 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 everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (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:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Johnetta can now know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tammy","Johnetta","Lisa","Anna"],"index":29035,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9783859849,"difficulty":0.0216140151}
{"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 John. Christopher's card is shown to Christopher. 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) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Christopher can now know whether John can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Christopher"],"index":61709,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.877900064,"difficulty":0.122099936}
{"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 Gary. Gary's card is shown to Valerie. Melvin's card is shown to Helen. Gary's card is shown to Melvin. Helen's card is shown to Melvin. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card. It is publicly announced that Gary picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Helen can now know that Valerie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Valerie","Helen","Melvin"],"index":46288,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7872343659,"difficulty":0.2127656341}
{"premise":"There are two 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 Paul. Paul's card is shown to Paul. 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)) ] (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&2)) ] 0","hypothesis":"Bruce can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bruce","Paul"],"index":13278,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984930754,"difficulty":0.0015069246}
{"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. Pablo's card is shown to Douglas. Dale's card is shown to Pablo. Pablo's card is shown to Pablo. 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:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Douglas can now know whether Pablo can know whether Dale picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dale","Douglas","Pablo"],"index":49685,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982275367,"difficulty":0.0017724633}
{"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 Veronica. Frances's card is shown to Norman. Norman's card is shown to Len. Veronica's card is shown to Frances. 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:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Veronica can now know whether Len picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Veronica","Norman","Len","Frances"],"index":18456,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9414410591,"difficulty":0.0585589409}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. John's card is shown to Anthony. Gregory's card is shown to Anthony. John's card is shown to Jose. Gregory's card is shown to Jose. John's card is shown to John. Gregory's card is shown to John. Anthony's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Jose knows whether or not everyone picked a red card. It is publicly announced that Gregory picked a black card. It is publicly announced that Anthony picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Anthony can now know that John can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Jose","John","Gregory"],"index":15928,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8031829596,"difficulty":0.1968170404}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Thomas's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Thomas knows whether someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card. It is publicly announced that Thomas does not know whether or not everyone picked a red card. It is publicly announced that 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)","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":"Joseph can now know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thomas","Joseph"],"index":42430,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.77985394,"difficulty":0.22014606}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Royal. Royal's card is shown to Frances. It is publicly announced that someone picked a red card. It is publicly announced that Royal does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Frances can now know whether Royal can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Royal","Frances"],"index":18389,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.994099021,"difficulty":0.005900979}
{"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 Orlando. Orlando's card is shown to Glen. Glen's card is shown to Glen. Jesus's card is shown to Glen. Thomas's card is shown to Glen. Glen's card is shown to Jesus. Orlando's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Jesus does not know whether Orlando picked a red card. It is publicly announced that Orlando knows whether 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:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Orlando can now know whether Glen can know that Glen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Orlando","Glen","Jesus","Thomas"],"index":51006,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8918110132,"difficulty":1.8918110132}
{"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 Michael. Michael's card is shown to Edith. Barbara's card is shown to Mary. Michael's card is shown to Barbara. Edith's card is shown to Barbara. Barbara'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:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Edith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Edith","Mary","Barbara"],"index":50511,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7629131079,"difficulty":0.2370868921}
{"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 Christopher. Debra's card is shown to Debra. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc: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 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Debra can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Debra","Richard"],"index":67079,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983065128,"difficulty":0.0016934872}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Mary. Alejandra's card is shown to Alejandra. Susan's card is shown to Susan. 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 Susan 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:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Alejandra","Susan"],"index":40442,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9481422305,"difficulty":1.9481422305}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Sherry. Sherry's card is shown to Maurice. 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 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 whether (Agenta knows that (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":"Maurice can now know whether Sherry can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sherry","Maurice"],"index":29603,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997677207,"difficulty":0.0002322793}
{"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 Elizabeth. Elizabeth's card is shown to Sue. Sue's card is shown to Sue. Elizabeth'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:3 Agentb:1,2 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:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know that Sue can know that Sue picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","Sue","Michael"],"index":1047,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949285984,"difficulty":0.0050714016}
{"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 Herman. Herman's card is shown to Jerry. Jerry's card is shown to Jerry. Herman's card is shown to James. Jerry'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:1,2 Agentc:1,2 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:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know whether Jesus picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Herman","Jerry","Jesus","James"],"index":56950,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.856844306,"difficulty":0.143155694}
{"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 Evelyn. Evelyn's card is shown to John. Amy's card is shown to John. Vivian's card is shown to Vivian. John's card is shown to Amy. 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 that (1&2&3&4))","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":"Vivian can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","John","Vivian","Amy"],"index":17487,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985175729,"difficulty":0.0014824271}
{"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 Crystal. Crystal's card is shown to Joe. John's card is shown to Joe. Crystal'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 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joe can now know that John can know whether Crystal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Joe","John"],"index":31903,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5776020288,"difficulty":1.5776020288}
{"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 Michael. Margaret's card is shown to Aaron. Aaron'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:2 Agentb: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 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Charles can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Charles","Margaret","Aaron"],"index":47296,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997121692,"difficulty":0.0002878308}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracie's card is shown to Tracie. Scott's card is shown to Roberto. Roberto's card is shown to Scott. Scott's card is shown to Scott. 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) ] Agentc knows whether (Agenta knows whether 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":"Scott can now know whether Tracie can know whether Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracie","Roberto","Scott"],"index":58174,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982103109,"difficulty":0.0017896891}
{"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 Sharon. Sharon'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 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sharon can now know that John can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","John","James"],"index":28517,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983631968,"difficulty":0.0016368032}
{"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 Ronald. Ronald's card is shown to Brooke. Raymond's card is shown to Brooke. Cleo's card is shown to Cleo. Raymond's card is shown to Cleo. 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:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know whether Brooke can know that Raymond picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Brooke","Cleo","Raymond"],"index":27580,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.886687696,"difficulty":1.886687696}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandi's card is shown to Carol. Karisa's card is shown to Carol. Carolyn's card is shown to Carol. Carolyn's card is shown to Brandi. Carol's card is shown to Karisa. Karisa's card is shown to Carolyn. 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:1 Agentd: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:2,3,4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Brandi can know whether Karisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Brandi","Karisa","Carolyn"],"index":30254,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6032894254,"difficulty":0.3967105746}
{"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 Heather. Elda's card is shown to Elda. Heather's card is shown to Allen. It is publicly announced that someone picked a red card. It is publicly announced that Heather picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Allen can now know that Elda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Heather","Elda","Allen","Mark"],"index":46395,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9514104724,"difficulty":0.0485895276}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilfred's card is shown to James. James's card is shown to James. Foster's card is shown to Stanley. Wilfred's card is shown to Foster. James's card is shown to Foster. 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:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilfred can now know that Stanley can know that Wilfred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wilfred","James","Stanley","Foster"],"index":53679,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956464171,"difficulty":0.0043535829}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danika's card is shown to Brandon. Danika's card is shown to Danika. Rogelio's card is shown to Allen. Brandon's card is shown to Rogelio. 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:4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rogelio can now know whether Brandon can know that Allen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandon","Danika","Allen","Rogelio"],"index":25385,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8469743133,"difficulty":0.1530256867}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annette's card is shown to Annette. Stephen's card is shown to Annette. Annette's card is shown to David. Susannah's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Annette does not know whether David picked a red card. It is publicly announced that David does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Susannah can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Annette","Susannah","David","Stephen"],"index":55879,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986067414,"difficulty":0.0013932586}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Jeremy. James's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether John 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 that (~(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":"Jeremy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeremy","James","John"],"index":15615,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984402061,"difficulty":0.0015597939}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Sharon. Sharon's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether Rosa 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 whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Sharon can now know whether Rosa can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosa","Sharon","Gary"],"index":17949,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5634890199,"difficulty":1.5634890199}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Renita's card is shown to Renita. Barbara's card is shown to Renita. Renita'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 Barbara knows whether or not nobody picked a red card. It is publicly announced that Barbara 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))) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 2 ] 0","hypothesis":"Renita can now know whether Barbara can know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Renita","Barbara"],"index":13874,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9965002537,"difficulty":0.0034997463}
{"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 Ruben. Sara's card is shown to Ruben. Don's card is shown to Don. Sara's card is shown to Don. Ruben's card is shown to Sara. Sara's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ruben can now know whether Don can know whether Don picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruben","Don","Sara"],"index":60051,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9949382544,"difficulty":0.0050617456}
{"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 Alton. Denny's card is shown to Richard. It is publicly announced that someone 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:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 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:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Maria can now know that Alton can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alton","Maria","Richard","Denny"],"index":18512,"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). Nicholas's card is shown to Melissa. Leila's card is shown to Melissa. Leila's card is shown to Nicholas. 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) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Melissa can now know whether Melissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melissa","Nicholas","Leila"],"index":51395,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.671191752,"difficulty":0.328808248}
{"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 Marie. Alexandria'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 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marie can now know that Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Anthony","Alexandria","Paul"],"index":21066,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979779124,"difficulty":0.0020220876}
{"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 Selena. Selena's card is shown to Nancy. 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 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that Selena can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Selena","Nancy","Mary"],"index":4519,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999776423,"difficulty":0.000223577}
{"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 Louise. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Louise can now know whether Mark can know that Lester picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Louise","Lester"],"index":53052,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9833292961,"difficulty":0.0166707039}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. Miguel's card is shown to Curtis. Kay's card is shown to Curtis. Curtis's card is shown to Kay. Kay's card is shown to Kay. 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 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Curtis can now know whether Miguel can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Curtis","Miguel","Kay"],"index":9198,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9916759729,"difficulty":0.0083240271}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adriana's card is shown to Jacqueline. Julie's card is shown to Jacqueline. Julie's card is shown to Sandy. Jacqueline's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Jacqueline 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)) ] (Agentb knows whether 2)","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":"Jacqueline can now know whether Jacqueline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adriana","Jacqueline","Sandy","Julie"],"index":63765,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9948164821,"difficulty":1.9948164821}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willis's card is shown to Linda. Kyle's card is shown to Linda. Willis's card is shown to Jason. Jason's card is shown to Jason. Jason's card is shown to Kyle. Kyle's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that Willis 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 that (1&2&3&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":"Willis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Willis","Jason","Kyle"],"index":8912,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9942212105,"difficulty":0.0057787895}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Gregory knows 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:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Gregory can now know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gregory","William"],"index":22897,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8983597755,"difficulty":1.8983597755}
{"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 Scott. Teresa's card is shown to Betty. James's card is shown to Teresa. Teresa'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:3 Agentb:3 Agentc:4 Agentd: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:3 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Teresa can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Scott","Betty","Teresa","James"],"index":51211,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997215867,"difficulty":0.0002784133}
{"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. Christine's card is shown to Edgar. Richard's card is shown to Richard. Richard's card is shown to James. Christine's card is shown to James. Christine's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Edgar 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:1,4 Agentb:2 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know whether Richard can know that Edgar picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edgar","Richard","James","Christine"],"index":11823,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9356552958,"difficulty":0.0643447042}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helene's card is shown to Helene. Michael's card is shown to Michael. Michael's card is shown to Amanda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc: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 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helene","Tanya","Michael","Amanda"],"index":27864,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997214675,"difficulty":0.0002785325}
{"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. Brian's card is shown to Mary. Joseph's card is shown to Mary. Mary's card is shown to Tracy. 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) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know whether Mary can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Joseph","Mary","Tracy"],"index":67247,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995889068,"difficulty":0.0004110932}
{"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 Esther. Kathy's card is shown to Esther. Sadie's card is shown to Sadie. Kathy's card is shown to Sadie. Esther's card is shown to Danny. Sadie's card is shown to Kathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 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:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sadie can now know that Kathy can know whether Esther picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Esther","Sadie","Danny","Kathy"],"index":21872,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6756051183,"difficulty":0.3243948817}
{"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 Micheal. Jesse's card is shown to Robert. Jesse's card is shown to Jesse. 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.","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)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Micheal can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Micheal","Robert","Jesse"],"index":17850,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978823066,"difficulty":0.0021176934}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glenn's card is shown to Glenn. Inga's card is shown to Glenn. Inga's card is shown to Mable. Inga's card is shown to Inga. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Inga can now know that Mable picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glenn","Mable","Inga"],"index":60112,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982631803,"difficulty":0.0017368197}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jody's card is shown to Jody. 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 Jody 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:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"William can now know whether Jody can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jody","William"],"index":52726,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9942147136,"difficulty":0.0057852864}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ali's card is shown to Patricia. Ronnie's card is shown to Mary. Ali's card is shown to Mary. Ali's card is shown to Ronnie. Ronnie's card is shown to Ali. 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) ] (Agenta knows that (1&2&3&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":"Patricia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Mary","Ronnie","Ali"],"index":30856,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985192418,"difficulty":0.0014807582}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Laura. Laura's card is shown to Jonathan. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan knows whether Jonathan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jonathan can now know that Laura picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Laura","Jonathan"],"index":64639,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99590379,"difficulty":0.00409621}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lula's card is shown to Elsy. Janet's card is shown to Elsy. Lula's card is shown to Lula. Harold's card is shown to Lula. Janet's card is shown to Harold. Harold's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Lula picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agenta knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Elsy can now know that Janet can know whether Elsy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elsy","Lula","Harold","Janet"],"index":61512,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9182085395,"difficulty":0.0817914605}
{"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 Ruth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that Ruth can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Ruth","Dessie"],"index":28016,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997702241,"difficulty":0.0002297759}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Charles. Albert's card is shown to Albert. Albert'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 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether Charles can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Albert","Joseph"],"index":48837,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6459270716,"difficulty":1.6459270716}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brett's card is shown to Robin. Regina's card is shown to Robin. Robin's card is shown to Brett. Regina's card is shown to Brett. Regina's card is shown to Homer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 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:2,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robin can now know whether Regina can know whether Homer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Brett","Regina","Homer"],"index":40121,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985521436,"difficulty":0.0014478564}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mindy's card is shown to Mindy. William's card is shown to William. Eric's card is shown to William. Eric's card is shown to Eric. Mindy's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 3)","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":"Robert can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mindy","William","Eric","Robert"],"index":6163,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7314906716,"difficulty":1.7314906716}
{"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 David. David'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 Michael knows whether Michael picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Michael"],"index":45664,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952716231,"difficulty":0.0047283769}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to Ben. Andrew's card is shown to Ben. Cheryl's card is shown to Cheryl. Cheryl's card is shown to Jesus. Jesus's card is shown to Jesus. Andrew's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Jesus knows whether Jesus picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ben can now know that Jesus picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ben","Cheryl","Jesus","Andrew"],"index":47901,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9926233292,"difficulty":0.0073766708}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristi's card is shown to Jackie. Gary's card is shown to Jackie. Jackie's card is shown to Kristi. Kristi's card is shown to Kristi. Gary's card is shown to Kristi. Jackie's card is shown to Gary. Raymond's card is shown to Gary. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Raymond does not know whether Gary picked a red card. It is publicly announced that Raymond does not know whether Kristi picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Gary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jackie","Kristi","Gary","Raymond"],"index":63897,"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). Bruce's card is shown to Pamela. Jefferson's card is shown to Pamela. Vito's card is shown to Pamela. Pamela's card is shown to Jefferson. Jefferson's card is shown to Jefferson. Jefferson's card is shown to Vito. 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) ] (Agentb knows that 2)","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":"Bruce can now know that Bruce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pamela","Bruce","Jefferson","Vito"],"index":37796,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974927902,"difficulty":0.0025072098}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanna's card is shown to Joanna. Donald's card is shown to Joanna. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether Joanna picked a red card. It is publicly announced that Donald does not know whether or not everyone 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Donald can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joanna","Donald"],"index":34365,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delilah's card is shown to Carole. Carole's card is shown to Delilah. Richard's card is shown to Delilah. Howard's card is shown to Howard. Richard's card is shown to Howard. Carole's card is shown to Richard. Howard's card is shown to Richard. 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 Agentb:1,4 Agentc:3,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Howard can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carole","Delilah","Howard","Richard"],"index":45967,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9859653711,"difficulty":0.0140346289}
{"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 Vincent. It is publicly announced that someone picked a red card. It is publicly announced that Vincent picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Vincent can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vincent","John"],"index":14106,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6373462081,"difficulty":1.6373462081}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lowell's card is shown to Anna. Anna's card is shown to Lowell. Joseph's card is shown to Lowell. Joseph'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 Anna 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 (1&2&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":"Lowell can now know whether Joseph can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anna","Lowell","Joseph"],"index":12755,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9960091114,"difficulty":0.0039908886}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Amy's card is shown to Robert. Amy's card is shown to Alfonso. Robert's card is shown to Donovan. It is publicly announced that someone picked a red card. It is publicly announced that Alfonso does not know whether Alfonso picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Donovan can now know whether Amy can know whether Amy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amy","Robert","Alfonso","Donovan"],"index":49847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9947675467,"difficulty":0.0052324533}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chanda's card is shown to Robert. Jose's card is shown to Karl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Karl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Jose","Karl","Chanda"],"index":2050,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985132813,"difficulty":0.0014867187}
{"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 Clara. John's card is shown to Clara. Cory's card is shown to Cory. Clara's card is shown to John. Louis's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Cory picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Cory can now know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clara","Cory","Louis","John"],"index":55492,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7247586846,"difficulty":1.7247586846}
{"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 Pamela. Pamela's card is shown to Christopher. Irma's card is shown to Christopher. Christopher's card is shown to Irma. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card. It is publicly announced that Irma does not know whether Pamela picked a red card. It is publicly announced that Pamela does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Irma can now know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pamela","Christopher","Irma"],"index":36808,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6103951335,"difficulty":0.3896048665}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Percy. Ola's card is shown to Carl. 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:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Carl can now know that Carl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Percy","Carl","Charles","Ola"],"index":8743,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8625539541,"difficulty":0.1374460459}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maxine's card is shown to Lacy. Lacy's card is shown to Wilma. Maxine's card is shown to Paula. It is publicly announced that someone picked a red card. It is publicly announced that Lacy picked a red card. It is publicly announced that Lacy does not know whether Wilma picked a red card. It is publicly announced that Wilma does not know whether Paula picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Wilma can now know whether Lacy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maxine","Lacy","Wilma","Paula"],"index":50410,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachel's card is shown to Kendall. Rachel's card is shown to Rachel. Robert's card is shown to Rachel. 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:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Rachel can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kendall","Rachel","Robert"],"index":30087,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985773563,"difficulty":0.0014226437}
{"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 Carlene. Scott's card is shown to Scott. Tina's card is shown to Scott. Scott's card is shown to Tina. Tina's card is shown to Tina. It is publicly announced that someone picked a red card. It is publicly announced that Tina picked a red card. It is publicly announced that Tina does not know whether Carlene picked a red card. It is publicly announced that Tina 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) ] (Agentc 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":"Tina can now know that Scott picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carlene","Scott","Tina"],"index":59279,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.573720634,"difficulty":0.426279366}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynette's card is shown to Alma. Christopher's card is shown to Alma. Alma's card is shown to Lynette. Alma'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 Lynette picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Christopher can now know whether Lynette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alma","Lynette","Christopher"],"index":13352,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8028267026,"difficulty":0.1971732974}
{"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 Michael. Michael's card is shown to Yvonne. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Nellie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Yvonne can now know that Michael can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Yvonne","Elizabeth","Nellie"],"index":15433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982084036,"difficulty":0.0017915964}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Greg's card is shown to Greg. Shirley's card is shown to Greg. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Greg can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Greg","Shirley"],"index":67684,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997208714,"difficulty":0.0002791286}
{"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. Dianna's card is shown to Dianna. Sulema's card is shown to Bonnie. Bonnie's card is shown to Bonnie. 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) ] (Agentc 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":"Dianna can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sulema","Sara","Dianna","Bonnie"],"index":67651,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Patrick. Michael's card is shown to Patrick. Patrick's card is shown to Suzanne. Suzanne's card is shown to Suzanne. Patrick'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:1,3 Agentb:1,2 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:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 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":["Patrick","Suzanne","Michael"],"index":58458,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997273088,"difficulty":0.0002726912}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether Jeffrey picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jeffrey can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jeffrey","Larry"],"index":22080,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9064131379,"difficulty":0.0935868621}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. 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 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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Frank","Patricia","Chris"],"index":61651,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997695088,"difficulty":0.0002304912}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. 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 whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Charles can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Robert"],"index":35471,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9971691966,"difficulty":0.0028308034}
{"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 Joan. Margaret's card is shown to Joan. Jason's card is shown to Jason. Jason's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether Joan 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 whether 1) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Margaret can now know that Joan can know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joan","Jason","Margaret"],"index":37704,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9393963218,"difficulty":1.9393963218}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dixie's card is shown to Mark. Randall's card is shown to Mark. Randall's card is shown to Randall. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dixie can now know whether Mark can know that Randall picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dixie","Mark","Randall"],"index":16668,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9383004904,"difficulty":0.0616995096}
{"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 Diane. Joseph's card is shown to Ruth. Richard's card is shown to Ruth. Diane's card is shown to Joseph. Ruth's card is shown to Joseph. Ruth's card is shown to Richard. Joseph'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 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 2)","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":"Diane can now know whether Ruth can know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Diane","Ruth","Joseph","Richard"],"index":18576,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8817247152,"difficulty":0.1182752848}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jewel's card is shown to Beverly. Don's card is shown to Don. Beverly's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Don picked a red card. It is publicly announced that Jewel knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Jewel can now know whether Beverly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jewel","Beverly","Don","Mary"],"index":49646,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6442716122,"difficulty":1.6442716122}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Dorris's card is shown to Angela. Darryl's card is shown to Dorris. Darryl's card is shown to Darryl. Darryl's card is shown to Violet. It is publicly announced that someone picked a red card. It is publicly announced that Darryl picked a red card. It is publicly announced that Angela picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(1) ] (Agenta knows that 1)","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":"Angela can now know that Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Dorris","Darryl","Violet"],"index":50142,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5390664339,"difficulty":0.4609335661}
{"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 Tonya. Tonya's card is shown to Glen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Tonya can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tonya","Mary","Jonathan","Glen"],"index":65934,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9447656274,"difficulty":0.0552343726}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rick's card is shown to Tyrone. Lydia's card is shown to Tyrone. Tyrone's card is shown to Leon. Lydia'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:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tyrone can now know that Rick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tyrone","Rick","Lydia","Leon"],"index":30724,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982333183,"difficulty":0.0017666817}
{"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 Regina. Janice's card is shown to Janice. Harvey's card is shown to Janice. Elizabeth's card is shown to Harvey. Janice's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Regina","Janice","Harvey","Elizabeth"],"index":19051,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997714162,"difficulty":0.0002285838}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandy's card is shown to Sandy. Curtis's card is shown to Lauren. It is publicly announced that someone picked a red card. It is publicly announced that Sandy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Curtis can now know that Sandy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Curtis","Sandy","Lauren"],"index":14704,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6633756757,"difficulty":0.3366243243}
{"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 Paul. It is publicly announced that someone picked a red card. It is publicly announced that Paul does not know whether Paul 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|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Paul"],"index":9464,"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). Erika's card is shown to Erika. Bessie's card is shown to Erika. Erika's card is shown to Michael. Michael's card is shown to Michael. Thomas's card is shown to Thomas. Bessie's card is shown to Thomas. Erika's card is shown to Bessie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3,4 Agentd:1 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:1,4 Agentb:1,2 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Erika can now know that Michael can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Erika","Michael","Thomas","Bessie"],"index":3255,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997158647,"difficulty":0.0002841353}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmie's card is shown to Jimmie. Larry's card is shown to Larry. 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 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Larry can now know whether Jimmie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jimmie","Larry"],"index":9169,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Joan picked a red card. It is publicly announced that Joan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] 0","hypothesis":"Joan can now know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joan","Barbara"],"index":49794,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6317077875,"difficulty":1.6317077875}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Audrey's card is shown to Audrey. Charlotte's card is shown to Howard. Earl's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Charlotte does not know whether or not everyone picked a red card. It is publicly announced that Earl 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 ] (Agenta knows that 2)","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":"Audrey can now know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Audrey","Charlotte","Howard","Earl"],"index":9930,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6028549075,"difficulty":1.6028549075}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Ronald. Anthony's card is shown to Ronald. Ronald's card is shown to Judith. Anthony's card is shown to Judith. Ronald's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether or not everyone picked a red card. 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) ] Agentb knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Judith can now know that Anthony can know whether Judith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Judith","Anthony"],"index":51751,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8505958915,"difficulty":1.8505958915}
{"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. Robert's card is shown to Elaine. It is publicly announced that someone picked a red card. It is publicly announced that Elaine does not know whether Elaine picked a red card. It is publicly announced that Elaine 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 (Agenta knows whether (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":"Elaine can now know that Robert can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Elaine"],"index":15844,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8872141242,"difficulty":0.1127858758}
{"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. Cecil's card is shown to Therese. Daniel's card is shown to Cecil. It is publicly announced that someone picked a red card. It is publicly announced that Daniel 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 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Therese can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daniel","Therese","Cecil","Elizabeth"],"index":24613,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7979804873,"difficulty":0.2020195127}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenny's card is shown to Anna. Kenny's card is shown to Kenny. 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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Kenny can now know whether Anna can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anna","Kenny"],"index":9344,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9750316739,"difficulty":0.0249683261}
{"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 Joan. Steven's card is shown to Steven. Joan's card is shown to Neal. Steven's card is shown to Neal. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc: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:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know that Joan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joan","Steven","Neal"],"index":36445,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980011582,"difficulty":0.0019988418}
{"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. Abigail's card is shown to Abigail. Julie's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Julie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Abigail can now know whether Julie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Abigail","Julie"],"index":29766,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Laura. Patricia's card is shown to Stanley. Jamie's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Patricia can now know that Laura picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Stanley","Patricia","Jamie"],"index":9806,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958945513,"difficulty":0.0041054487}
{"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 Mark. Mark's card is shown to Jill. Virginia's card is shown to Virginia. It is publicly announced that someone 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 that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Virginia can now know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Jill","Virginia"],"index":251,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977655411,"difficulty":0.0022344589}
{"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. Shelby's card is shown to Carol. Robert's card is shown to Carol. Gregory's card is shown to Shelby. Shelby's card is shown to Shelby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Carol can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Carol","Shelby","Robert"],"index":64437,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997753501,"difficulty":0.0002246499}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonell's card is shown to Jonell. Jennifer's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Jonell picked a red card. It is publicly announced that Jonell knows whether or not nobody picked a red card. It is publicly announced that Jonell 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) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jennifer can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonell","Jennifer","Lawrence"],"index":53240,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
{"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 David. Jane's card is shown to Robert. David'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 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 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:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jane can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Robert","Jane"],"index":64378,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997702241,"difficulty":0.0002297759}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Katherine. Katherine's card is shown to Judy. Edna's card is shown to Judy. Katherine's card is shown to Edna. 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 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Edna can now know that Katherine can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katherine","Judy","Edna"],"index":66836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997153878,"difficulty":0.0002846122}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucas's card is shown to William. William's card is shown to Lucas. Lucas's card is shown to Lucas. Donna's card is shown to Lucas. Lucas's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Lucas can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Lucas","Donna"],"index":29670,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7835858464,"difficulty":1.7835858464}
{"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 Barbara. Nathan's card is shown to Nathan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 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:2 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barbara","David","Margie","Nathan"],"index":7710,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997614026,"difficulty":0.0002385974}
{"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. Blanche's card is shown to Laura. Laura's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 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 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Blanche can now know that Laura picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Blanche","Laura"],"index":38321,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983248115,"difficulty":0.0016751885}
{"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 Mary. Brian's card is shown to Mary. Peter's card is shown to Mignon. Mary's card is shown to Peter. Brian's card is shown to Peter. Mary's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Mignon does not know whether Brian 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) ] (Agentd knows that 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":"Brian can now know that Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Mignon","Peter","Brian"],"index":27634,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9466736913,"difficulty":0.0533263087}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Billy. Michael's card is shown to Billy. Billy's card is shown to Michael. Billy's card is shown to Kirk. It is publicly announced that someone picked a red card. It is publicly announced that Kirk knows whether Billy 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) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Billy can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","Michael","Kirk","Faith"],"index":67026,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8974481821,"difficulty":1.8974481821}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cliff's card is shown to Brian. Brian's card is shown to Cliff. It is publicly announced that someone picked a red card. It is publicly announced that Brian knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Brian can now know whether Cliff picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brian","Cliff"],"index":61027,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9101877809,"difficulty":1.9101877809}
{"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 Roger. John's card is shown to Donald. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know whether Roger picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roger","Donald","John"],"index":13555,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9250535965,"difficulty":0.0749464035}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Peter. Catherine's card is shown to Lois. Nadine's card is shown to Nadine. Catherine's card is shown to Nadine. 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) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nadine can now know whether Lois can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Lois","Nadine","Catherine"],"index":19878,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9164472222,"difficulty":1.9164472222}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeff's card is shown to Joy. Patrick's card is shown to Patrick. Patrick's card is shown to Jeff. It is publicly announced that someone picked a red card. It is publicly announced that Patrick picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Joy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joy","Patrick","Jeff"],"index":12063,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984995127,"difficulty":0.0015004873}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holly's card is shown to Kristal. Carlota's card is shown to Carlota. Carlota's card is shown to Holly. It is publicly announced that someone picked a red card. It is publicly announced that Kristal does not know whether Kristal picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 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 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kristal can now know that Holly can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kristal","Carlota","Holly"],"index":54457,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981003404,"difficulty":0.0018996596}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Crystal's card is shown to Michael. Marlene's card is shown to Marlene. It is publicly announced that someone picked a red card. It is publicly announced that Marlene picked a red card. It is publicly announced that Michael does not know whether Michael picked a red card. It is publicly announced that everyone 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:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3) ] [ ! (1&2&3) ] 0","hypothesis":"Michael can now know that Crystal can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Crystal","Michael","Marlene"],"index":1995,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9907994866,"difficulty":0.0092005134}
{"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 Larry. Mark's card is shown to Barbara. Barbara'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 Agentb: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:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that Mark can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Larry","Barbara","Mark"],"index":54034,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983063936,"difficulty":0.0016936064}
{"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. Paul's card is shown to Michael. Denise's card is shown to Michael. Denise's card is shown to Denise. 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 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Paul","Denise"],"index":5267,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5950528383,"difficulty":0.4049471617}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlotte's card is shown to Charlotte. Dennis's card is shown to Dennis. Yajaira's card is shown to Dennis. Dennis's card is shown to Yajaira. Dennis's card is shown to Debora. It is publicly announced that someone picked a red card. It is publicly announced that Charlotte does not know whether Dennis picked a red card. It is publicly announced that Dennis 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) ] (Agenta knows that 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":"Charlotte can now know that Debora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlotte","Dennis","Yajaira","Debora"],"index":11041,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9494527578,"difficulty":0.0505472422}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henry's card is shown to Pamela. Geraldine's card is shown to Geraldine. Geraldine's card is shown to Henry. It is publicly announced that someone picked a red card. It is publicly announced that Geraldine does not know whether Henry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentc knows that (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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Geraldine can now know whether Henry can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pamela","Geraldine","Henry"],"index":9105,"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). Gertrude's card is shown to Robert. David's card is shown to Robert. Gertrude's card is shown to Gertrude. 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:2,3 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:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Gertrude","David"],"index":49864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998136282,"difficulty":0.001863718}
{"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 Dorathy. Dorathy's card is shown to Wade. Bobby's card is shown to Wade. Wade's card is shown to Bobby. It is publicly announced that someone picked a red card. It is publicly announced that Dorathy does not know whether Dorathy picked a red card. It is publicly announced that Dorathy knows whether Bobby 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) ] [ ! (Agenta knows whether 3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Dorathy can now know whether Bobby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dorathy","Wade","Bobby"],"index":19962,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5091670752,"difficulty":1.5091670752}
{"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 Judy. Judy's card is shown to Louis. Judy's card is shown to James. Louis's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Judy","Louis","James"],"index":21935,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6024140716,"difficulty":1.6024140716}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelo's card is shown to Joe. Joe's card is shown to Timothy. Angelo's card is shown to Timothy. Joe's card is shown to Carlos. 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:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Timothy can now know that Carlos picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joe","Timothy","Angelo","Carlos"],"index":17663,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984619617,"difficulty":0.0015380383}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Kennith's card is shown to Kennith. Louis's card is shown to Kennith. Edward's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Kennith does not know whether Angela picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kennith can now know that Louis can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Kennith","Louis","Edward"],"index":42775,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985415936,"difficulty":0.0014584064}
{"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. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Johnny","Louis"],"index":21011,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986251593,"difficulty":0.0013748407}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"John can now know whether Frank picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Arlene","Frank","Bryan"],"index":2858,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8878768682,"difficulty":0.1121231318}
{"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. Don's card is shown to Leann. Michael's card is shown to Daryl. Leann's card is shown to Don. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 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:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Don can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Leann","Daryl","Don"],"index":46818,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997662902,"difficulty":0.0002337098}
{"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 Mary. Margaret's card is shown to Margaret. Margaret's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Margaret","Janice"],"index":59018,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979029894,"difficulty":0.0020970106}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Margaret. Manuel's card is shown to Manuel. Herman's card is shown to Herman. It is publicly announced that someone picked a red card. It is publicly announced that Manuel 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 Manuel does not know whether Margaret 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) ] Agentb knows whether (Agentc knows that (1|2|3))","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":"Manuel can now know whether Herman can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Manuel","Herman"],"index":52885,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
{"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 Thomas. Michael's card is shown to Thomas. Clarence's card is shown to Thomas. Thomas's card is shown to Michael. Michael's card is shown to Michael. Clarence's card is shown to Clarence. 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:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Carl can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Thomas","Michael","Clarence"],"index":7362,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997131228,"difficulty":0.0002868772}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Sheila. Conrad's card is shown to Sheila. Sheila's card is shown to Conrad. It is publicly announced that someone picked a red card. It is publicly announced that Conrad does not know whether Conrad picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (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 2) ] 0","hypothesis":"Sheila can now know that Conrad can know whether Conrad picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sheila","Conrad"],"index":15463,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8250254393,"difficulty":1.8250254393}
{"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 Claire. Karen's card is shown to Claire. Laurence's card is shown to Karen. Karen's card is shown to Laurence. 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 Claire picked a black card. It is publicly announced that Faye does not know whether Faye picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Karen can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Claire","Faye","Karen","Laurence"],"index":11382,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997823834,"difficulty":0.0002176166}
{"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 Morgan. Kenneth's card is shown to Kenneth. Morgan's card is shown to Leroy. Kenneth's card is shown to Leroy. 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:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Minda can now know whether Morgan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Morgan","Kenneth","Minda","Leroy"],"index":44827,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
{"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 Miguel. Chris's card is shown to Miguel. Dorothy's card is shown to Dorothy. Chris's card is shown to Dorothy. 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:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know that Miguel can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anna","Miguel","Dorothy","Chris"],"index":3735,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984381795,"difficulty":0.0015618205}
{"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 Mary. Elizabeth's card is shown to Genaro. Rodney's card is shown to Elizabeth. Genaro's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2,3 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:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Genaro can now know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Rodney","Genaro","Elizabeth"],"index":14470,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9320977926,"difficulty":1.9320977926}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tricia's card is shown to Charmaine. Charmaine's card is shown to Charmaine. Charmaine's card is shown to Zachary. 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 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tricia can now know whether Charmaine can know whether Zachary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tricia","Charmaine","Zachary","Mary"],"index":39884,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985339642,"difficulty":0.0014660358}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beau's card is shown to Donna. Laura's card is shown to Donna. Beau's card is shown to Beau. Natalie's card is shown to Beau. Laura's card is shown to Beau. Beau's card is shown to Natalie. Beau's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Natalie knows whether Beau picked a red card. It is publicly announced that Laura does not know whether Donna picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Laura can now know whether Natalie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Beau","Natalie","Laura"],"index":39787,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997723699,"difficulty":0.0002276301}
{"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 George. George's card is shown to George. Joseph's card is shown to Andrew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] (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":"Joseph can now know that George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","George","Andrew"],"index":14509,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982349873,"difficulty":0.0017650127}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Renee's card is shown to Renee. Renee's card is shown to Nicholas. Nicholas's card is shown to Nicholas. It is publicly announced that someone picked a red card. It is publicly announced that Nicholas knows whether Nicholas 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 (Agenta knows that (1|2))","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":"Nicholas can now know that Renee can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Renee","Nicholas"],"index":5302,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernest's card is shown to William. William's card is shown to Ernest. It is publicly announced that someone picked a red card. It is publicly announced that Ernest does not know whether or not everyone picked a red card. It is publicly announced that Ernest does not know whether Ernest picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(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 (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ernest can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Ernest"],"index":55069,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981765747,"difficulty":0.0018234253}
{"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. Amanda's card is shown to Amanda. 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amanda can now know whether Anthony can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Amanda","Robyn"],"index":27752,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995519519,"difficulty":0.0004480481}
{"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 Virginia. Mary's card is shown to Virginia. Virginia's card is shown to Elizabeth. Virginia's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Elizabeth can now know that Virginia can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Soon","Virginia","Elizabeth","Mary"],"index":37660,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7308598757,"difficulty":1.7308598757}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Eugene's card is shown to Daniel. Warren's card is shown to Daniel. Warren's card is shown to Warren. Daniel'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 Dorothy does not know whether Warren picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Dorothy can now know that Eugene can know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eugene","Daniel","Warren","Dorothy"],"index":61107,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993386209,"difficulty":0.006613791}
{"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. Susan's card is shown to Alice. Alice's card is shown to Tara. Tara's card is shown to Tara. Susan's card is shown to Cynthia. Cynthia's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether or not everyone picked a red card. It is publicly announced that Susan picked a red card. It is publicly announced that Susan 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)) ] Agenta knows whether (Agentd knows whether 2)","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":"Susan can now know whether Cynthia can know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Alice","Tara","Cynthia"],"index":3069,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980758429,"difficulty":0.0019241571}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lasonya's card is shown to Lasonya. Lasonya's card is shown to Stuart. Stuart's card is shown to Stuart. Lasonya's card is shown to Darlene. Stuart's card is shown to Darlene. Darlene's card is shown to Darlene. 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:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Lasonya can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lasonya","Stuart","Darlene"],"index":33688,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982878566,"difficulty":0.0017121434}
{"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. Emily's card is shown to Helen. Emily's card is shown to Judith. Annie's card is shown to Judith. Judith's card is shown to Emily. Emily's card is shown to Emily. Emily's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that Helen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentc knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Emily can now know whether Helen can know that Annie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Judith","Emily","Annie"],"index":6365,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9199985862,"difficulty":0.0800014138}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jaqueline's card is shown to Kerri. Cathy's card is shown to Cathy. Cathy's card is shown to Jaqueline. Jaqueline's card is shown to Jaqueline. Jaqueline's card is shown to Martha. It is publicly announced that someone picked a red card. It is publicly announced that Kerri 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))) ] (Agentc knows whether 2)","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":"Jaqueline can now know whether Cathy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kerri","Cathy","Jaqueline","Martha"],"index":20202,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7301183939,"difficulty":1.7301183939}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Janet. Eugene's card is shown to Eugene. It is publicly announced that someone picked a red card. It is publicly announced that Eugene does not know whether Janet 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 that (Agentb 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":"Janet can now know that Eugene can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janet","Eugene"],"index":47225,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997028708,"difficulty":0.0002971292}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holley's card is shown to Holley. Judy's card is shown to Holley. Judy's card is shown to Annis. Holley's card is shown to Judy. It is publicly announced that someone picked a red card. It is publicly announced that Judy 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 ] Agenta knows that (Agentb knows that 1)","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":"Holley can now know that Annis can know that Holley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Holley","Annis","Judy"],"index":62767,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.578053534,"difficulty":0.421946466}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ethel's card is shown to Tracey. Tracey's card is shown to Donna. Ethel'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:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tracey can now know whether Ethel can know that Tracey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tracey","Ethel","Donna"],"index":58432,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6649048924,"difficulty":1.6649048924}
{"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 Audrey. Jody's card is shown to Audrey. Aaron's card is shown to Jody. Jody's card is shown to Aaron. It is publicly announced that someone picked a red card. It is publicly announced that Audrey 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 that (Agenta knows whether (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":"Jody can now know that Audrey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Audrey","Jody","Aaron"],"index":23487,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7931936979,"difficulty":1.7931936979}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lien's card is shown to Lien. Charles's card is shown to Charles. Lien's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lien can now know whether Joseph can know whether Lien picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lien","Charles","Joseph"],"index":35787,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986948371,"difficulty":0.0013051629}
{"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 Adriene. Ruth's card is shown to Adriene. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb: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:1,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Adriene can now know that Paula can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paula","Adriene","Ruth"],"index":35005,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983550906,"difficulty":0.0016449094}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryn's card is shown to Cheryl. Cheryl's card is shown to Kathryn. It is publicly announced that someone picked a red card. It is publicly announced that Cheryl 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 (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Kathryn can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cheryl","Kathryn"],"index":24423,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997732043,"difficulty":0.0002267957}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jannie's card is shown to Jannie. Cynthia's card is shown to Jannie. Denise's card is shown to Florence. Jannie's card is shown to Denise. Denise's card is shown to Denise. Jannie's card is shown to Cynthia. Denise's card is shown to Cynthia. Cynthia's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether Florence 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 (Agenta knows that 1)","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":"Florence can now know that Jannie can know that Jannie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jannie","Florence","Denise","Cynthia"],"index":29289,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.982838273,"difficulty":0.017161727}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ilona's card is shown to Ilona. Brian's card is shown to Ilona. Karen's card is shown to Jennifer. Brian's card is shown to Jennifer. Jennifer's card is shown to Karen. Karen's card is shown to Karen. Brian's card is shown to Karen. Ilona's card is shown to Brian. Jennifer'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 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 Agentc:2,3,4 Agentd:1,2,4 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:1,4 Agentb:3,4 Agentc:2,3,4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ilona","Jennifer","Karen","Brian"],"index":65602,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984785914,"difficulty":0.0015214086}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Percy's card is shown to Percy. Steve's card is shown to Percy. Percy's card is shown to Steve. Yon's card is shown to Steve. Steve's card is shown to Yon. 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:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Yon can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Percy","Steve","Yon"],"index":48381,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997832179,"difficulty":0.0002167821}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Philip's card is shown to Philip. Charles's card is shown to Philip. Philip's card is shown to Charles. Cynthia's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Philip can now know that Cynthia can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Philip","Cynthia","Charles"],"index":19613,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997156262,"difficulty":0.0002843738}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Amanda. Frank's card is shown to Amanda. Frank's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank knows whether or not nobody picked a red card. It is publicly announced that Amanda picked a red card. It is publicly announced that Amanda knows whether Frank picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Frank can now know whether Amanda can know whether Amanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Amanda","Frank"],"index":42684,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9948988557,"difficulty":0.0051011443}
{"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. Catherine's card is shown to Edward. Catherine's card is shown to Mark. Mark's card is shown to Catherine. Carolyn's card is shown to Catherine. 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:1,4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Carolyn can now know whether Edward can know whether Carolyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Mark","Carolyn","Catherine"],"index":15889,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983573556,"difficulty":0.0016426444}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Reginald. Reginald's card is shown to Laura. Mary's card is shown to Laura. Opal's card is shown to Mary. Reginald's card is shown to Opal. Laura's card is shown to Opal. It is publicly announced that someone picked a red card. It is publicly announced that Reginald does not know whether Opal picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Laura can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Reginald","Laura","Mary","Opal"],"index":3414,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985937476,"difficulty":0.0014062524}
{"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 John. Glen's card is shown to John. John's card is shown to Glen. Glen's card is shown to Glen. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"John can now know that Glen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Glen"],"index":38028,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984258413,"difficulty":0.0015741587}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Juan. Juan's card is shown to Vanessa. It is publicly announced that someone picked a red card. It is publicly announced that Juan 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 (~(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) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Juan can now know whether Vanessa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Juan","Vanessa"],"index":22042,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
{"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 David. Brenda's card is shown to David. David'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: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:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Gregory","Jason","Brenda"],"index":13119,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
{"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 Della. Della'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 Della knows whether Mary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Della can now know whether Mary can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Della","Mary"],"index":43279,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9048362374,"difficulty":0.0951637626}
{"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 Erika. Erika's card is shown to Mary. Mary's card is shown to Mary. Sidney's card is shown to Mary. Mary's card is shown to Sidney. Sidney's card is shown to Sidney. Albert's card is shown to Sidney. Albert's card is shown to Albert. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether Sidney picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mary can now know that Erika picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erika","Mary","Sidney","Albert"],"index":2922,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964601398,"difficulty":0.0035398602}
{"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 Brad. Brad's card is shown to Brad. Anna's card is shown to Brad. Chris's card is shown to Anna. 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) ] (Agenta knows whether 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":"Chris can now know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Chris","Casey","Brad","Anna"],"index":58041,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7429926395,"difficulty":1.7429926395}
{"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. Robert's card is shown to Brenda. 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 Robert does not know whether Brenda picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Brenda can now know whether Robert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Brenda"],"index":47402,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996763468,"difficulty":0.0003236532}
{"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 Tori. John's card is shown to John. John's card is shown to Teresa. 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 John 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 whether 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":"Tori can now know whether Teresa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Tori","John","Teresa"],"index":1218,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8799639344,"difficulty":1.8799639344}
{"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. Charles's card is shown to Laura. Laura's card is shown to Laura. Laura's card is shown to Margareta. It is publicly announced that someone picked a red card. It is publicly announced that Margareta knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Laura can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Laura","Margareta"],"index":43341,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997199178,"difficulty":0.0002800822}
{"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. Mary's card is shown to Eleanor. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Eleanor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Mary","Valerie","Eleanor"],"index":31905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998414278,"difficulty":0.001585722}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathy's card is shown to Laura. Laura's card is shown to Cathy. Laura's card is shown to Wanda. Cathy's card is shown to Wanda. Wanda's card is shown to Wanda. It is publicly announced that someone picked a red card. It is publicly announced that Wanda knows whether Cathy 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 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) ] [ ! (Agentc knows whether 2) ] 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":["Laura","Cathy","Wanda"],"index":4226,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9557747245,"difficulty":1.9557747245}
{"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 Mary. Shawn's card is shown to Shawn. Andrew's card is shown to Shawn. It is publicly announced that someone picked a red card. It is publicly announced that Mary 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) ] (Agentb knows whether (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":"Shawn can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Shawn","Andrew"],"index":47353,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8272404075,"difficulty":0.1727595925}
{"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 Ocie. Scott's card is shown to Ocie. Chris's card is shown to Chris. Chris's card is shown to Gary. 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:2,4 Agentb:2 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ocie can now know whether Scott can know that Gary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ocie","Chris","Gary","Scott"],"index":39865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9710044265,"difficulty":0.0289955735}
{"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 Jerry. Mark's card is shown to Jerry. Mark's card is shown to Lakisha. Jerry's card is shown to Jean. Jean's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Jean does not know whether Mark picked a red card. It is publicly announced that Lakisha does not know whether Jean 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 that 2)","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":"Lakisha can now know that Lakisha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Lakisha","Jean","Mark"],"index":49104,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9775231481,"difficulty":0.0224768519}
{"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. Ronnie's card is shown to Elizabeth. Elizabeth's card is shown to Louis. Pamela's card is shown to Ronnie. Elizabeth's card is shown to Pamela. Louis's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Louis does not know whether Louis picked a red card. It is publicly announced that Louis does not know whether Ronnie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Ronnie can now know whether Louis can know whether Ronnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Louis","Ronnie","Pamela"],"index":54695,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970288873,"difficulty":0.0029711127}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virgina's card is shown to Don. Don's card is shown to Virgina. Virgina's card is shown to Virgina. It is publicly announced that someone picked a red card. It is publicly announced that Virgina knows whether someone picked a red card. It is publicly announced that Virgina knows whether Don picked a red card. It is publicly announced that Don does not know whether or not everyone 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)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Virgina can now know that Don can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Don","Virgina"],"index":47929,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997005463,"difficulty":0.0002994537}
{"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. Sean's card is shown to Sean. Sean's card is shown to Gerald. Linda's card is shown to Nellie. 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) ] (Agenta knows whether 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":"Linda can now know whether Nellie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Sean","Gerald","Nellie"],"index":45415,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9357181787,"difficulty":0.0642818213}
{"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. Kenneth's card is shown to John. Kenneth's card is shown to Kenneth. John's card is shown to Paul. 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. 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|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":"John can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Kenneth","Paul"],"index":62285,"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). Hannah's card is shown to Hannah. Geraldine's card is shown to Hannah. Hannah's card is shown to Shawn. It is publicly announced that someone picked a red card. It is publicly announced that Hannah knows whether someone picked a red card. It is publicly announced that Hannah 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)) ] Agentb knows whether (Agenta knows whether (1&2&3))","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":"Geraldine can now know whether Hannah can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hannah","Geraldine","Shawn"],"index":59619,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9819907546,"difficulty":0.0180092454}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jayne's card is shown to Susan. Susan's card is shown to John. Beatrice's card is shown to Jayne. Susan's card is shown to Beatrice. John's card is shown to Beatrice. Beatrice's card is shown to Beatrice. 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 3)","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":"Jayne can now know whether Jayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","John","Jayne","Beatrice"],"index":52830,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8590472937,"difficulty":1.8590472937}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryce's card is shown to Bryce. Sylvia's card is shown to Bryce. Bryce's card is shown to Justin. Justin's card is shown to Justin. Sylvia's card is shown to Justin. Bryce's card is shown to Sylvia. Sylvia's card is shown to Sylvia. 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:1,3 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:1,3 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bryce can now know whether Justin can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bryce","Justin","Sylvia"],"index":42676,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
{"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 Brandy. William's card is shown to William. Brandy's card is shown to Terry. William's card is shown to Terry. It is publicly announced that someone picked a red card. It is publicly announced that Terry does not know whether Terry picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Terry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Brandy can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brandy","William","Terry"],"index":16391,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.720779717,"difficulty":0.279220283}
{"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. Andrew's card is shown to Andrew. Guadalupe's card is shown to Guadalupe. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Guadalupe can now know whether Andrew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Andrew","Guadalupe"],"index":17621,"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). Saul's card is shown to Saul. Carol's card is shown to Saul. Aaron's card is shown to Saul. Andrew's card is shown to Saul. Saul's card is shown to Carol. Aaron's card is shown to Aaron. Saul'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:1,2,3,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know whether Aaron can know that Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Saul","Carol","Aaron","Andrew"],"index":15223,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7080956697,"difficulty":0.2919043303}
{"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 Rebeca. Rebeca's card is shown to Jonathan. George's card is shown to Jonathan. Rebeca's card is shown to George. George's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jonathan can now know whether Rebeca can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebeca","Jonathan","George"],"index":33528,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8324301839,"difficulty":0.1675698161}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billie's card is shown to Billie. Billie's card is shown to Grover. 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 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Grover can now know that Billie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Billie","Grover"],"index":20730,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982340336,"difficulty":0.0017659664}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresita's card is shown to Carol. Angela's card is shown to Dorothy. Teresita's card is shown to Dorothy. Carol's card is shown to Teresita. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether Angela picked a red card. It is publicly announced that Carol 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 3) ] [ ! 1 ] (Agenta knows whether 3)","n_announcements":2,"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 3) ] [ ! 1 ] 0","hypothesis":"Carol can now know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Dorothy","Angela","Teresita"],"index":52150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6824221611,"difficulty":0.3175778389}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fallon's card is shown to Fallon. Stella's card is shown to Fallon. Tristan's card is shown to Fallon. Tristan's card is shown to Stella. Tristan's card is shown to Tristan. It is publicly announced that someone picked a red card. It is publicly announced that Tristan does not know whether or not everyone picked a red card. It is publicly announced that Tristan does not know whether or not everyone picked a red card. It is publicly announced that Stella does not know whether Stella picked a red card. It is publicly announced that Fallon 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))) ] (Agentc knows that 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":"Tristan can now know that Stella picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Fallon","Stella","Tristan"],"index":49395,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5449723005,"difficulty":0.4550276995}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernard's card is shown to Patrick. Velma's card is shown to Velma. Velma's card is shown to Bernard. Bernard's card is shown to Bernard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Velma can now know whether Velma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Velma","Bernard"],"index":3910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9362908602,"difficulty":0.0637091398}
{"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 Hailey. Hailey's card is shown to Connie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Hailey can now know that Connie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Hailey","Connie","Tanya"],"index":42985,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984419942,"difficulty":0.0015580058}
{"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 Yvonne. Yvonne's card is shown to Jerri. Mike's card is shown to Jerri. Jerri's card is shown to Mike. Mike's card is shown to Mike. It is publicly announced that someone picked a red card. It is publicly announced that Jerri does not know whether Jerri 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 that 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":"Mike can now know that Jerri picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yvonne","Jerri","Mike"],"index":60403,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9934030175,"difficulty":0.0065969825}
{"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 Jon. Wilburn's card is shown to Jon. Patrick's card is shown to Jon. Jon's card is shown to Patricia. Wilburn's card is shown to Patricia. Patrick's card is shown to Wilburn. Jon's card is shown to Patrick. Wilburn's card is shown to Patrick. 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) ] Agenta knows that (Agentd knows that 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":"Jon can now know that Patrick can know that Patrick picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jon","Patricia","Wilburn","Patrick"],"index":64191,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996237278,"difficulty":0.003762722}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billie's card is shown to Thomas. Ora's card is shown to Thomas. Thomas's card is shown to Billie. Billie's card is shown to Billie. Thomas's card is shown to Ora. 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:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Billie","Ora"],"index":24090,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983820915,"difficulty":0.0016179085}
{"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 Anna. Donald's card is shown to Donald. 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:3 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:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anna can now know that Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anna","Donald","James"],"index":50781,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981926084,"difficulty":0.0018073916}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terese's card is shown to Terese. Terese's card is shown to Jennifer. Anthony'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 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terese","Anthony","Jennifer"],"index":30146,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983377457,"difficulty":0.0016622543}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wesley's card is shown to Wesley. Penny's card is shown to Penny. Clara's card is shown to Penny. Clara's card is shown to Clara. Wesley's card is shown to Sarah. 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)) ] (Agenta knows that 4)","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":"Wesley can now know that Sarah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wesley","Penny","Clara","Sarah"],"index":64515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945300221,"difficulty":0.0054699779}
{"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 William. Mary's card is shown to Mary. Lawrence's card is shown to Tony. William's card is shown to Tony. 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) ] Agenta knows that (Agentc knows whether 3)","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":"Lawrence can now know that Mary can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lawrence","William","Mary","Tony"],"index":58976,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7715022564,"difficulty":0.2284977436}
{"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 Eric. Eric's card is shown to Harold. Annette's card is shown to Annette. It is publicly announced that someone picked a red card. It is publicly announced that Eric picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Eric can now know whether Harold can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Harold","Annette"],"index":53066,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997119308,"difficulty":0.0002880692}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnson's card is shown to Leonard. Leonard's card is shown to Phyllis. Leonard's card is shown to Johnson. Phyllis's card is shown to Johnson. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Johnson can now know that Phyllis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leonard","Phyllis","Johnson"],"index":24731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982084036,"difficulty":0.0017915964}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caleb's card is shown to Caleb. Merlin's card is shown to Caleb. Brian's card is shown to Merlin. Brian's card is shown to Brian. 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:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know whether Merlin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Caleb","Merlin","Brian","Matthew"],"index":53724,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8760768771,"difficulty":0.1239231229}
{"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. Eleanor's card is shown to William. Ernest's card is shown to William. William's card is shown to Ernest. 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 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":"William can now know that Eleanor can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Eleanor","Ernest"],"index":5916,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982703924,"difficulty":0.0017296076}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Gracie. Gracie's card is shown to Irene. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card. It is publicly announced that Carmen knows whether Carmen 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 3)","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":"Irene can now know that Carmen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gracie","Irene","Carmen"],"index":18215,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965211153,"difficulty":0.0034788847}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irving's card is shown to Irving. Irving's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Gregory 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)","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":"Irving can now know that Irving picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Irving","Gregory"],"index":4747,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9928887486,"difficulty":0.0071112514}
{"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. John's card is shown to Mack. Robert's card is shown to Mack. It is publicly announced that someone picked a red card. It is publicly announced that Mack picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 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:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"John can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Mack","Robert"],"index":8924,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978721142,"difficulty":0.0021278858}
{"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 Roland. Shirley's card is shown to Roland. Thomas's card is shown to Thomas. Roland's card is shown to Shirley. It is publicly announced that someone picked a red card. It is publicly announced that Roland knows whether Thomas 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) ] (Agenta knows whether (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 2) ] 0","hypothesis":"Roland can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roland","Thomas","Shirley"],"index":54841,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Ann. Ann's card is shown to Phyllis. Phyllis's card is shown to Phyllis. It is publicly announced that someone picked a red card. It is publicly announced that Ann does not know whether or not everyone 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)) ] Agentb knows whether (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 (1&2)) ] 0","hypothesis":"Phyllis can now know whether Ann can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ann","Phyllis"],"index":33180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
{"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. Robert's card is shown to Helen. Debbie's card is shown to Robert. Robert's card is shown to Debbie. It is publicly announced that someone picked a red card. It is publicly announced that Helen 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)) ] 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:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Helen can now know whether Debbie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Robert","Debbie"],"index":5563,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996855259,"difficulty":0.0003144741}
{"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. Beverly's card is shown to Sheila. 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 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 that (~(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":"Robert can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Sheila","Beverly"],"index":21184,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998021245,"difficulty":0.001978755}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernestine's card is shown to Ernestine. Ernestine's card is shown to Janet. 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 that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Janet can now know whether Ernestine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ernestine","Janet"],"index":25679,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994966984,"difficulty":0.0005033016}
{"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 Yolanda. Lissette's card is shown to Yolanda. Derek's card is shown to Yolanda. Yolanda's card is shown to Lissette. Lissette's card is shown to Lissette. Yolanda's card is shown to Derek. 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:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alexis can now know whether Yolanda can know whether Yolanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alexis","Yolanda","Lissette","Derek"],"index":48680,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9974345565,"difficulty":0.0025654435}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shane's card is shown to Debra. Debra's card is shown to Shane. It is publicly announced that someone picked a red card. It is publicly announced that Shane does not know whether Shane picked a red card. It is publicly announced that Shane does not know whether Shane 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 whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Shane can now know whether Debra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debra","Shane"],"index":10183,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.696952045,"difficulty":1.696952045}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rita's card is shown to Rita. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Rita can now know that Jill can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jill","Rita","Mary"],"index":10040,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7653334141,"difficulty":0.2346665859}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doreen's card is shown to Doreen. Doreen's card is shown to Carolyn. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn knows whether someone picked a red card. It is publicly announced that Carolyn does not know whether Carolyn picked a red card. It is publicly announced that Carolyn does not know whether Carolyn picked a red card. It is publicly announced that Carolyn does not know whether Carolyn 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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that 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 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Carolyn can now know that Doreen can know that Carolyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Doreen","Carolyn"],"index":43141,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8951873183,"difficulty":0.1048126817}
{"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 Stephanie. Sherry's card is shown to Stephanie. Stephanie's card is shown to Kevin. Kevin's card is shown to Kevin. Stephanie's card is shown to Sherry. Ruth's card is shown to Sherry. It is publicly announced that someone picked a red card. It is publicly announced that Stephanie does not know whether Ruth picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kevin can now know that Stephanie can know whether Sherry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Kevin","Ruth","Sherry"],"index":64783,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9098221064,"difficulty":1.9098221064}
{"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 Sol. Manuel's card is shown to Keith. Manuel's card is shown to Manuel. 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:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Keith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sol","Keith","Manuel","William"],"index":26820,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9273033738,"difficulty":0.0726966262}
{"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 Latesha. Latesha's card is shown to Curtis. Curtis's card is shown to Curtis. Curtis's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Latesha can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Latesha","Curtis","Donald"],"index":64701,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997233748,"difficulty":0.0002766252}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Marvin. Jennie's card is shown to Marvin. Jason's card is shown to Marvin. Jennie's card is shown to Luis. Marvin's card is shown to Jason. Jennie'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:1,3,4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marvin can now know that Jennie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","Luis","Jennie","Jason"],"index":52104,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982690811,"difficulty":0.0017309189}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Gloria. Judith's card is shown to Gloria. Judith's card is shown to Judith. Brian's card is shown to Judith. Gloria's card is shown to Eric. Judith's card is shown to Eric. Gloria's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Gloria knows whether Gloria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Judith can now know that Brian can know that Brian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Judith","Eric","Brian"],"index":42080,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9780765772,"difficulty":0.0219234228}
{"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. Troy's card is shown to Mark. Jame's card is shown to Mark. Jame's card is shown to Troy. Troy's card is shown to Jame. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether Mark picked a red card. It is publicly announced that Rebecca does not know whether or not everyone picked a red card. It is publicly announced that Mark knows whether Jame picked a red card. It is publicly announced that Troy 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:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Troy can now know that Rebecca picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Rebecca","Troy","Jame"],"index":51549,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6476830244,"difficulty":0.3523169756}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Edwin. Brian's card is shown to Edwin. Vanessa's card is shown to Eve. Edwin's card is shown to Brian. Vanessa's card is shown to Brian. Eve's card is shown to Vanessa. It is publicly announced that someone picked a red card. It is publicly announced that Vanessa does not know whether Edwin picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Vanessa does not know whether Brian 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) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 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":"Brian can now know whether Vanessa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edwin","Eve","Brian","Vanessa"],"index":10772,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994968176,"difficulty":0.0005031824}
{"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 Margo. Cecil's card is shown to Donald. Margo's card is shown to Cecil. Cecil'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 Cecil does not know whether or not everyone picked a red card. It is publicly announced that Cecil picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 3 ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Donald can now know that Margo can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margo","Donald","Cecil","Clarence"],"index":38061,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5697113872,"difficulty":1.5697113872}
{"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 Jack. Jim's card is shown to Jack. Thelma's card is shown to Jack. Thelma's card is shown to Betty. Jack's card is shown to Jim. Betty's card is shown to Jim. Jim's card is shown to Jim. Jack's card is shown to Thelma. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1,2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1,2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thelma can now know whether Jack can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jack","Betty","Jim","Thelma"],"index":46735,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996882677,"difficulty":0.0003117323}
{"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 Etsuko. Kyle's card is shown to Etsuko. Charles's card is shown to David. David's card is shown to David. David's card is shown to Kyle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc: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:2,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Charles can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Etsuko","Charles","David","Kyle"],"index":36204,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
{"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. Evelyn's card is shown to Brett. Evelyn's card is shown to Nolan. It is publicly announced that someone picked a red card. It is publicly announced that Nolan does not know whether or not everyone picked a red card. It is publicly announced that Evelyn picked a red card. It is publicly announced that Brett does not know whether Brett 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 (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Nolan can now know that Brett can know that Brett picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Evelyn","Brett","Nolan"],"index":48885,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5165461898,"difficulty":0.4834538102}
{"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 Clarence. Clarence's card is shown to Josephine. Josephine's card is shown to Josephine. Josephine's card is shown to Marie. 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) ] (Agenta knows whether 1)","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":"Clarence can now know whether Clarence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clarence","Josephine","Marie"],"index":46503,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7029163837,"difficulty":1.7029163837}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to David. David's card is shown to David. Bobby's card is shown to David. Bobby's card is shown to Bobby. 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 (~(1|2|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":"David can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","David","Bobby"],"index":26724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999725163,"difficulty":0.000274837}
{"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 Joanne. Michelle's card is shown to Joanne. Joanne's card is shown to Michelle. Michelle's card is shown to Vanessa. Ryan's card is shown to Vanessa. Vanessa's card is shown to Ryan. It is publicly announced that someone picked a red card. It is publicly announced that Michelle 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) ] Agentc knows whether (Agentd knows whether 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":"Vanessa can now know whether Ryan can know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joanne","Michelle","Vanessa","Ryan"],"index":56972,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988176227,"difficulty":0.0011823773}
{"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 Agnes. Agnes's card is shown to Arthur. Jessica's card is shown to Arthur. Agnes's card is shown to Jessica. Edward's card is shown to Jessica. Arthur's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Agnes can now know whether Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Agnes","Edward","Arthur","Jessica"],"index":61692,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8204336762,"difficulty":0.1795663238}
{"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 Raymond. Stephen's card is shown to Raymond. Raymond's card is shown to Stephen. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Stephen picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Raymond can now know whether Mary can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raymond","Stephen","Mary"],"index":5968,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.734384656,"difficulty":0.265615344}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Homer's card is shown to Homer. Marquetta's card is shown to Marquetta. Nancy's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 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:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marquetta can now know that Homer can know whether Marquetta picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Homer","Marquetta","Elizabeth","Nancy"],"index":17653,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8415921926,"difficulty":0.1584078074}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Patti. Aaron's card is shown to Aaron. Grace's card is shown to Aaron. Patti's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Aaron 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|2|3)))","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":"Grace can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patti","Aaron","Grace"],"index":60008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984967709,"difficulty":0.0015032291}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kai's card is shown to Carrie. Paula's card is shown to Carrie. Kai's card is shown to Kai. Pat's card is shown to Kai. Kai's card is shown to Pat. 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 that 2)","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":"Kai can now know that Carrie can know that Kai picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carrie","Kai","Pat","Paula"],"index":27965,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962911606,"difficulty":0.0037088394}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Ivan. Ivan's card is shown to Matthew. Matthew's card is shown to Matthew. Matthew's card is shown to Amy. Matthew's card is shown to Charles. Amy'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:3 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ivan can now know whether Matthew can know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ivan","Matthew","Amy","Charles"],"index":56491,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9964380264,"difficulty":0.0035619736}
{"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 Philip. Samuel's card is shown to Judith. Judith's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Samuel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Judith can now know whether Philip picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Philip","Judith","Samuel"],"index":52510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7628574371,"difficulty":0.2371425629}
{"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 Rodney. Steven's card is shown to Rodney. Steven's card is shown to Stephen. Rodney's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Virgil can now know that Steven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rodney","Stephen","Virgil","Steven"],"index":28545,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982182384,"difficulty":0.0017817616}
{"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 Sean. Gary's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sean can now know whether Robert can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Sean","Gary"],"index":11650,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9952183366,"difficulty":0.0047816634}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to Monica. Christina's card is shown to Monica. 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 or not everyone picked a red card. It is publicly announced that Christina does not know whether Monica 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:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Christina can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Monica","Christina"],"index":26742,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997825563,"difficulty":0.002174437}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dewey's card is shown to Beatrice. Dewey's card is shown to Dewey. Frances's card is shown to Dewey. Beatrice's card is shown to Frances. 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 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:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dewey can now know that Beatrice can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Beatrice","Dewey","Frances"],"index":39709,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984422326,"difficulty":0.0015577674}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harlan's card is shown to Harlan. Thomas's card is shown to Thomas. Nicole's card is shown to Nicole. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nicole can now know whether Thomas can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harlan","Thomas","Nicole"],"index":24936,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9958406091,"difficulty":0.0041593909}
{"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. Howard's card is shown to Nancy. Maria's card is shown to Howard. Howard's card is shown to Howard. Ralph's card is shown to Howard. Nancy's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Ralph does not know whether or not everyone picked a red card. It is publicly announced that Ralph does not know whether Ralph picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentd 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:3 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Ralph can now know that Nancy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Nancy","Howard","Ralph"],"index":2886,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947597384,"difficulty":0.0052402616}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Frances. Frances's card is shown to Cori. Cori's card is shown to Cori. It is publicly announced that someone picked a red card. It is publicly announced that Cori knows whether Cori 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 whether (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":"Frances can now know whether Cori can know that Frances picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frances","Cori"],"index":39831,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8199663162,"difficulty":0.1800336838}
{"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. Eddie's card is shown to Mozelle. Raymond's card is shown to Eddie. Eddie's card is shown to Eddie. Bruce's card is shown to Eddie. Mozelle's card is shown to Bruce. It is publicly announced that someone picked a red card. It is publicly announced that Bruce does not know whether or not everyone picked a red card. It is publicly announced that Bruce does not know whether Bruce picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentb knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Mozelle can now know whether Bruce can know that Bruce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Mozelle","Eddie","Bruce"],"index":16513,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9416290522,"difficulty":0.0583709478}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Opal's card is shown to Opal. Mary's card is shown to Opal. Nina's card is shown to Nina. Mary's card is shown to Katherine. Opal's card is shown to Mary. Nina'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:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Opal can now know whether Katherine can know that Opal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Opal","Nina","Katherine","Mary"],"index":54487,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.795209527,"difficulty":0.204790473}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobbie's card is shown to Shari. Shari's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Frank's card is shown to Elizabeth. Shari's card is shown to Bobbie. Frank's card is shown to Bobbie. 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 Agentc:1,3 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:4 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shari can now know whether Frank can know whether Bobbie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shari","Elizabeth","Frank","Bobbie"],"index":8881,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998013854,"difficulty":0.001986146}
{"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 Mary. Judith's card is shown to Judith. Mary's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that Gerald knows whether Mary 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 whether 1) ] Agenta knows whether (Agentc knows whether (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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mary can now know whether Gerald can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Judith","Gerald"],"index":40957,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5120469332,"difficulty":1.5120469332}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricardo's card is shown to Maryann. Anita's card is shown to Ricardo. Maryann's card is shown to Anita. Ricardo's card is shown to Anita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ricardo can now know that Maryann can know that Maryann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maryann","Ricardo","Anita"],"index":3021,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993830502,"difficulty":0.006169498}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tina's card is shown to Helen. Lisa's card is shown to Helen. Casey's card is shown to Casey. Lisa's card is shown to Casey. Helen's card is shown to Tina. Casey'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:2,4 Agentc:1 Agentd:2 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:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know that Tina can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Casey","Tina","Lisa"],"index":5586,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997143149,"difficulty":0.0002856851}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Sandra. Cheryl's card is shown to Helen. Helen's card is shown to Helen. Rex's card is shown to Helen. Sandra's card is shown to Rex. 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 Cheryl picked a black card. It is publicly announced that Cheryl 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) ] Agentc knows whether (Agentb knows that (1&2&3&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":"Helen can now know whether Cheryl can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Cheryl","Helen","Rex"],"index":50009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9943528175,"difficulty":0.0056471825}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anita's card is shown to Mike. Anita's card is shown to Anita. It is publicly announced that someone picked a red card. It is publicly announced that Mike picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Anita can now know that Mike can know that Mike picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mike","Anita"],"index":30747,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5794347525,"difficulty":1.5794347525}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Howard. Anthony's card is shown to Howard. Howard's card is shown to Irene. Irene's card is shown to Anthony. 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) ] Agentb knows that (Agentc knows whether 1)","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":"Irene can now know that Anthony can know whether Howard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Howard","Irene","Anthony"],"index":63438,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7196663022,"difficulty":0.2803336978}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Francis. Francis's card is shown to Janie. Janie's card is shown to Janie. Charles's card is shown to Janie. Francis's card is shown to Charles. 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:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Francis can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francis","Janie","Charles"],"index":4982,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8144107461,"difficulty":0.1855892539}
{"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. Lynn's card is shown to Michael. Roy's card is shown to Michael. Michael's card is shown to Lynn. Lynn's card is shown to Lynn. Roy's card is shown to Lynn. Lynn's card is shown to Roy. Roy'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:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Lynn","Roy"],"index":3790,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997729659,"difficulty":0.0002270341}
{"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 John. John's card is shown to Lee. John's card is shown to Russell. Lee's card is shown to Russell. It is publicly announced that someone picked a red card. It is publicly announced that Russell does not know whether Russell picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Lee","Russell"],"index":63522,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997162223,"difficulty":0.0002837777}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fred's card is shown to Fred. Christie's card is shown to Fred. Christie's card is shown to Christie. John's card is shown to Christie. John'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:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Fred can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Fred","Christie","John"],"index":26280,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997268319,"difficulty":0.0002731681}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carroll's card is shown to Calvin. Bradley's card is shown to Carroll. Carroll's card is shown to Dustin. It is publicly announced that someone picked a red card. It is publicly announced that Carroll does not know whether or not everyone picked a red card. It is publicly announced that Carroll does not know whether or not everyone picked a red card. It is publicly announced that Calvin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Dustin can now know that Carroll picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Calvin","Carroll","Dustin","Bradley"],"index":52439,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9386384487,"difficulty":0.0613615513}
{"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 Susan. Susan's card is shown to Elinor. 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) ] Agenta knows whether (Agentb knows whether 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":"Susan can now know whether Brenda can know whether Elinor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Brenda","Elinor","James"],"index":62949,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988425374,"difficulty":0.0011574626}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ian's card is shown to Matt. Matt's card is shown to Tracy. Ian's card is shown to Tracy. Tracy's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Ian knows whether Tracy picked a red card. It is publicly announced that Matt does not know whether Tracy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ian can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matt","Ian","Tracy"],"index":14525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998617053,"difficulty":0.001382947}
{"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 Tammy. Tammy's card is shown to Robert. John's card is shown to Robert. Tammy'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 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tammy can now know whether Robert can know whether Tammy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tammy","Robert","John"],"index":65994,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99774158,"difficulty":0.00225842}
{"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 Elliott. Elliott's card is shown to Brian. Brian's card is shown to Brian. Brian's card is shown to Kristin. Kristin's card is shown to Kristin. 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:2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kristin can now know whether Kristin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elliott","Brian","Kristin"],"index":38469,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9316671491,"difficulty":0.0683328509}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diann's card is shown to Joe. Joe's card is shown to Ismael. Diann's card is shown to Ismael. Joe's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 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:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ismael can now know whether Joe picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joe","Ismael","Diann","Melissa"],"index":24463,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8322622776,"difficulty":0.1677377224}
{"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 William. William's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Eric knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows 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":"William can now know that Eric can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Eric"],"index":31746,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9742281437,"difficulty":0.0257718563}
{"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. Carol's card is shown to Mildred. Mildred's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Mildred knows whether Mildred picked a red card. It is publicly announced that Carol does not know whether or not everyone picked a red card. It is publicly announced that Carol does not know whether Carol 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 whether (Agenta knows that (1|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":"Carol can now know whether Mildred can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mildred","Carol"],"index":34090,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997728467,"difficulty":0.0002271533}
{"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 John. Darryl's card is shown to Darryl. Darryl's card is shown to Lucille. 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 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 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Maurice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Darryl","Lucille","Maurice"],"index":34884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984058738,"difficulty":0.0015941262}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chantel's card is shown to Chana. Chana's card is shown to James. Chantel's card is shown to James. Chana's card is shown to Chantel. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Chana can now know whether James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chana","James","Chantel"],"index":6127,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997726083,"difficulty":0.0002273917}
{"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 Thomas. Thomas's card is shown to Ruby. Ruby's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether Ruby picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Thomas can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thomas","Ruby"],"index":23034,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9189993739,"difficulty":0.0810006261}
{"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 Florence. Mike's card is shown to Mike. Mike's card is shown to Will. 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) ] (Agentc 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":"Will can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Florence","Mike","Will"],"index":55091,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983410835,"difficulty":0.0016589165}
{"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 Carol. Jason's card is shown to Carmen. Carol'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:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carol","Fredrick","Carmen","Jason"],"index":38326,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
{"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 Terry. Burton's card is shown to Terry. Mary's card is shown to Terry. Terry's card is shown to Burton. Burton's card is shown to Burton. Mary's card is shown to Burton. Burton'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 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terry can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terry","Burton","Mary"],"index":20220,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998380661,"difficulty":0.001619339}
{"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 Jared. Marianne's card is shown to Jared. Jared's card is shown to Marianne. 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 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 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Jared can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jared","Marianne"],"index":2173,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997215867,"difficulty":0.0002784133}
{"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. Bonita's card is shown to Timothy. Candace's card is shown to Candace. Bonita's card is shown to Bonita. 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: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:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Candace can now know whether Timothy can know whether Bonita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Candace","Bonita"],"index":54856,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987596273,"difficulty":0.0012403727}
{"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. It is publicly announced that someone picked a red card. It is publicly announced that Kimberly does not know whether or not everyone picked a red card. It is publicly announced that John picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Kimberly can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Kimberly","Christina","John"],"index":6784,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7766483426,"difficulty":1.7766483426}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henry's card is shown to Heriberto. Ralph's card is shown to Ralph. Henry's card is shown to Ralph. Henry's card is shown to John. John's card is shown to Henry. 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) ] Agenta knows that (Agentd 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":"Heriberto can now know that Henry can know whether Heriberto picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heriberto","Ralph","John","Henry"],"index":59266,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8191835284,"difficulty":0.1808164716}
{"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 Doris. Doris's card is shown to Beverly. Doris's card is shown to Mary. Beverly's card is shown to Mary. William's card is shown to Mary. 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"William can now know whether Doris can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doris","Beverly","William","Mary"],"index":54814,"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). David's card is shown to Stephen. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether or not everyone picked a red card. It is publicly announced that Stephen does not know whether or not everyone picked a red card. It is publicly announced that Stephen 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: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":"Stephen can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Stephen","David"],"index":66918,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9138738513,"difficulty":1.9138738513}
{"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 Kimberly. Jose's card is shown to Jose. Kimberly's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that Annie does not know whether Annie 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 whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kimberly can now know that Kimberly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kimberly","Jose","Annie"],"index":40361,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.982169807,"difficulty":0.017830193}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Abraham's card is shown to Stella. Abraham's card is shown to Abraham. Bertha's card is shown to Abraham. Francine's card is shown to Abraham. Francine's card is shown to Bertha. Abraham'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 Bertha does not know whether Stella 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) ] (Agentd knows that (~(1|2|3|4)))","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":"Francine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stella","Abraham","Bertha","Francine"],"index":15993,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984948635,"difficulty":0.0015051365}
{"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 Cheryl. Robert's card is shown to Cheryl. Cheryl's card is shown to Shawn. Cheryl's card is shown to Robert. Robert'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:1,4 Agentb:2 Agentc:2,4 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:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know whether Cheryl can know that Shawn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Cheryl","Shawn","Robert"],"index":63356,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9149885774,"difficulty":0.0850114226}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leroy's card is shown to Leroy. Grace's card is shown to Leroy. Grace's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Grace knows whether or not everyone picked a red card. It is publicly announced that Grace knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Grace can now know that Leroy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leroy","Grace"],"index":21521,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997006655,"difficulty":0.0002993345}
{"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 Marvin. Margaret's card is shown to Margaret. Sara's card is shown to Matthew. Margaret'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 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marvin can now know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marvin","Sara","Margaret","Matthew"],"index":30940,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8896787167,"difficulty":0.1103212833}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marquita's card is shown to Hattie. Marquita's card is shown to Eric. Jack's card is shown to Jack. 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 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jack can now know that Eric can know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hattie","Eric","Jack","Marquita"],"index":6238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9627619982,"difficulty":0.0372380018}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Kathleen's card is shown to Calvin. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Kathleen can now know that Mary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Kathleen","Calvin"],"index":8214,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983302951,"difficulty":0.0016697049}
{"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 Gloria. Jason's card is shown to Elizabeth. Jason's card is shown to Leah. 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 that (Agentb knows that 1)","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":"Leah can now know that Elizabeth can know that Gloria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Elizabeth","Leah","Jason"],"index":54380,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983238578,"difficulty":0.0016761422}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Ann. Kimberly's card is shown to Kimberly. 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:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb 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":"Kimberly can now know that Kimberly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ann","Kimberly"],"index":28433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9385529757,"difficulty":0.0614470243}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Laura. Laura's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Ruby 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)) ] (Agentb knows whether (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":"Ruby can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Laura","Ruby"],"index":53534,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997567534,"difficulty":0.0002432466}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynn's card is shown to Christopher. Christopher's card is shown to Shelley. Shelley's card is shown to Debra. Lynn'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:3 Agentb:1 Agentc:2,3 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:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know whether Lynn can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Shelley","Lynn","Debra"],"index":39130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997109771,"difficulty":0.0002890229}
{"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. Ann's card is shown to Barbara. Helen's card is shown to Barbara. Barbara's card is shown to Ann. Ann's card is shown to Ann. Barbara's card is shown to Helen. 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:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ann can now know whether Barbara can know that Nicholas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicholas","Barbara","Ann","Helen"],"index":10313,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9731701612,"difficulty":0.0268298388}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Miriam's card is shown to Louise. Louise's card is shown to Miriam. It is publicly announced that someone picked a red card. It is publicly announced that Louise does not know whether Louise picked a red card. It is publicly announced that Louise does not know whether Louise picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Miriam can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Louise","Miriam"],"index":30212,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8714039922,"difficulty":1.8714039922}
{"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. Yvonne's card is shown to James. James's card is shown to Cheryl. Cheryl's card is shown to Cheryl. James's card is shown to Yvonne. 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 (1&2&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":"Yvonne can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Cheryl","Yvonne"],"index":67,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9923007488,"difficulty":0.0076992512}
{"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. William's card is shown to Anna. William's card is shown to Stephen. Stephen's card is shown to Stephen. Barbara's card is shown to Stephen. Stephen'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:1 Agentb:1 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know that Stephen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Anna","Stephen","Barbara"],"index":49553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979209304,"difficulty":0.0020790696}
{"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 Gary. Harold's card is shown to Frank. Harold's card is shown to Jean. Frank'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 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harold","Gary","Frank","Jean"],"index":19463,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
{"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 Jan. Justina's card is shown to Justina. Justina's card is shown to Rickey. Rickey's card is shown to Rickey. 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:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know whether Jan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jan","Justina","William","Rickey"],"index":59855,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9884747863,"difficulty":0.0115252137}
{"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. Drew's card is shown to Robert. Robert's card is shown to James. James's card is shown to James. Drew's card is shown to James. Robert's card is shown to Drew. James's card is shown to Drew. 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:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Drew can now know whether James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","James","Drew"],"index":9977,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9927138686,"difficulty":1.9927138686}
{"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 Monte. Thomas's card is shown to Thomas. Cheryl's card is shown to Cheryl. Thomas's card is shown to Danny. 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) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know whether Cheryl can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monte","Thomas","Cheryl","Danny"],"index":9053,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9925910234,"difficulty":0.0074089766}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Courtney's card is shown to Charles. Charles's card is shown to Courtney. Courtney's card is shown to Courtney. Courtney's card is shown to Douglas. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Douglas does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 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:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Douglas can now know that Charles can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Courtney","Douglas"],"index":61069,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5265925527,"difficulty":0.4734074473}
{"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. Keith's card is shown to Robert. Robert's card is shown to Keith. Marcia's card is shown to Keith. Marcia's card is shown to Marcia. It is publicly announced that someone picked a red card. It is publicly announced that Keith knows whether someone picked a red card. It is publicly announced that Marcia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Robert can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Keith","Marcia"],"index":16019,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9853736162,"difficulty":0.0146263838}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Derrick. Derrick's card is shown to Steven. Norman's card is shown to Steven. Steven's card is shown to Clara. Derrick's card is shown to Norman. Clara's card is shown to Norman. It is publicly announced that someone picked a red card. It is publicly announced that Norman does not know whether Norman picked a red card. It is publicly announced that Derrick knows whether or not nobody picked a red card. It is publicly announced that Clara 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 (Agenta knows whether 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":"Clara can now know that Derrick can know whether Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Derrick","Steven","Clara","Norman"],"index":32002,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5091288686,"difficulty":1.5091288686}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mellisa's card is shown to Hae. Matilda's card is shown to Matilda. Hae's card is shown to Mellisa. It is publicly announced that someone picked a red card. It is publicly announced that Mellisa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether 1)","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":"Mellisa can now know whether Hae picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hae","Matilda","Mellisa"],"index":15288,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8432338834,"difficulty":0.1567661166}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelby's card is shown to Shelby. Walter's card is shown to Shelby. Frances's card is shown to Shelby. Walter's card is shown to Walter. Walter's card is shown to Frances. It is publicly announced that someone picked a red card. It is publicly announced that Walter knows whether or not everyone picked a red card. It is publicly announced that Frances knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Shelby can now know that Walter can know that Shelby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shelby","Walter","Frances"],"index":54504,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6714131236,"difficulty":0.3285868764}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Joseph. Joseph's card is shown to Duane. It is publicly announced that someone picked a red card. It is publicly announced that Duane does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(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":"Duane can now know that Joseph can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joseph","Duane"],"index":32350,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978475571,"difficulty":0.0021524429}
{"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 Robert. Robert's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Michael can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Michael"],"index":8217,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985182881,"difficulty":0.0014817119}
{"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 Mary. Mary'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 Mary does not know whether Keith picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 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:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Keith can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Keith","Rhonda"],"index":8618,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997820258,"difficulty":0.0002179742}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Nina. Nina's card is shown to Nina. Nellie'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 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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Scott can now know that Nina can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Nina","Nellie"],"index":59995,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
{"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 Florine. Calvin's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Calvin does not know whether or not everyone picked a red card. It is publicly announced that Calvin does not know whether Florine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Calvin can now know whether Florine can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Calvin","Florine","Anna"],"index":63501,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9756270051,"difficulty":0.0243729949}
{"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 Christy. Tyrell's card is shown to Helen. Kenneth's card is shown to Tyrell. Helen's card is shown to Tyrell. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card. It is publicly announced that Kenneth picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Tyrell can now know whether Christy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Christy","Helen","Tyrell"],"index":67363,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5682901144,"difficulty":0.4317098856}
{"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. Rita's card is shown to Maria. Valerie's card is shown to Maria. Shirley's card is shown to Rita. Valerie's card is shown to Rita. Rita's card is shown to Valerie. Valerie's card is shown to Valerie. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Maria picked a red card. It is publicly announced that Maria does not know whether Maria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Rita can now know whether Maria can know that Shirley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirley","Maria","Rita","Valerie"],"index":66211,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9396256804,"difficulty":1.9396256804}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lauren's card is shown to Sandra. Sandra's card is shown to Lauren. Sandra's card is shown to Alicia. It is publicly announced that someone picked a red card. It is publicly announced that Sandra does not know whether or not everyone picked a red card. It is publicly announced that Sandra does not know whether Sandra picked a red card. It is publicly announced that Alicia knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Lauren can now know whether Alicia can know whether Alicia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Lauren","Alicia"],"index":50397,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9892495871,"difficulty":0.0107504129}
{"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 Jacob. Jacob's card is shown to Ruth. Ruth's card is shown to Karen. Jacob's card is shown to Thurman. Ruth's card is shown to Thurman. Karen's card is shown to Thurman. 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) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacob","Ruth","Karen","Thurman"],"index":7056,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984949827,"difficulty":0.0015050173}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Amanda. German's card is shown to Amanda. Austin's card is shown to Austin. German's card is shown to German. 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:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Austin can now know whether German can know whether Austin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Austin","German"],"index":31845,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979135394,"difficulty":0.0020864606}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Levi. David's card is shown to Levi. Levi's card is shown to Harold. David's card is shown to Harold. Levi's card is shown to David. 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:2,3 Agentb:1,3 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:2,3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether Levi can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Levi","Harold","David"],"index":10977,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9947708249,"difficulty":0.0052291751}
{"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. Ashley's card is shown to Patricia. Patricia's card is shown to Ashley. Ashley's card is shown to Ashley. Patricia's card is shown to Ray. Robert's card is shown to Ray. Ray's card is shown to Robert. Robert'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:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know whether Ashley can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Ashley","Ray","Robert"],"index":41970,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Katherine. Angel's card is shown to Alice. Katherine's card is shown to Angel. 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":"Ronald can now know that Katherine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katherine","Ronald","Alice","Angel"],"index":56195,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998449564,"difficulty":0.001550436}
{"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 Kelly. James's card is shown to Kelly. James's card is shown to Jose. Kelly'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 that (Agentb 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 that Jose can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelly","Jose","James"],"index":1874,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
{"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 Alexander. Paul's card is shown to Alexander. Paul's card is shown to Paul. Raymond's card is shown to Paul. Paul'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 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alexander can now know that Raymond can know that Alexander picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alexander","Paul","Raymond"],"index":57129,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977305532,"difficulty":0.0022694468}
{"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. Jay's card is shown to Jay. Guadalupe's card is shown to Mary. Guadalupe'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:1 Agentb:2 Agentc:1 Agentd:1 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:1 Agentb:2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Jay can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Guadalupe","Jay","Mary","Marie"],"index":56401,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997748733,"difficulty":0.0002251267}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Clyde. Carla's card is shown to Clyde. Clyde's card is shown to Kim. Kim's card is shown to Kim. Carla's card is shown to Carla. Carla's card is shown to Cora. It is publicly announced that someone picked a red card. It is publicly announced that Cora does not know whether Clyde picked a red card. It is publicly announced that Clyde knows whether or not nobody picked a red card. It is publicly announced that Carla does not know whether Cora picked a red card. It is publicly announced that Kim 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)) ] Agenta knows whether (Agentb knows whether 1)","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":"Clyde can now know whether Kim can know whether Clyde picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clyde","Kim","Carla","Cora"],"index":49901,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973456264,"difficulty":0.0026543736}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adele's card is shown to Gladys. Adele's card is shown to Micheal. 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 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Gladys can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adele","Gladys","Micheal"],"index":32730,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985530972,"difficulty":0.0014469028}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hope's card is shown to Jonathan. Jonathan's card is shown to Virginia. Ashley's card is shown to Ashley. 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 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:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jonathan can now know whether Virginia can know that Hope picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonathan","Virginia","Hope","Ashley"],"index":6777,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9300118089,"difficulty":0.0699881911}
{"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 Troy. Maria'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:3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Daniel can now know that Troy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Troy","Daniel","Maria"],"index":65862,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985247254,"difficulty":0.0014752746}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to Brenda. Erin's card is shown to Erin. 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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Brenda can now know that Brenda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brenda","Erin"],"index":3436,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9853656292,"difficulty":0.0146343708}
{"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 Lisa. Traci's card is shown to John. John's card is shown to Catherine. Lisa's card is shown to Traci. 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. It is publicly announced that John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] Agentb knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"John can now know whether Traci can know that Traci picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","John","Catherine","Traci"],"index":46267,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8955866098,"difficulty":0.1044133902}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Donna 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:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Donna can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Donna","Cindy"],"index":4436,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983778,"difficulty":0.0016222}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Inez's card is shown to Garland. Inez'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 or not everyone picked a red card. It is publicly announced that Garland 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)) ] (Agentb 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)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Inez can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Garland","Inez"],"index":9819,"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). Susan's card is shown to Pauline. Pauline's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Pauline does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Susan can now know that Pauline can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pauline","Susan"],"index":56844,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9846040606,"difficulty":0.0153959394}
{"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 Jill. Bruce's card is shown to Bruce. Bruce's card is shown to Leo. It is publicly announced that someone picked a red card. It is publicly announced that Leo picked a red card. It is publicly announced that Denise knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Bruce can now know that Jill can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jill","Bruce","Denise","Leo"],"index":5132,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
{"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 Joseph. Kimberly's card is shown to Kimberly. 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) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Kimberly can now know whether Joseph can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Kimberly"],"index":31994,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9938588738,"difficulty":0.0061411262}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alisa's card is shown to Alisa. Josephine's card is shown to Alisa. Alisa's card is shown to Josephine. 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) ] (Agenta knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Alisa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alisa","Josephine"],"index":14755,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983550906,"difficulty":0.0016449094}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandon's card is shown to Felicia. Ruth's card is shown to Felicia. Felicia's card is shown to Felicia. It is publicly announced that someone picked a red card. It is publicly announced that Brandon knows whether Ruth picked a red card. It is publicly announced that Felicia picked a black card. It is publicly announced that Brandon knows whether Brandon picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Brandon can now know whether Felicia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brandon","Rodney","Ruth","Felicia"],"index":12584,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6297100186,"difficulty":0.3702899814}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michele's card is shown to Kenneth. Virginia's card is shown to Kenneth. Kenneth's card is shown to Michele. Virginia's card is shown to Michele. Michele's card is shown to Virginia. 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:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know that Virginia can know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Michele","Virginia"],"index":62029,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9588502645,"difficulty":0.0411497355}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacy's card is shown to Terrell. Freddie's card is shown to Stacy. 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:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Terrell can now know that Freddie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terrell","Stacy","Catherine","Freddie"],"index":25534,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943401814,"difficulty":0.0056598186}
{"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 Hallie. Nathan'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:4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nathan can now know whether Hallie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hallie","Nathan","Anna","Richard"],"index":48738,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9585729241,"difficulty":0.0414270759}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Gary. Russell's card is shown to Gary. Russell's card is shown to Evan. 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:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Gary can now know whether Russell picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gary","Evan","Russell"],"index":65682,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7900267839,"difficulty":1.7900267839}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joellen's card is shown to Joellen. Natasha's card is shown to Ken. Joellen's card is shown to Natasha. 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 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:1 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ken can now know that Mitchell can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joellen","Mitchell","Ken","Natasha"],"index":37525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9847352505,"difficulty":0.0152647495}
{"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. Louis's card is shown to Louis. Louis's card is shown to Lois. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Louis can now know that Lois can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Louis","Lois"],"index":63115,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997708201,"difficulty":0.0002291799}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roger's card is shown to Kathryn. Susan's card is shown to Kathryn. Kathryn's card is shown to Roger. Roger's card is shown to Roger. Kathryn'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 Susan 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 (1&2&3))","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":"Roger can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathryn","Roger","Susan"],"index":56806,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848367572,"difficulty":0.0151632428}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwina's card is shown to John. John's card is shown to Janice. 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 Janice 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) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether Edwina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Janice","Edwina"],"index":26731,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8403966427,"difficulty":0.1596033573}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Dennis picked a black card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (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) ] [ ! (1|2) ] 0","hypothesis":"Dennis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dennis","Nancy"],"index":14543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983353019,"difficulty":0.0016646981}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Jesse. Wilfred's card is shown to Jesse. Nancy's card is shown to Wilfred. Jesse's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Wilfred 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) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Nancy can now know whether Wilfred can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Jesse","Wilfred","Richard"],"index":12751,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995449185,"difficulty":0.0004550815}
{"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. Tisha's card is shown to Richard. Richard's card is shown to Erica. Erica's card is shown to Tisha. Tisha's card is shown to Tisha. Tisha'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:1,3 Agentb:1 Agentc:2,3 Agentd:3 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:1,3 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Thomas can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Erica","Tisha","Thomas"],"index":12634,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997755885,"difficulty":0.0002244115}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresa's card is shown to Theresa. Theresa's card is shown to Jose. David's card is shown to David. Jose's card is shown to Morris. It is publicly announced that someone picked a red card. It is publicly announced that Theresa does not know whether Morris 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) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Morris can now know that Theresa can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Theresa","Jose","David","Morris"],"index":30905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998219192,"difficulty":0.001780808}
{"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. Sarah's card is shown to Sarah. 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 whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Sarah can now know that Michael can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Sarah"],"index":44854,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.992739737,"difficulty":0.007260263}
{"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 Angie. Angie's card is shown to Angie. Angie's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Angie 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 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Angie can now know that Richard can know whether Angie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Angie","Kelly"],"index":47221,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8319690824,"difficulty":0.1680309176}
{"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 Sheena. Leroy's card is shown to Sheena. Elizabeth's card is shown to Joe. Joe's card is shown to Joe. Elizabeth's card is shown to Leroy. 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 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sheena can now know whether Joe can know whether Sheena picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Sheena","Joe","Leroy"],"index":44782,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982517362,"difficulty":0.0017482638}
{"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 Sherman. Scott's card is shown to Scott. Sherman's card is shown to Tony. It is publicly announced that someone picked a red card. It is publicly announced that Tony knows whether Sherman 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 whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Sherman can now know that Scott can know whether Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sherman","Scott","Tony"],"index":52813,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8864437938,"difficulty":1.8864437938}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dewey's card is shown to Dewey. Jill's card is shown to Dewey. Jill's card is shown to Jill. Dewey's card is shown to Ralph. Jill's card is shown to Ralph. 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 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:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jill can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dewey","Jill","Ralph"],"index":29690,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Tim. Tim's card is shown to Carla. Tim's card is shown to Phillip. It is publicly announced that someone picked a red card. It is publicly announced that Phillip does not know whether Phillip picked a red card. It is publicly announced that Carla knows whether or not everyone picked a red card. It is publicly announced that Carla 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&2&3))","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":"Phillip can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tim","Carla","Phillip"],"index":56226,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8866236806,"difficulty":0.1133763194}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Nicholas. Nicholas'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 Richard 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 (Agentb knows whether 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":"Nicholas can now know whether Richard can know whether Nicholas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nicholas","Richard"],"index":26462,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981437922,"difficulty":0.0018562078}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandon's card is shown to Jesse. Jesse's card is shown to Brandon. Brandon's card is shown to Brandon. 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. It is publicly announced that Brandon knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Brandon can now know whether Jesse can know that Jesse picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jesse","Brandon"],"index":61416,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9190450907,"difficulty":0.0809549093}
{"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 Amy. Bud's card is shown to Bud. Amy'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 Bud 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 whether 2) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Amy can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amy","Bud","Margaret"],"index":58523,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954564571,"difficulty":0.0045435429}
{"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 Francisco. Michelle's card is shown to Francisco. Joseph's card is shown to Joseph. Michelle's card is shown to Joseph. Francisco's card is shown to Michelle. Joseph's card is shown to Michelle. Michelle's card is shown to Michelle. It is publicly announced that someone picked a red card. It is publicly announced that Michelle picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Michelle can now know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Francisco","Joseph","Michelle"],"index":53567,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7384377718,"difficulty":0.2615622282}
{"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. John's card is shown to Marvin. Marvin's card is shown to Marvin. John's card is shown to Dorothy. Marvin'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 someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"John can now know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Marvin","Dorothy"],"index":22523,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6486126781,"difficulty":0.3513873219}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Marion. Marion's card is shown to Natalie. Natalie's card is shown to Natalie. It is publicly announced that someone picked a red card. It is publicly announced that Marion knows whether Stephen 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) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Marion can now know whether Stephen can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephen","Marion","Natalie"],"index":1409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Peter. Carroll's card is shown to Heather. Heather's card is shown to Heather. 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 that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carroll can now know that Carroll picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peter","Carroll","Heather"],"index":64710,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965033531,"difficulty":0.0034966469}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maynard's card is shown to Yolanda. Maynard's card is shown to Maynard. It is publicly announced that someone picked a red card. It is publicly announced that Yolanda does not know whether or not everyone picked a red card. It is publicly announced that Yolanda does not know whether Yolanda picked a red card. It is publicly announced that Yolanda 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)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 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) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Yolanda can now know whether Yolanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Yolanda","Maynard"],"index":3339,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9929555655,"difficulty":1.9929555655}
{"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. Denise's card is shown to Ronald. Denise's card is shown to Tracy. 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 whether 1)","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":"Ronald can now know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Denise","Ronald","Tracy"],"index":38555,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9965795875,"difficulty":0.0034204125}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curt's card is shown to Martin. Katherine's card is shown to Martin. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that Curt knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Curt can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Curt","Martin","Katherine"],"index":55365,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997523427,"difficulty":0.0002476573}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mabel's card is shown to Alexandra. Carmelo's card is shown to Carmelo. Carmelo's card is shown to Mabel. Alexandra'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:3 Agentb:2 Agentc:2 Agentd: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:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carmelo can now know that Alexandra can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alexandra","Carmelo","Mabel","Justin"],"index":51349,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983729124,"difficulty":0.0016270876}
{"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. Kenneth's card is shown to Charles. Brian's card is shown to Charles. Patrice's card is shown to Kenneth. Charles's card is shown to Brian. Charles's card is shown to Patrice. Kenneth's card is shown to Patrice. Brian's card is shown to Patrice. Patrice's card is shown to Patrice. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Brian 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) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:1 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Patrice can now know whether Brian can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Kenneth","Brian","Patrice"],"index":66581,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997727275,"difficulty":0.0002272725}
{"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 Larry. Larry's card is shown to Jeff. Jeff's card is shown to Jeff. Steven's card is shown to Jeff. Larry'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 Agentb:1,2,3 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:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Larry","Jeff","Steven"],"index":38501,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997269511,"difficulty":0.0002730489}
{"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 Yvonne. Yvonne's card is shown to Stephanie. Stephanie's card is shown to Stephanie. Sarah's card is shown to Stephanie. It is publicly announced that someone picked a red card. It is publicly announced that Sarah picked a black card. It is publicly announced that Sarah picked a black card. It is publicly announced that Yvonne does not know whether Stephanie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Yvonne can now know that Sarah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yvonne","Stephanie","Sarah"],"index":6544,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7144064903,"difficulty":0.2855935097}
{"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 Laurence. 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 Laurence does not know whether or not everyone picked a red card. It is publicly announced that Laurence does not know whether Laurence picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Laurence can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Laurence"],"index":30241,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979332685,"difficulty":0.0020667315}
{"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 James. Oliver's card is shown to Oliver. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Oliver"],"index":67285,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946311712,"difficulty":0.0053688288}
{"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. Ariana's card is shown to Ariana. It is publicly announced that someone picked a red card. It is publicly announced that Bobby does not know whether Bobby picked a red card. It is publicly announced that Marty picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Marty can now know whether Bobby can know that Marty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marty","Bobby","Ariana","Christine"],"index":57139,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7615947127,"difficulty":0.2384052873}
{"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. Dorothy's card is shown to Gary. Kenneth's card is shown to Gary. Jennifer's card is shown to Jennifer. Kenneth's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 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:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Gary can know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Gary","Jennifer","Kenneth"],"index":49302,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8896104097,"difficulty":0.1103895903}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. Frank's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether Angela picked a red card. It is publicly announced that Frank 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 whether (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":"Frank can now know that Angela can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frank","Angela"],"index":37781,"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). Thomas's card is shown to Thomas. Thomas's card is shown to Barbara. James's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Barbara can now know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Barbara","James"],"index":57053,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9812605381,"difficulty":0.0187394619}
{"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 Maria. Penny's card is shown to Maria. Sigrid's card is shown to Penny. Maria's card is shown to Sigrid. It is publicly announced that someone picked a red card. It is publicly announced that Sigrid 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 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Maria can now know that Sigrid can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Penny","Sigrid"],"index":62426,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Minnie's card is shown to Anthony. Minnie's card is shown to Minnie. Minnie's card is shown to Gerardo. 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)) ] Agenta knows that (Agentc 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":"Anthony can now know that Gerardo can know whether Minnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Minnie","Gerardo"],"index":49741,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9715806842,"difficulty":0.0284193158}
{"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 Melissa. Melissa's card is shown to Ofelia. Melissa's card is shown to James. Ofelia'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:2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ofelia can now know that Melissa can know that Ofelia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joann","Melissa","Ofelia","James"],"index":52515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972202778,"difficulty":0.0027797222}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alfred's card is shown to Jose. Alfred's card is shown to Michael. 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:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (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":["Jose","Alfred","Michael"],"index":62702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985095859,"difficulty":0.0014904141}
{"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 Larry. 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 David picked a red card. It is publicly announced that David does not know whether Larry picked a red card. It is publicly announced that David 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) ] (Agentb 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":"Gary can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Gary","David"],"index":50522,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981681108,"difficulty":0.0018318892}
{"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 Robert. Julio's card is shown to Robert. Robert's card is shown to Carrie. Carrie'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:1,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carrie can now know that Eugene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Carrie","Julio","Eugene"],"index":24466,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983897209,"difficulty":0.0016102791}
{"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 Roxanne. Roxanne's card is shown to Joe. Joe's card is shown to Joe. Jessie's card is shown to Jean. Jean's card is shown to Jean. It is publicly announced that 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 everyone 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jessie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roxanne","Jessie","Joe","Jean"],"index":55825,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962332845,"difficulty":0.0037667155}
{"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 Richard. Mark's card is shown to Lacresha. Richard's card is shown to Mark. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 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":"Lacresha can now know that Richard can know whether Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Lacresha","Mark","Sharon"],"index":48146,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7274039984,"difficulty":0.2725960016}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laurie's card is shown to Laurie. Regina's card is shown to Laurie. Regina's card is shown to Regina. It is publicly announced that someone picked a red card. It is publicly announced that Regina does not know whether Laurie 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 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 1) ] 0","hypothesis":"Regina can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Laurie","Regina"],"index":60569,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986178875,"difficulty":0.0013821125}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adriana's card is shown to Charles. Truman's card is shown to Truman. Adriana's card is shown to Truman. Grace's card is shown to Adriana. Grace's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Grace picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Grace can now know whether Adriana can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Truman","Adriana","Grace"],"index":57925,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9470048547,"difficulty":0.0529951453}
{"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 James. Donald's card is shown to Donald. Richard's card is shown to Richard. 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 Richard 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:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Donald","Richard"],"index":1235,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997208714,"difficulty":0.0002791286}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandy's card is shown to Sandy. Maria's card is shown to Sandy. Marie's card is shown to Marie. Sandy's card is shown to Maria. Marie's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Maria picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Sandy can now know whether Marie can know that Marie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sandy","Marie","Maria"],"index":13378,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8750285506,"difficulty":1.8750285506}
{"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 Jeannette. Scott's card is shown to Jeannette. Jose's card is shown to Scott. Anthony's card is shown to Scott. Anthony'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:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeannette can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Jeannette","Scott","Anthony"],"index":54553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985758066,"difficulty":0.0014241934}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glenda's card is shown to Glenda. Glenda's card is shown to Sandy. Sandy's card is shown to Sandy. It is publicly announced that someone picked a red card. It is publicly announced that Sandy knows whether or not nobody picked a red card. It is publicly announced that Sandy knows whether Glenda 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":"Sandy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Glenda","Sandy"],"index":11096,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997726083,"difficulty":0.0002273917}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. Cynthia's card is shown to Cynthia. Susan's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Gregory picked a red card. It is publicly announced that Gregory does not know whether Cynthia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gregory can now know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregory","Cynthia","Susan"],"index":39631,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7719113827,"difficulty":0.2280886173}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephenie's card is shown to Stephenie. Stephenie's card is shown to Grant. Stephenie's card is shown to Terry. Grant's card is shown to Terry. It is publicly announced that someone picked a red card. It is publicly announced that Stephenie 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 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":"Terry can now know that Terry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephenie","Grant","Terry"],"index":50372,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6319549084,"difficulty":0.3680450916}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcelina's card is shown to Dale. Jose's card is shown to Dale. Kim's card is shown to Marcelina. Marcelina's card is shown to Jose. Dale's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Marcelina 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)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kim can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dale","Marcelina","Jose","Kim"],"index":18220,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953898191,"difficulty":0.0046101809}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Traci. Betty's card is shown to Betty. Betty's card is shown to Carl. 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 (Agentb 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":"Traci can now know that Betty can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Traci","Betty","Carl"],"index":61584,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984840751,"difficulty":0.0015159249}
{"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 Jamaal. Eva's card is shown to Jamaal. Deborah's card is shown to Deborah. Eva's card is shown to Deborah. Jamaal's card is shown to Eva. Deborah's card is shown to Eva. Eva's card is shown to Eva. It is publicly announced that someone picked a red card. It is publicly announced that Eva picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Jamaal can now know whether Deborah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jamaal","Deborah","Eva"],"index":41483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6396291256,"difficulty":0.3603708744}
{"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 Sidney. Anthony's card is shown to Anthony. Kelly's card is shown to Anthony. Sidney'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 Agentb:2,3 Agentc:1 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 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kelly can now know whether Anthony can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sidney","Anthony","Kelly"],"index":20356,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997134805,"difficulty":0.0002865195}
{"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 Rose. 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 VALID? [ ! (1|2|3) ] (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":"Helen can now know whether Adam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rose","Helen","Adam"],"index":6431,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.963357389,"difficulty":0.036642611}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Jennifer's card is shown to Carmen. Marguerite's card is shown to Marguerite. Jennifer's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether Carmen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Carmen","Marguerite","Jennifer"],"index":647,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9233222604,"difficulty":0.0766777396}
{"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 Vicky. Vicky's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Vicky knows whether Vicky picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"James can now know that Vicky can know whether Vicky picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vicky","James"],"index":1975,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9185154438,"difficulty":0.0814845562}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Natasha's card is shown to Monica. Teri's card is shown to Natasha. 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) ] Agentb knows whether (Agenta 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":"Monica can now know whether Teri can know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Teri","Monica","Natasha","Kenneth"],"index":48751,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9270102978,"difficulty":0.0729897022}
{"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. Daniel's card is shown to Junior. Junior's card is shown to Junior. Wilma's card is shown to Junior. Junior's card is shown to Wilma. Junior's card is shown to Bruce. Bruce's card is shown to Bruce. 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:2 Agentd:2,4 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:1 Agentb:1,2,3 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that Bruce can know whether Wilma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Junior","Wilma","Bruce"],"index":61736,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5890257955,"difficulty":0.4109742045}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dustin's card is shown to Dustin. It is publicly announced that someone picked a red card. It is publicly announced that Dustin 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 whether (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":"Dustin can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dustin","Andrew"],"index":18222,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9906734824,"difficulty":0.0093265176}
{"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 Gary. Moises's card is shown to Gary. Moises's card is shown to Moises. Gary's card is shown to Deborah. Deborah's card is shown to Deborah. Moises'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 someone picked a red card. It is publicly announced that Moises picked a red card. It is publicly announced that Moises 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 that (Agenta knows that (1|2|3|4))","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":"Deborah can now know that Gary can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Moises","Deborah","Clyde"],"index":22907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997790456,"difficulty":0.0002209544}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemarie's card is shown to Eva. Eva's card is shown to Rosemarie. Rosemarie's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Eva picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Donna 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) ] (Agentc knows that 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":"Rosemarie can now know that Donna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Santiago","Eva","Rosemarie","Donna"],"index":54022,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9330555797,"difficulty":0.0669444203}
{"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 Timothy. Robert's card is shown to Timothy. Timothy'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 Timothy 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":"Robert can now know that Timothy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Timothy","Robert"],"index":61668,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6504498124,"difficulty":1.6504498124}
{"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. Mary's card is shown to Lucas. Lucas's card is shown to Lucas. Rachel's card is shown to Rachel. 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:4 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:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lucas can now know that Mary can know whether Lorraine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Lucas","Lorraine","Rachel"],"index":64736,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.890239656,"difficulty":0.109760344}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelic's card is shown to Angelic. Angelic's card is shown to Katherine. Angelic'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 Angelic picked a red card. It is publicly announced that Katherine does not know whether Katherine 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 (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know that Angelic can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angelic","Katherine","James"],"index":56013,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981904626,"difficulty":0.0018095374}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Estelle's card is shown to Patricia. Susan's card is shown to Estelle. Estelle's card is shown to Estelle. 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 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Susan can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Patricia","Estelle"],"index":44117,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8670428395,"difficulty":0.1329571605}
{"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 Marguerite. Marguerite's card is shown to Thelma. Marguerite's card is shown to Laura. Thelma's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thelma can now know whether Marguerite can know that Thelma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marguerite","Thelma","Laura"],"index":51923,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8637832999,"difficulty":1.8637832999}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernie's card is shown to Dianne. Ernie's card is shown to Roger. 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 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:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Dianne can now know that Ernie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dianne","Roger","Ernie"],"index":28458,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945856929,"difficulty":0.0054143071}
{"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 Kimberly. Kyle's card is shown to Kimberly. Kimberly's card is shown to Laura. Laura's card is shown to Laura. Kyle's card is shown to Laura. Kimberly's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that Laura 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))) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Laura can now know whether Kyle can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","Laura","Kyle"],"index":16602,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9951598048,"difficulty":0.0048401952}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Brian. James's card is shown to Brian. James's card is shown to James. 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 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Brian can now know whether James can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brian","James"],"index":35336,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9733012319,"difficulty":0.0266987681}
{"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 Mary. Mary's card is shown to Joshua. Mary's card is shown to Hugh. 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) ] (Agenta 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) ] [ ! (1&2&3) ] 0","hypothesis":"Mary can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Joshua","Hugh"],"index":9427,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9933425784,"difficulty":0.0066574216}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josh's card is shown to Josh. Joshua's card is shown to Josh. Joshua's card is shown to Joshua. Vonda's card is shown to Joshua. Josh's card is shown to James. Joshua's card is shown to James. Josh's card is shown to Vonda. Vonda's card is shown to Vonda. It is publicly announced that someone picked a red card. It is publicly announced that Josh knows whether Josh picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"James can now know whether Vonda can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josh","Joshua","James","Vonda"],"index":39259,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittany's card is shown to Dennis. Marshall's card is shown to Brittany. Dennis's card is shown to Marshall. Marshall's card is shown to Marshall. It is publicly announced that someone picked a red card. It is publicly announced that Brittany does not know whether Dennis 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) ] (Agentc 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":"Marshall can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Brittany","Marshall"],"index":12365,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986074567,"difficulty":0.0013925433}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwight's card is shown to Sandra. Sandra's card is shown to Dwight. Sandra's card is shown to Cathy. Dwight'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:2 Agentb:1 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:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sandra can now know whether Cathy can know whether Dwight picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Dwight","Cathy"],"index":2283,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989504814,"difficulty":0.0010495186}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Megan. Burton's card is shown to Francis. Francis's card is shown to Francis. It is publicly announced that someone picked a red card. It is publicly announced that Megan does not know whether or not everyone 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)) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Megan can now know whether Burton can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Megan","Burton","Francis"],"index":65009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996830225,"difficulty":0.0003169775}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jackie's card is shown to Sarah. Jackie's card is shown to Jackie. 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)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Sarah can now know that Jackie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sarah","Jackie"],"index":44145,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986227751,"difficulty":0.0013772249}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Velma. Velma's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Dana knows whether Velma picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Velma can now know that Velma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Velma","Dana","Ronald"],"index":52664,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917347431,"difficulty":0.0082652569}
{"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 James. Maire's card is shown to Maire. 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 James does not know whether Maire picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Maire can now know that James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Maire"],"index":40769,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982481003,"difficulty":0.0017518997}
{"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. Thomas's card is shown to Edward. Roosevelt's card is shown to Edward. Janet's card is shown to Thomas. Janet's card is shown to Roosevelt. Roosevelt's card is shown to Roosevelt. 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) ] (Agentc knows that (1&2&3&4))","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":"Janet can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edward","Thomas","Janet","Roosevelt"],"index":1490,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984554052,"difficulty":0.0015445948}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shanda's card is shown to Dale. Shanda's card is shown to Shanda. It is publicly announced that someone picked a red card. It is publicly announced that Dale knows whether Shanda 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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Dale can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dale","Shanda"],"index":51747,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
{"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 Leonard. Leonard's card is shown to Katherine. Katherine's card is shown to Katherine. 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 Agentb:1,2 Agentc: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:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leonard can now know that Katherine can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leonard","Katherine","Kevin","Hang"],"index":3638,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997768998,"difficulty":0.0002231002}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Aaron. Aaron's card is shown to Tony. Gwendolyn's card is shown to Gwendolyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tony can now know that Deborah can know whether Aaron picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Aaron","Tony","Deborah","Gwendolyn"],"index":65605,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6892246604,"difficulty":0.3107753396}
{"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 Dylan. Dylan's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Dylan does not know whether Dylan picked a red card. It is publicly announced that Dylan does not know whether Dylan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dylan can now know that Dylan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dylan","Gary"],"index":43667,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8753803372,"difficulty":0.1246196628}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christa's card is shown to Christa. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Christa picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 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:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Christa can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christa","Juanita","Robert"],"index":38497,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997250438,"difficulty":0.0002749562}
{"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 Ross. Mary's card is shown to Helen. George's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 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:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether Ross can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Ross","Helen","Mary"],"index":40204,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
{"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. Christine's card is shown to Timothy. 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":"Timothy can now know that Christine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Christine","Timothy"],"index":58503,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984773993,"difficulty":0.0015226007}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqueline's card is shown to James. Eldon's card is shown to Eldon. Paul's card is shown to Eldon. 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 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eldon can now know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Eldon","Jacqueline","Paul"],"index":49792,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8411147594,"difficulty":1.8411147594}
{"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. Charles's card is shown to Evelyn. Evelyn's card is shown to Lezlie. Lezlie's card is shown to Lezlie. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Lezlie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Debra can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Debra","Charles","Evelyn","Lezlie"],"index":13346,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997196794,"difficulty":0.0002803206}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Blanche's card is shown to Carroll. Carroll's card is shown to Blanche. Blanche'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 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carroll can now know whether Blanche can know whether Blanche picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carroll","Blanche","Brian"],"index":66964,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9922661185,"difficulty":0.0077338815}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mandy's card is shown to Mandy. Mary's card is shown to Mandy. Rodney's card is shown to Mandy. Del's card is shown to Rodney. 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 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mandy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Del","Mandy","Mary","Rodney"],"index":4385,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985204339,"difficulty":0.0014795661}
{"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. David's card is shown to Paul. Paul's card is shown to David. Raymond's card is shown to David. 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:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Raymond can now know that Paul can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Raymond","David"],"index":37926,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9722161889,"difficulty":0.0277838111}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sam's card is shown to Rodney. Joanne's card is shown to Sam. Sam's card is shown to Joanne. It is publicly announced that someone picked a red card. It is publicly announced that Rodney knows whether someone picked a red card. It is publicly announced that Sam does not know whether Rodney 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|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Sam can now know that Sam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rodney","Sam","Joanne"],"index":3942,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8127759099,"difficulty":0.1872240901}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nikki's card is shown to Ruth. Ruth's card is shown to Nikki. Nikki's card is shown to Nikki. It is publicly announced that someone picked a red card. It is publicly announced that Ruth knows whether Ruth 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 (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ruth can now know whether Nikki can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ruth","Nikki"],"index":20588,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995234013,"difficulty":0.0004765987}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dave's card is shown to Robert. Alvin's card is shown to Robert. Dave's card is shown to Alvin. It is publicly announced that someone picked a red card. It is publicly announced that Dave does not know whether Robert 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 2) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dave can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dave","Robert","Alvin"],"index":33430,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9853643775,"difficulty":0.0146356225}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gladys's card is shown to Anthony. Anthony'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 Anthony does not know whether or not everyone picked a red card. It is publicly announced that Gladys does not know whether Robert 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&2&3)) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Anthony can now know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Gladys","Robert"],"index":26698,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9872729182,"difficulty":1.9872729182}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to Donald. Connie's card is shown to Connie. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether Donald 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) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Donald can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Donald","Connie"],"index":20349,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997193217,"difficulty":0.0002806783}
{"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 Paula. Cathy's card is shown to Paula. Paula's card is shown to Nancy. Stephanie's card is shown to Cathy. It is publicly announced that someone picked a red card. It is publicly announced that Paula does not know whether Nancy picked a red card. It is publicly announced that Nancy does not know whether Nancy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Paula can now know that Stephanie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paula","Stephanie","Nancy","Cathy"],"index":239,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9838543534,"difficulty":0.0161456466}
{"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 Amber. Amber's card is shown to Dora. Dora's card is shown to Dora. Amber's card is shown to David. Dora's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Dora knows whether Dora picked a red card. It is publicly announced that Amber does not know whether Dora 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) ] (Agentc 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":"David can now know that Amber picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amber","Dora","David"],"index":38060,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9839443564,"difficulty":0.0160556436}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Dorothy. Brian's card is shown to Dorothy. Angela's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Angela 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 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":"Angela can now know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Angela","Brian"],"index":11266,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6992571354,"difficulty":1.6992571354}
{"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 Shawn. Shawn's card is shown to Burton. 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 Burton 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) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Burton can now know whether Shawn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shawn","Burton","Paul"],"index":41454,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9739708304,"difficulty":0.0260291696}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilbur's card is shown to Roberta. Aaron's card is shown to Roberta. Sandra's card is shown to Sandra. Roberta's card is shown to Wilbur. Sandra's card is shown to Wilbur. Roberta's card is shown to Aaron. It is publicly announced that someone picked a red card. It is publicly announced that Wilbur does not know whether Wilbur picked a red card. It is publicly announced that Wilbur does not know whether Wilbur 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 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":"Aaron can now know whether Sandra can know that Aaron picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roberta","Sandra","Wilbur","Aaron"],"index":11775,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.914177537,"difficulty":0.085822463}
{"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. Tricia's card is shown to Christopher. Paul's card is shown to Christopher. Christopher's card is shown to Joseph. Tricia's card is shown to Joseph. 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:1,3,4 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that Joseph can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Joseph","Tricia","Paul"],"index":22890,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974822402,"difficulty":0.0025177598}
{"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 Cassondra. Beverly's card is shown to Cassondra. Linda's card is shown to Carol. Cassondra's card is shown to Carol. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc: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:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cassondra can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Cassondra","Carol","Beverly"],"index":17104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clayton's card is shown to Alvin. Charles's card is shown to Alvin. Alvin's card is shown to Stephanie. Alvin's card is shown to Clayton. Stephanie's card is shown to Charles. Clayton'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:3,4 Agentb:1 Agentc:1 Agentd:2,3 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 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stephanie can now know that Charles can know whether Clayton picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alvin","Stephanie","Clayton","Charles"],"index":50736,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6507501602,"difficulty":1.6507501602}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Barbara. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know whether Rosa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosa","Barbara","Richard"],"index":26483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997677207,"difficulty":0.0002322793}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roberta's card is shown to David. Roberta's card is shown to Jocelyn. Jocelyn's card is shown to Roberta. It is publicly announced that someone picked a red card. It is publicly announced that Roberta picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"David can now know that Roberta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Jocelyn","Roberta"],"index":65487,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6641392708,"difficulty":0.3358607292}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lane's card is shown to Lane. Anna's card is shown to Lane. Sarah's card is shown to Lane. Anna's card is shown to Ruth. Sarah's card is shown to Ruth. Anna's card is shown to Anna. Sarah's card is shown to Anna. Lane's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Ruth knows whether or not everyone picked a red card. It is publicly announced that Sarah picked a black card. It is publicly announced that Lane picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Lane can now know whether Ruth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lane","Ruth","Anna","Sarah"],"index":35168,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997768998,"difficulty":0.0002231002}
{"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 Jean. Victoria's card is shown to Jean. Thomas's card is shown to Jean. Jaime's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Victoria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Jean can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jean","Victoria","Jaime","Thomas"],"index":36201,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985230565,"difficulty":0.0014769435}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandon's card is shown to Arthur. Arthur's card is shown to Arthur. Betty's card is shown to Arthur. Brandon's card is shown to Betty. Patrick's card is shown to Betty. Patrick's card is shown to Patrick. It is publicly announced that someone picked a red card. It is publicly announced that Patrick 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 ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Arthur can now know that Betty can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandon","Arthur","Betty","Patrick"],"index":21892,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997166991,"difficulty":0.0002833009}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to William. William's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether Jeffrey picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jeffrey can now know that William can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Jeffrey"],"index":39296,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9268274903,"difficulty":0.0731725097}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Pamela. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Pamela 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 1) ] (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) ] 0","hypothesis":"Pamela can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Pamela","Daniel"],"index":21306,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998428762,"difficulty":0.001571238}
{"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 Ashley. Kenneth's card is shown to Ashley. Kenneth's card is shown to Maria. Thomas's card is shown to Maria. Kenneth's card is shown to Kenneth. Maria's card is shown to Thomas. Thomas's card is shown to Thomas. 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 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kenneth can now know that Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ashley","Maria","Kenneth","Thomas"],"index":24692,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7281561494,"difficulty":0.2718438506}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Christopher. Barbara's card is shown to Barbara. Jason's card is shown to Barbara. Christopher'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 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Jason can know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Barbara","Jason"],"index":66320,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9037210345,"difficulty":0.0962789655}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frederick's card is shown to Elizabeth. Imogene's card is shown to Elizabeth. Imogene's card is shown to Frederick. Elizabeth's card is shown to Daniel. Imogene's card is shown to Imogene. 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 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":"Elizabeth can now know whether Imogene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Frederick","Daniel","Imogene"],"index":54552,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8640942574,"difficulty":0.1359057426}
{"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 Jessica. 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: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":"Jessica can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Monica","Matthew","Leonard"],"index":61310,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997683167,"difficulty":0.0002316833}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Seth's card is shown to James. James's card is shown to Timothy. Timothy's card is shown to Debra. James's card is shown to Seth. Seth's card is shown to Seth. It is publicly announced that someone picked a red card. It is publicly announced that Debra does not know whether Debra picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb: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 4)","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":"Seth can now know that Seth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Timothy","Debra","Seth"],"index":60043,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6619893909,"difficulty":0.3380106091}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reginald's card is shown to Reginald. Kyle's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that Kyle does not know whether Reginald 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 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":"Kyle can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Reginald","Kyle"],"index":55095,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Essie's card is shown to Essie. Irene's card is shown to Essie. Daniel's card is shown to Essie. Essie's card is shown to Irene. Daniel's card is shown to Irene. Irene's card is shown to Daniel. Daniel's card is shown to Alejandro. Alejandro's card is shown to Alejandro. 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:1,3 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,3 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Essie can now know whether Irene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Essie","Irene","Daniel","Alejandro"],"index":60693,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5824351311,"difficulty":1.5824351311}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Richard. Richard'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 Roy does not know whether James 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 3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Richard can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Roy","James","Fred"],"index":20248,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997187257,"difficulty":0.0002812743}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Alice. 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 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Alice","Linda","Avery"],"index":47646,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986547232,"difficulty":0.0013452768}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Joanne. Joanne's card is shown to Maria. Maria's card is shown to Maria. Maria's card is shown to Alice. 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 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:1,2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know that Catherine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joanne","Maria","Alice","Catherine"],"index":4222,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983199239,"difficulty":0.0016800761}
{"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. Effie's card is shown to James. Pauline's card is shown to Pauline. James's card is shown to Effie. It is publicly announced that someone picked a red card. It is publicly announced that Pauline does not know whether James 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) ] Agentb 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":"Pauline can now know whether James can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Pauline","Effie"],"index":60525,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996960163,"difficulty":0.0003039837}
{"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. Erin's card is shown to Sharon. Beatrice's card is shown to Beatrice. Sharon's card is shown to Erin. Erin's card is shown to Erin. 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) ] (Agentc knows that (~(1|2|3)))","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":"Erin can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Beatrice","Erin"],"index":57415,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983496666,"difficulty":0.0016503334}
{"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 Penny. Jason's card is shown to Martin. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Martin knows whether Robert picked a red card. It is publicly announced that Jason does not know whether Penny 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) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Martin can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Penny","Jason","Martin","Robert"],"index":11592,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6961813569,"difficulty":0.3038186431}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vera's card is shown to Vera. Vera's card is shown to Diane. Diane's card is shown to Diane. Diane's card is shown to Gail. Gail's card is shown to Gail. 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:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vera","Diane","Barbara","Gail"],"index":17379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8948226571,"difficulty":0.1051773429}
{"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 Joan. Leon's card is shown to Joan. Sherri's card is shown to Leon. 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 that (Agenta 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":"Leon can now know that Joan can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joan","Leon","Sherri"],"index":18019,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.98451823,"difficulty":0.01548177}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Todd. Todd's card is shown to Timothy. Timothy's card is shown to Timothy. Todd's card is shown to Darrin. Darrin's card is shown to Darrin. It is publicly announced that someone picked a red card. It is publicly announced that Todd 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:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Todd can now know whether Todd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Todd","Timothy","Darrin"],"index":23420,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9911109209,"difficulty":0.0088890791}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cecelia's card is shown to Jame. Joe's card is shown to Joe. Cecelia's card is shown to Cecelia. It is publicly announced that someone picked a red card. It is publicly announced that Cecelia does not know whether Joe picked a red card. It is publicly announced that Joe does not know whether Cecelia 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 (Agentb knows that 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":"Cecelia can now know whether Joe can know that Jame picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jame","Joe","Cecelia"],"index":63738,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9571020603,"difficulty":0.0428979397}
{"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 Earl. Brian's card is shown to Charles. Betty'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 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc: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:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earl","Betty","Charles","Brian"],"index":9214,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993963778,"difficulty":0.006036222}
{"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 Lena. Michael's card is shown to Ian. Lena's card is shown to Beverly. Beverly's card is shown to Beverly. 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) ] Agentc knows that (Agenta knows that 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":"Michael can now know that Lena can know that Beverly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lena","Ian","Michael","Beverly"],"index":1855,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978393316,"difficulty":0.0021606684}
{"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 Allen. Charles's card is shown to Allen. Allen's card is shown to Raymundo. Allen's card is shown to Karen. Raymundo's card is shown to Charles. Karen'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:3,4 Agentb:1 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymundo can now know whether Charles can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allen","Raymundo","Karen","Charles"],"index":58422,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9935147762,"difficulty":0.0064852238}
{"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 Patricia. Margie's card is shown to Patricia. Samuel's card is shown to Patricia. Patricia's card is shown to Margie. Cynthia's card is shown to Margie. Samuel's card is shown to Margie. Cynthia's card is shown to Samuel. 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:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know that Samuel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Cynthia","Margie","Samuel"],"index":14043,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979896545,"difficulty":0.0020103455}
{"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 Dana. Mary's card is shown to Dana. Christopher's card is shown to Christopher. Mary's card is shown to Christopher. Mary's card is shown to Alice. Christopher's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether Christopher 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) ] Agentc knows that (Agentd 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":"Alice can now know that Mary can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dana","Christopher","Alice","Mary"],"index":26198,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.952221632,"difficulty":0.047778368}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Carolyn. Carolyn'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 someone picked a red card. It is publicly announced that Carolyn picked a red card. It is publicly announced that Jose picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] 0","hypothesis":"Jose can now know that Carolyn can know whether Jose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carolyn","Jose"],"index":4643,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9727957845,"difficulty":0.0272042155}
{"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 Bobby. Lucien's card is shown to Bobby. Richard's card is shown to Bobby. Lucien's card is shown to Lucien. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Lucien does not know whether Bobby 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 1) ] (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 1) ] 0","hypothesis":"Lucien can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bobby","Lucien","Richard"],"index":22254,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984752536,"difficulty":0.0015247464}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to William. Johnnie's card is shown to William. William's card is shown to Shirley. Shirley's card is shown to Shirley. Johnnie's card is shown to Shirley. William's card is shown to Johnnie. It is publicly announced that someone picked a red card. It is publicly announced that Shirley 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))) ] Agenta knows that (Agentc knows whether 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) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"William can now know that Johnnie can know whether Johnnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Shirley","Johnnie"],"index":19354,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9711692929,"difficulty":1.9711692929}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Ruby. Andrea's card is shown to Ruby. Ruby's card is shown to Bradley. Andrea's card is shown to Bradley. Bradley's card is shown to Andrea. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 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:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bradley can now know whether Ruby can know that Ruby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Bradley","Andrea"],"index":566,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7936102748,"difficulty":0.2063897252}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristopher's card is shown to Mary. Kristopher's card is shown to Lela. Candis's card is shown to Lela. Lela's card is shown to Kristopher. Lela's card is shown to Candis. 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) ] (Agenta knows that 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":"Mary can now know that Lela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Lela","Kristopher","Candis"],"index":17819,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980169535,"difficulty":0.0019830465}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rolando's card is shown to Rolando. Rolando's card is shown to Phillip. Katherine's card is shown to Phillip. Phillip's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that Rolando knows 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) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Katherine can now know that Phillip picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rolando","Phillip","Katherine"],"index":63288,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8491322994,"difficulty":0.1508677006}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Artie's card is shown to Donald. Artie's card is shown to Artie. 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 Artie 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)) ] Agentb knows that (Agenta knows whether 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":"Artie can now know that Donald can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donald","Artie"],"index":52308,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9548256397,"difficulty":0.0451743603}
{"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 Nathaniel. Jeannetta's card is shown to Jeannetta. Christopher's card is shown to Jeannetta. Nathaniel's card is shown to Christopher. 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) ] (Agentb knows whether (1|2|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":"Jeannetta can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nathaniel","Jeannetta","Christopher"],"index":53194,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997733235,"difficulty":0.0002266765}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Wayne. William's card is shown to Wayne. Gregory's card is shown to Gregory. William's card is shown to Gregory. Wayne'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) ] Agentb knows that (Agentc knows whether (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":"Gregory can now know that William can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wayne","Gregory","William"],"index":47588,"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). Charles's card is shown to Charles. Charles's card is shown to Darron. William's card is shown to Darron. 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 that 3)","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":"Leah can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Leah","William","Darron"],"index":9147,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981102943,"difficulty":0.0018897057}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverlee's card is shown to Beverlee. Beverlee's card is shown to Charles. Beverlee's card is shown to Antoinette. It is publicly announced that someone picked a red card. It is publicly announced that Antoinette does not know whether or not everyone picked a red card. It is publicly announced that Beverlee picked a red card. It is publicly announced that Charles does not know whether Charles picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Beverlee can now know that Antoinette can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Beverlee","Charles","Antoinette"],"index":35842,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982066154,"difficulty":0.0017933846}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Norman. Craig's card is shown to Craig. Norman's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Norman picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"William can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norman","Craig","William","Terry"],"index":23705,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9509490728,"difficulty":1.9509490728}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lanette's card is shown to Lanette. Kenneth's card is shown to Lanette. Lanette'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 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 that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Lanette can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lanette","Kenneth"],"index":33337,"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). Stephen's card is shown to Brett. Brett's card is shown to Ann. Stephen's card is shown to Ann. 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 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:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brett can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Homer","Brett","Ann","Stephen"],"index":65516,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997233748,"difficulty":0.0002766252}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peggy's card is shown to Jimmy. Peggy's card is shown to Donald. Sandra's card is shown to Sandra. Donald's card is shown to Peggy. Sandra's card is shown to Peggy. It is publicly announced that someone picked a red card. It is publicly announced that Sandra does not know whether Donald picked a red card. It is publicly announced that Jimmy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Sandra can now know whether Donald can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jimmy","Donald","Sandra","Peggy"],"index":40777,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9957980514,"difficulty":0.0042019486}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. Eva's card is shown to Eva. Gabrielle's card is shown to Eva. Cindy's card is shown to Gabrielle. 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 whether (Agentb knows that 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":"Cindy can now know whether Eva can know that Gabrielle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cindy","Eva","Gabrielle"],"index":33975,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8330398798,"difficulty":1.8330398798}
{"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 Charles. Bill's card is shown to Bill. 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 Bill does not know whether Charles 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 1) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Bill can now know whether Charles can know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Bill"],"index":16200,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.992102325,"difficulty":0.007897675}
{"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 Ashleigh. Larry's card is shown to Renea. Vickie's card is shown to Renea. Renea's card is shown to Vickie. 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 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know that Renea can know whether Renea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Ashleigh","Renea","Vickie"],"index":35120,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8503804803,"difficulty":1.8503804803}
{"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. Danielle's card is shown to Steven. Steven's card is shown to Nathan. It is publicly announced that someone picked a red card. It is publicly announced that Nathan does not know whether Nathan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nathan can now know whether Danielle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danielle","Steven","Nathan"],"index":14827,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6722883582,"difficulty":0.3277116418}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gilbert's card is shown to Gloria. Gloria's card is shown to Gilbert. Gilbert's card is shown to Gilbert. Gilbert'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:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gilbert can now know that Jennifer can know whether Gloria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Gilbert","Jennifer"],"index":46575,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6892079711,"difficulty":0.3107920289}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Mattie. Jill's card is shown to Mattie. Eugene's card is shown to Mattie. Eugene's card is shown to Jill. Jill's card is shown to Eugene. 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:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","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":"Mattie can now know whether Mattie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Mattie","Jill","Eugene"],"index":3473,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9585621953,"difficulty":1.9585621953}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leah's card is shown to Gilberto. Leah's card is shown to Leah. It is publicly announced that someone picked a red card. It is publicly announced that Leah does not know whether or not everyone picked a red card. It is publicly announced that Gilberto 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 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)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Gilberto can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gilberto","Leah"],"index":59650,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.945972085,"difficulty":1.945972085}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shawn's card is shown to Steve. Tristan's card is shown to Steve. Steve's card is shown to Shawn. Shawn's card is shown to Shawn. Tristan's card is shown to Shawn. Shawn's card is shown to Jarrod. Tristan's card is shown to Jarrod. It is publicly announced that someone picked a red card. It is publicly announced that Jarrod knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Steve can now know that Jarrod can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steve","Shawn","Jarrod","Tristan"],"index":49242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985584617,"difficulty":0.0014415383}
{"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 Christopher. Ty's card is shown to Christopher. Christopher's card is shown to Ty. It is publicly announced that someone picked a red card. It is publicly announced that Ty knows whether or not everyone picked a red card. It is publicly announced that Christopher 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) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Ty can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Ty"],"index":47444,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958533049,"difficulty":0.0041466951}
{"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 Theresa. Theresa's card is shown to Elaine. Elaine's card is shown to Elaine. Theresa's card is shown to Martin. Elaine's card is shown to Martin. Martin'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:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elaine can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Theresa","Elaine","Martin"],"index":53726,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985167384,"difficulty":0.0014832616}
{"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 Marvin. Renda's card is shown to Marvin. Renda's card is shown to Renda. Pamela's card is shown to Pamela. 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) ] Agentc knows whether (Agentb knows whether 2)","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":"Pamela can now know whether Renda can know whether Renda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marvin","Renda","Pamela"],"index":20453,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9914668798,"difficulty":0.0085331202}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evan's card is shown to Terrence. James's card is shown to Gerald. Evan's card is shown to Evan. 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 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:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terrence can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Terrence","Gerald","James","Evan"],"index":40720,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771893,"difficulty":0.000228107}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Pamela. Pamela's card is shown to Pamela. Terry's card is shown to Pamela. Anthony's card is shown to Terry. Pamela's card is shown to Stacy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 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:1,2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pamela can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Pamela","Terry","Stacy"],"index":51229,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983483553,"difficulty":0.0016516447}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Helen. James's card is shown to James. James's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether 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 that (Agentb knows that (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":"John can now know that James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","James","John"],"index":10238,"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). Mark's card is shown to Mark. Mark's card is shown to Jessica. It is publicly announced that someone picked a red card. It is publicly announced that Willie does not know whether or not everyone picked a red card. It is publicly announced that Willie does not know whether or not everyone picked a red card. It is publicly announced that Willie knows whether Mark 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 (1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":3,"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 (1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Willie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Willie","Jessica"],"index":61118,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9479308724,"difficulty":1.9479308724}
{"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 Manuel. David's card is shown to Manuel. David's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Manuel can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Manuel","Richard","David"],"index":8395,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983065128,"difficulty":0.0016934872}
{"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 David. Amanda's card is shown to Ann. Margaret's card is shown to Ann. David's card is shown to Amanda. Margaret's card is shown to Amanda. Margaret's card is shown to Margaret. 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:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know whether Amanda can know that Amanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Ann","Amanda","Margaret"],"index":10348,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7412679195,"difficulty":0.2587320805}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Isabelle's card is shown to Danny. It is publicly announced that someone picked a red card. It is publicly announced that Danny knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Danny can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Danny","Isabelle"],"index":1498,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983522892,"difficulty":0.0016477108}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dustin's card is shown to Dustin. Dustin's card is shown to Ricky. It is publicly announced that someone picked a red card. It is publicly announced that Dustin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dustin can now know whether Ricky can know whether Dustin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dustin","Ricky","Michael"],"index":41550,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981160164,"difficulty":0.0018839836}
{"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 Jane. Lauri's card is shown to Lauri. Christina's card is shown to Christina. Jane's card is shown to Angelo. Christina's card is shown to Angelo. 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 that 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":"Angelo can now know that Christina can know that Angelo picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jane","Lauri","Christina","Angelo"],"index":14413,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978708029,"difficulty":0.0021291971}
{"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 Ashley. Harry's card is shown to Ashley. Ashley's card is shown to Harry. Mark's card is shown to Bella. Harry's card is shown to Bella. 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:2 Agentd:1,3 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:1,3 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bella can now know that Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Ashley","Harry","Bella"],"index":67309,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978193045,"difficulty":0.0021806955}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Branden's card is shown to Miguel. Miguel's card is shown to Branden. Miguel's card is shown to Juanita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (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":"Miguel can now know whether Juanita can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Miguel","Branden","Juanita"],"index":56593,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9253015518,"difficulty":0.0746984482}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zoe's card is shown to Zoe. Sara's card is shown to Zoe. Timothy's card is shown to Sara. Zoe's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Timothy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 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:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know that Zoe can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Zoe","Sara","Timothy"],"index":22788,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
{"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 Willodean. David's card is shown to Virgie. Willodean's card is shown to Virgie. Virgie's card is shown to Virgie. 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) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Willodean can now know that David can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Willodean","Virgie"],"index":53296,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7134512067,"difficulty":0.2865487933}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Judith. Diane's card is shown to Diane. Donna's card is shown to Diane. Judith'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 (Agentc 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":"Judith can now know that Donna can know that Judith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Judith","Diane","Donna"],"index":48410,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973968267,"difficulty":0.0026031733}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Wanda. Robert's card is shown to Wanda. William's card is shown to Robert. Wanda'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 Robert 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 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) ] [ ! ~(2) ] 0","hypothesis":"William can now know that Robert can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wanda","Robert","William"],"index":65046,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997842908,"difficulty":0.0002157092}
{"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 Herbert. Herbert's card is shown to Melinda. Herbert's card is shown to Bobby. Melinda's card is shown to Bobby. Bobby'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 Herbert 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) ] (Agentc 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":"Bobby can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Herbert","Melinda","Bobby","Richard"],"index":30077,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963328838,"difficulty":0.0036671162}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that Ashley knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Ashley can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ashley","Robert"],"index":38809,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996995926,"difficulty":0.0003004074}
{"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. Michael's card is shown to Charles. Charles's card is shown to Michael. Michael's card is shown to Michael. Sarah's card is shown to Michael. Sarah's card is shown to Kelly. Charles's card is shown to Sarah. Kelly'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:1,2 Agentb:1,2,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know that Michael can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Michael","Kelly","Sarah"],"index":52713,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971982241,"difficulty":0.0028017759}
{"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. Irma's card is shown to Theresa. James's card is shown to Angel. Irma's card is shown to Angel. 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:1,2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Irma can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Irma","Theresa","Angel"],"index":16880,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
{"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 Arnold. Daniel's card is shown to Daniel. Jerry's card is shown to Daniel. Arnold's card is shown to Jerry. Daniel's card is shown to Jerry. Jerry's card is shown to Jerry. Daniel's card is shown to Rickey. 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:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Arnold can now know that Rickey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arnold","Daniel","Jerry","Rickey"],"index":61147,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9740575552,"difficulty":0.0259424448}
{"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 Kelly. Lori's card is shown to Kelly. Lori's card is shown to Maria. Kelly's card is shown to Lori. 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) ] (Agentb 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":"Maria can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kelly","Maria","Lori"],"index":13725,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983525276,"difficulty":0.0016474724}
{"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 Terry. Richard's card is shown to Terry. Shannon's card is shown to Richard. Terry's card is shown to Shannon. Richard's card is shown to Shannon. 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:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shannon can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terry","Richard","Shannon"],"index":19343,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983242154,"difficulty":0.0016757846}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clifford's card is shown to Clifford. Ruth's card is shown to Clifford. Joshua's card is shown to Wanda. Clifford's card is shown to Ruth. Wanda's card is shown to Joshua. Ruth's card is shown to Joshua. 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) ] Agenta knows whether (Agentc knows whether 4)","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":"Clifford can now know whether Ruth can know whether Joshua picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clifford","Wanda","Ruth","Joshua"],"index":39233,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983112812,"difficulty":0.0016887188}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ebony's card is shown to Ebony. Sylvia's card is shown to Sylvia. Sylvia's card is shown to Bradley. 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) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bradley can now know whether Ebony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ebony","Sylvia","Bradley"],"index":19820,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6340808868,"difficulty":1.6340808868}
{"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. Dennis's card is shown to Beth. Beth's card is shown to Dennis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 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 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joe can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joe","Beth","Dennis"],"index":11484,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985253215,"difficulty":0.0014746785}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phyllis's card is shown to Tom. Paul's card is shown to Tom. Phyllis's card is shown to Phyllis. 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 Tom picked a red card. It is publicly announced that Phyllis knows whether Phyllis picked a red card. It is publicly announced that Phyllis does not know whether or not everyone picked a red card. It is publicly announced that Paul knows whether Phyllis 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) ] (Agentb knows that 2)","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":"Phyllis can now know that Phyllis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tom","Phyllis","Paul"],"index":39165,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7454686165,"difficulty":0.2545313835}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Jonathan. Santo's card is shown to Santo. Anton's card is shown to Santo. Santo's card is shown to Anton. Santo's card is shown to Gene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Santo can now know whether Gene can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonathan","Santo","Anton","Gene"],"index":22015,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9934409261,"difficulty":0.0065590739}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brad's card is shown to Brad. Cody's card is shown to Tanya. It is publicly announced that someone picked a red card. It is publicly announced that Cody does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brad can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cody","Brad","Tanya"],"index":65210,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980583787,"difficulty":0.0019416213}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frederick's card is shown to Frederick. Frederick's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Frederick does not know whether John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"John can now know that Frederick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Frederick","John"],"index":20151,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9933251739,"difficulty":1.9933251739}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathy's card is shown to Kathy. Donna's card is shown to Kathy. Kathy's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Donna does not know whether Donna picked a red card. It is publicly announced that Kathy knows whether Donna picked a red card. It is publicly announced that Kathy 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Kathy can now know whether Donna can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathy","Donna"],"index":39200,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995476604,"difficulty":0.0004523396}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Winifred's card is shown to Pamela. Pamela's card is shown to Winifred. Winifred's card is shown to Winifred. 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)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Winifred can now know that Pamela can know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pamela","Winifred"],"index":54104,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997168839,"difficulty":0.002831161}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nina's card is shown to Roger. Roger's card is shown to Nina. 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 Nina knows whether or not nobody picked a red card. It is publicly announced that Roger knows whether Nina 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) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Roger can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roger","Nina"],"index":24480,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997186065,"difficulty":0.0002813935}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Roscoe. Marie's card is shown to Roscoe. Marie's card is shown to Kevin. Kevin's card is shown to Marie. 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: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:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kevin can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roscoe","Kevin","Marie"],"index":8736,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942066669,"difficulty":0.0057933331}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julio's card is shown to Nancy. Jamika's card is shown to Nancy. Nancy's card is shown to Julio. Julio's card is shown to Julio. Nancy's card is shown to Jamika. Jamika's card is shown to Jamika. It is publicly announced that someone picked a red card. It is publicly announced that Jamika knows whether Julio picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Nancy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Julio","Jamika"],"index":32799,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998595655,"difficulty":0.001404345}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Dawn. Scott's card is shown to Scott. Daniel's card is shown to Scott. 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:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Dawn can now know that Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dawn","Scott","Daniel"],"index":49677,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951020479,"difficulty":0.0048979521}
{"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 Sally. Sally's card is shown to Sally. 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 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Timothy can now know that Crystal picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Janet","Crystal","Sally"],"index":22709,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983514547,"difficulty":0.0016485453}
{"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. Raymond's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Raymond knows whether someone picked a red card. It is publicly announced that Deborah knows whether Deborah 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) ] (Agenta 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":"Raymond can now know whether Deborah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Raymond","Deborah"],"index":48546,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6987192631,"difficulty":1.6987192631}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dean's card is shown to Dean. Carroll's card is shown to Dean. Barbara's card is shown to Dean. Dean's card is shown to Brenda. Carroll's card is shown to Brenda. Barbara'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:1,3,4 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brenda can now know that Dean can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dean","Brenda","Carroll","Barbara"],"index":53217,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997166991,"difficulty":0.0002833009}
{"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 John. John's card is shown to Marlene. Willie's card is shown to Willie. 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 that (Agentb knows that (~(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":"John can now know that Marlene can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Marlene","Willie","Doris"],"index":56801,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984537363,"difficulty":0.0015462637}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Milton. Ronnie's card is shown to Ronnie. Patricia's card is shown to Ronnie. Milton's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Milton does not know whether Milton picked a red card. It is publicly announced that Ronnie picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Ronnie can now know that Milton can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Milton","Ronnie","Patricia"],"index":55440,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985826015,"difficulty":0.0014173985}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bennie's card is shown to Bennie. Benita's card is shown to Bennie. Bennie's card is shown to Benita. Benita's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Benita 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 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Bennie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bennie","Benita","Cynthia"],"index":37289,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
{"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 Pat. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether Pat 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 that (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":"Pat can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Pat","Larry"],"index":53706,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laverne's card is shown to Laverne. Laverne's card is shown to Lucas. Lucas's card is shown to Lucas. It is publicly announced that someone picked a red card. It is publicly announced that Laverne knows whether or not nobody picked a red card. It is publicly announced that Laverne knows whether Lucas picked a red card. It is publicly announced that Lucas knows whether or not nobody picked a red card. It is publicly announced that Lucas knows whether Lucas 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 whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1&2))","n_announcements":4,"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) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lucas can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Laverne","Lucas"],"index":21873,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6809573174,"difficulty":1.6809573174}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olivia's card is shown to James. James's card is shown to Olivia. James's card is shown to Miguel. Olivia's card is shown to Miguel. It is publicly announced that someone picked a red card. It is publicly announced that Miguel does not know whether Miguel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Olivia can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Olivia","Miguel"],"index":24591,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771893,"difficulty":0.000228107}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Linda. Eugene's card is shown to Jennifer. Jennifer's card is shown to Angelina. Linda'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:4 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Jennifer","Angelina","Eugene"],"index":29364,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9797410965,"difficulty":1.9797410965}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Jerry. Kimberly's card is shown to Jerry. Kimberly's card is shown to Kimberly. 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 (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Jerry can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jerry","Kimberly"],"index":47877,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Irwin. Irwin's card is shown to Lawrence. 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 Lawrence 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 whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Lawrence can now know whether Irwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Irwin","Lawrence"],"index":64272,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.674826622,"difficulty":0.325173378}
{"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 William. Andrea's card is shown to Andrea. Andrea's card is shown to Curtis. 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) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Curtis can now know whether William can know that Andrea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Andrea","Curtis"],"index":39115,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9733960032,"difficulty":0.0266039968}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wendy's card is shown to Jared. Michael's card is shown to Wendy. 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:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Wendy can now know that Yun picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jared","Wendy","Yun","Michael"],"index":41788,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9950535893,"difficulty":0.0049464107}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. 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 whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Barbara can now know whether Rita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Barbara","Rita"],"index":742,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9952138662,"difficulty":0.0047861338}
{"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 Angelo. Ronald's card is shown to Ronald. Juanita's card is shown to Ronald. Mary's card is shown to Ronald. Ronald'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 Angelo does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 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:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Ronald can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angelo","Ronald","Juanita","Mary"],"index":29790,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953130484,"difficulty":0.0046869516}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Ellen. Randall's card is shown to Randall. Ellen's card is shown to Janice. Randall's card is shown to Janice. Kevin's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc: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:2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ellen can now know that Randall picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ellen","Randall","Kevin","Janice"],"index":45529,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979711175,"difficulty":0.0020288825}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mohammed's card is shown to Linda. Sabrina's card is shown to Linda. Linda's card is shown to Mohammed. Sabrina's card is shown to Mohammed. Mohammed's card is shown to Donald. Sabrina's card is shown to Donald. Linda's card is shown to Sabrina. 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) ] (Agentc knows that 1)","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":"Donald can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Mohammed","Donald","Sabrina"],"index":32187,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978821874,"difficulty":0.0021178126}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randolph's card is shown to Randolph. Josephine's card is shown to Josephine. Larry's card is shown to Josephine. Josephine'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:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know whether Randolph can know that Larry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Randolph","Josephine","Larry"],"index":20079,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6568216085,"difficulty":0.3431783915}
{"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 Richard. Richard's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Stephen can now know that Richard can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Stephen"],"index":19295,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997026324,"difficulty":0.0002973676}
{"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 David. Daniel's card is shown to David. David's card is shown to Sharon. Sharon's card is shown to Sharon. Lisa's card is shown to Daniel. 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 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Lisa can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Lisa","Sharon","Daniel"],"index":4582,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997707009,"difficulty":0.0002292991}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Forrest's card is shown to Samantha. Samantha's card is shown to Samantha. John's card is shown to Samantha. Samantha'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: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":"Forrest can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Forrest","Samantha","John"],"index":7407,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983577132,"difficulty":0.0016422868}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dora's card is shown to Jack. Dora's card is shown to Dora. Jack's card is shown to Lauren. Dora's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Lauren 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 (Agentd knows that 3)","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":"Dora can now know that Christopher can know that Lauren picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jack","Dora","Lauren","Christopher"],"index":64694,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9734340906,"difficulty":0.0265659094}
{"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. Louis's card is shown to Louis. James's card is shown to Louis. Gina's card is shown to James. Gina's card is shown to Concepcion. Louis's card is shown to Concepcion. 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:1 Agentd: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:1 Agentb:2,3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gina","Louis","James","Concepcion"],"index":43678,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998380661,"difficulty":0.001619339}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leah's card is shown to Leah. Leah's card is shown to Arturo. It is publicly announced that someone picked a red card. It is publicly announced that Arturo knows whether Arturo picked a red card. It is publicly announced that Arturo knows whether or not nobody picked a red card. It is publicly announced that Leah picked a black card. It is publicly announced that Arturo knows whether Leah 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) ] [ ! (Agentb knows whether 1) ] (Agenta 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 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Leah can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Leah","Arturo"],"index":25561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
{"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 Gloria. Gloria's card is shown to Emilee. George's card is shown to Emilee. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Gloria does not know whether Emilee picked a red card. It is publicly announced that George 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:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Emilee can now know whether George can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gloria","Emilee","George"],"index":23542,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994107485,"difficulty":0.0005892515}
{"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 Suzanne. Alan's card is shown to Ervin. Suzanne's card is shown to Harold. 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:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 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":"Suzanne can now know whether Ervin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Suzanne","Ervin","Harold","Alan"],"index":55626,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9445678592,"difficulty":0.0554321408}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmen's card is shown to Carmen. Natasha's card is shown to Carmen. Adam's card is shown to Adam. Carmen's card is shown to Natasha. It is publicly announced that someone picked a red card. It is publicly announced that Adam does not know whether Carmen 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 that (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":"Natasha can now know that Carmen can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carmen","Adam","Natasha"],"index":58072,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
{"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 Maria. Robert'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 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:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know that Robert can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Robert","William"],"index":44550,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9901233315,"difficulty":0.0098766685}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wesley's card is shown to Brad. Brad's card is shown to Wesley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brad can now know whether Jared can know whether Wesley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brad","Jared","Wesley"],"index":62832,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990280867,"difficulty":0.0009719133}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frederick's card is shown to Norman. Norman's card is shown to Frederick. It is publicly announced that someone picked a red card. It is publicly announced that Norman does not know whether or not everyone picked a red card. It is publicly announced that Frederick picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Pauline can now know whether Pauline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","Norman","Joyce","Frederick"],"index":241,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5281592607,"difficulty":0.4718407393}
{"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 Norma. Clayton's card is shown to Norma. Alishia's card is shown to Norma. Virginia's card is shown to Norma. Clayton's card is shown to Clayton. Norma's card is shown to Alishia. Norma's card is shown to Virginia. Alishia's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Alishia does not know whether Alishia picked a red card. It is publicly announced that Norma knows whether Alishia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Clayton can now know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norma","Clayton","Alishia","Virginia"],"index":39543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8699272871,"difficulty":0.1300727129}
{"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. Glenn's card is shown to Gloria. Gloria'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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Glenn can now know that Gloria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Glenn","Gloria"],"index":47554,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996750474,"difficulty":0.003249526}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Blanca. Sherrie's card is shown to Blanca. Duane's card is shown to Sherrie. 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) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Blanca can now know whether Duane can know that Duane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Blanca","Duane","Sherrie"],"index":11286,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9412952065,"difficulty":0.0587047935}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hermina's card is shown to Hermina. Barbara's card is shown to Hermina. Marjorie's card is shown to Hermina. Hermina's card is shown to Barbara. Barbara's card is shown to Barbara. Marjorie's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Hermina knows whether Hermina picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Marjorie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hermina","Barbara","Marjorie"],"index":16028,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997213483,"difficulty":0.0002786517}
{"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 Holly. Don's card is shown to Don. Dean's card is shown to Don. Dean's card is shown to Gregory. Holly's card is shown to Dean. Don's card is shown to Dean. Gregory's card is shown to Dean. 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) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Dean can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Holly","Don","Gregory","Dean"],"index":21133,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983243346,"difficulty":0.0016756654}
{"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. Theodore's card is shown to Denise. Brian's card is shown to Denise. Theodore's card is shown to James. James's card is shown to Theodore. Theodore's card is shown to Theodore. Denise's card is shown to Brian. James'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 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:2,3 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:2,3 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Theodore can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Denise","James","Theodore","Brian"],"index":2855,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6042077541,"difficulty":1.6042077541}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Truman's card is shown to Truman. Justin's card is shown to Truman. William's card is shown to William. Justin's card is shown to Justin. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether Truman 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 (Agentb knows whether (~(1|2|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":"Justin can now know whether William can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Truman","William","Justin"],"index":66097,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997088313,"difficulty":0.0002911687}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. Calvin's card is shown to Calvin. It is publicly announced that someone picked a red card. It is publicly announced that Andrea knows 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 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":"Andrea can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andrea","Calvin"],"index":61277,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981948733,"difficulty":0.0018051267}
{"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 Rex. Rex's card is shown to Rex. Myrtle's card is shown to Rex. Steven's card is shown to Myrtle. Rex's card is shown to Melanie. 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 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Myrtle can now know whether Steven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Rex","Myrtle","Melanie"],"index":19404,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6544733047,"difficulty":1.6544733047}
{"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 Lindsay. Sam's card is shown to Sam. Sam's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Lindsay picked a red card. It is publicly announced that Lindsay 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)) ] Agentb knows that (Agentc knows that 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":"Sam can now know that Matthew can know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lindsay","Sam","Matthew"],"index":33177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9368979931,"difficulty":0.0631020069}
{"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 Gerald. Tamara's card is shown to Gerald. Roman's card is shown to Juan. Tamara's card is shown to Juan. 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) ] (Agentb knows that (~(1|2|3|4)))","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":"Juan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gerald","Juan","Roman","Tamara"],"index":38510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983541965,"difficulty":0.0016458035}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Abraham. Abraham's card is shown to Darrell. 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 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Darrell can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Abraham","Darrell","Donna"],"index":65738,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997563958,"difficulty":0.0002436042}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawanda's card is shown to Beth. Lucille's card is shown to Beth. Lucille's card is shown to Lucille. It is publicly announced that someone picked a red card. It is publicly announced that Lawanda does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lawanda can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lawanda","Beth","Lucille"],"index":6839,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980034232,"difficulty":0.0019965768}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peggie's card is shown to Whitney. Richard's card is shown to Whitney. Peggie's card is shown to Peggie. Whitney's card is shown to Chester. Richard's card is shown to Chester. It is publicly announced that someone picked a red card. It is publicly announced that Whitney does not know whether or not everyone picked a red card. It is publicly announced that Richard does not know whether Chester picked a red card. It is publicly announced that Richard does not know whether Chester 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:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Whitney can now know whether Peggie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Whitney","Peggie","Richard","Chester"],"index":30898,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9476546049,"difficulty":0.0523453951}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dean's card is shown to Dean. Steven's card is shown to Dean. Dean's card is shown to Steven. It is publicly announced that someone picked a red card. It is publicly announced that Steven knows whether Steven picked a red card. It is publicly announced that Steven picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! 2 ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! 2 ] 0","hypothesis":"Steven can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dean","Steven"],"index":495,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997245669,"difficulty":0.0002754331}
{"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. Ruth's card is shown to Florence. Kimberlee's card is shown to Florence. Florence's card is shown to Judy. Judy's card is shown to Judy. Kimberlee's card is shown to Judy. Florence's card is shown to Kimberlee. 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:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Judy can now know whether Judy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Florence","Ruth","Judy","Kimberlee"],"index":40387,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9039846659,"difficulty":1.9039846659}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Julie. Jerome's card is shown to Jerome. Harvey's card is shown to Jerome. 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 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that Jerome picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julie","Jerome","Harvey"],"index":47791,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982783794,"difficulty":0.0017216206}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Louise's card is shown to Kathleen. Adrienne's card is shown to Louise. Louise's card is shown to Adrienne. It is publicly announced that someone picked a red card. It is publicly announced that Adrienne does not know whether Adrienne 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) ] (Agentc knows that 1)","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":"Adrienne can now know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Louise","Adrienne"],"index":17201,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959321618,"difficulty":0.0040678382}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delbert's card is shown to Melda. Melda's card is shown to Delbert. Delbert's card is shown to Delbert. James's card is shown to Delbert. Melda's card is shown to James. 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:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Melda can now know whether Delbert can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melda","Delbert","James"],"index":52006,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982958436,"difficulty":0.0017041564}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lourdes's card is shown to Patricia. Lourdes's card is shown to Lourdes. It is publicly announced that someone picked a red card. It is publicly announced that Lourdes does not know whether or not everyone picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] Agentb knows that (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 ] 0","hypothesis":"Lourdes can now know that Patricia can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Lourdes"],"index":32733,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8827950358,"difficulty":0.1172049642}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christy's card is shown to Christy. Ivan's card is shown to Christy. Donald's card is shown to Ivan. Ivan's card is shown to William. William'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 Ivan does not know whether William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"William can now know that Ivan can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christy","Ivan","William","Donald"],"index":62302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925552011,"difficulty":0.0074447989}
{"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 Jessica. Stephen's card is shown to Jessica. Stephen's card is shown to Stephen. Tim's card is shown to Stephen. Jessica's card is shown to Tim. Stephen's card is shown to Tim. It is publicly announced that someone picked a red card. It is publicly announced that Tim knows whether Stephen 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 1)","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":"Stephen can now know that Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessica","Stephen","Tim"],"index":57723,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995888412,"difficulty":0.004111588}
{"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. Renee's card is shown to Shirley. Jean's card is shown to Renee. Renee's card is shown to Kathleen. Kathleen's card is shown to Jean. Jean's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Renee does not know whether Kathleen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentd knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jean can now know that Kathleen can know whether Renee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Renee","Kathleen","Jean"],"index":4950,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9052764773,"difficulty":1.9052764773}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirlee's card is shown to Shirlee. Shirlee's card is shown to Marla. It is publicly announced that someone picked a red card. It is publicly announced that Shirlee does not know whether Marla picked a red card. It is publicly announced that Shirlee does not know whether Marla picked a red card. It is publicly announced that Marla does not know whether Marla picked a red card. It is publicly announced that Marla 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 2) ] [ ! 2 ] (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 2) ] [ ! 2 ] 0","hypothesis":"Shirlee can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shirlee","Marla"],"index":44905,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9976796508,"difficulty":1.9976796508}
{"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 Harold. Harold's card is shown to Harold. 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:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Sara can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sara","Gloria","Harold"],"index":46145,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997196794,"difficulty":0.0002803206}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Raymond. Elizabeth's card is shown to Raymond. Darrell's card is shown to Darrell. Raymond's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Raymond does not know whether Raymond 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:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Raymond can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Darrell","Elizabeth"],"index":35568,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957695007,"difficulty":0.0042304993}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Arthur. Emanuel's card is shown to Arthur. Emanuel's card is shown to Glen. 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)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Arthur can now know that Arthur picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arthur","Emanuel","Glen"],"index":3594,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961531758,"difficulty":0.0038468242}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheri's card is shown to Matthew. Merrill's card is shown to Merrill. Merrill's card is shown to Alicia. 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 whether 3)","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":"Merrill can now know whether Merrill picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sheri","Matthew","Merrill","Alicia"],"index":28589,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9903241396,"difficulty":0.0096758604}
{"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 Catherine. Karen's card is shown to Karen. Karen's card is shown to Courtney. 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. It is publicly announced that Karen 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)) ] (Agenta 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":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Catherine","Karen","Courtney"],"index":32177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974797368,"difficulty":0.0025202632}
{"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 Richard. Marian's card is shown to Marian. Jesus's card is shown to Marian. Jesus's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Jesus does not know whether Marian 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) ] Agentc knows that (Agenta knows whether 1)","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":"Jesus can now know that Richard can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Marian","Jesus"],"index":34996,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6259359121,"difficulty":0.3740640879}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lee's card is shown to Lee. George's card is shown to Lee. 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 George picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"George can now know whether Lee can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lee","George"],"index":40346,"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). Steven's card is shown to Ryan. Johnathan's card is shown to Johnathan. Ryan's card is shown to Steven. Johnathan'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:3 Agentb:2 Agentc:1 Agentd:2 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:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tammy can now know whether Johnathan can know whether Ryan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ryan","Johnathan","Steven","Tammy"],"index":44375,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998290956,"difficulty":0.001709044}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Frances. Paz's card is shown to Paz. It is publicly announced that someone picked a red card. It is publicly announced that Frances picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Frances can now know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frances","Gregory","Paz"],"index":67404,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8582607508,"difficulty":0.1417392492}
{"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 Virginia. Roger's card is shown to Virginia. Roger's card is shown to John. Roger's card is shown to Roger. 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:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Roger can now know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Virginia","John","Roger"],"index":43201,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9893653393,"difficulty":0.0106346607}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tanya's card is shown to Tanya. Tanya's card is shown to Jesse. 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 (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Jesse can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tanya","Jesse"],"index":39495,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997678399,"difficulty":0.0002321601}
{"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 Jenifer. Jenifer's card is shown to Jenifer. William's card is shown to Jerry. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Charles can now know that Jenifer can know whether Jenifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Charles","Jenifer","Jerry"],"index":30968,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.878796041,"difficulty":0.121203959}
{"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 Dorothy. Mary's card is shown to Mary. Arthur's card is shown to Mary. Dorothy's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Arthur 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 3)","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":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Theresa","Mary","Arthur"],"index":24852,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9715989828,"difficulty":1.9715989828}
{"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 Timothy. Timothy's card is shown to Theresa. Theresa's card is shown to Theresa. 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 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Timothy can now know that Theresa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Timothy","Theresa"],"index":13397,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984966516,"difficulty":0.0015033484}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grover's card is shown to Carolyn. Adam's card is shown to Adam. Carolyn's card is shown to Maria. Carolyn's card is shown to Grover. Adam's card is shown to Grover. 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) ] Agentd 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 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Grover can now know that Carolyn can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Adam","Maria","Grover"],"index":49404,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984487295,"difficulty":0.0015512705}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Virginia. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that Virginia does not know whether or not everyone picked a red card. It is publicly announced that Katherine 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 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":"Katherine can now know that Virginia can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Virginia","Katherine"],"index":32868,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7228581905,"difficulty":1.7228581905}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myrtle's card is shown to Myrtle. Dorothy's card is shown to Dorothy. 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 Myrtle does not know whether Dorothy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Myrtle can now know whether Dorothy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Myrtle","Dorothy"],"index":62698,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9949076772,"difficulty":1.9949076772}
{"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 Megan. Samantha's card is shown to Samantha. Maria's card is shown to Samantha. 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:2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Megan can now know whether Maria can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Megan","Samantha","Maria"],"index":59502,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995675683,"difficulty":0.0004324317}
{"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. Constance's card is shown to Priscilla. James's card is shown to Constance. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Constance can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Priscilla","Constance"],"index":42237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997814298,"difficulty":0.0002185702}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jewell's card is shown to Gary. William's card is shown to William. Jewell's card is shown to Guy. Jewell's card is shown to Jewell. It is publicly announced that someone picked a red card. It is publicly announced that Guy does not know whether Guy picked a red card. It is publicly announced that William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] 0","hypothesis":"Jewell can now know whether Gary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","William","Guy","Jewell"],"index":60372,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8053713441,"difficulty":0.1946286559}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myrtle's card is shown to Myrtle. Ester's card is shown to Myrtle. Myrtle's card is shown to Ester. Ester's card is shown to Ester. 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) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Ester can now know that Myrtle can know whether Ester picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Myrtle","Ester"],"index":15056,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7038181424,"difficulty":1.7038181424}
{"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 Jerry. Chad's card is shown to Jerry. Jerry's card is shown to Herbert. Herbert's card is shown to Herbert. Jerry's card is shown to Chad. Jack's card is shown to Chad. It is publicly announced that someone picked a red card. It is publicly announced that Jerry does not know whether Jack picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Herbert can now know that Jack can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Herbert","Jack","Chad"],"index":44406,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997141957,"difficulty":0.0002858043}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Greg's card is shown to Greg. Derrick's card is shown to Greg. Zoe's card is shown to Zoe. Greg's card is shown to Derrick. 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 (~(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":"Derrick can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Greg","Zoe","Derrick"],"index":58452,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997263551,"difficulty":0.0002736449}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Al's card is shown to Al. Jerry's card is shown to Al. Al's card is shown to Gloria. Gloria's card is shown to Gloria. Jerry's card is shown to Gloria. Al's card is shown to Jerry. Gloria'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:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gloria can now know whether Jerry can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Al","Gloria","Jerry"],"index":34161,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
{"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. Dona's card is shown to William. Dwayne's card is shown to Dwayne. Dona's card is shown to Dwayne. William's card is shown to Dona. Dwayne's card is shown to Dona. 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 Dona picked a red card. 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:1,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dona can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Dwayne","Dona"],"index":16515,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997015595,"difficulty":0.0002984405}
{"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 Norman. Richard's card is shown to Phyllis. Richard's card is shown to Richard. Richard's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd: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:4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Phyllis can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norman","Phyllis","Richard","Mark"],"index":20205,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983528852,"difficulty":0.0016471148}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ella's card is shown to Charles. Charles's card is shown to Ella. It is publicly announced that someone 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 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Monica can now know whether Charles can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Monica","Ella"],"index":17662,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9960243702,"difficulty":0.0039756298}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Sarita. Louise's card is shown to Louise. 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 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Louise can now know whether Louise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sarita","Louise"],"index":47946,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9866720438,"difficulty":0.0133279562}
{"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 David. Florence's card is shown to Florence. Timothy's card is shown to Erica. 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:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Florence can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","David","Florence","Erica"],"index":15632,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984540939,"difficulty":0.0015459061}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Robin. Walter's card is shown to Walter. Al's card is shown to Walter. Robin's card is shown to Al. Walter's card is shown to Al. It is publicly announced that someone picked a red card. It is publicly announced that Walter picked a black card. It is publicly announced that Robin knows whether Robin 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)) ] (Agenta knows that 3)","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":"Robin can now know that Al picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robin","Walter","Al"],"index":30685,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9346330166,"difficulty":0.0653669834}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fannie's card is shown to Fannie. Tracey's card is shown to Katherine. Katherine's card is shown to Michael. Fannie's card is shown to Tracey. Katherine's card is shown to Tracey. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentd knows that 1)","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":"Tracey can now know that Fannie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fannie","Katherine","Michael","Tracey"],"index":27285,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8366032243,"difficulty":0.1633967757}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Concetta's card is shown to Concetta. Regina's card is shown to Regina. Karen's card is shown to Nicholas. 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 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Regina can now know that Concetta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Concetta","Regina","Nicholas"],"index":36631,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7961477637,"difficulty":1.7961477637}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maricela's card is shown to Troy. Troy's card is shown to Jasmine. Jasmine's card is shown to Jasmine. Maricela's card is shown to Jasmine. Troy'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 Jasmine does not know whether Joseph 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 whether 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":"Maricela can now know that Jasmine can know whether Maricela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Troy","Jasmine","Maricela","Joseph"],"index":44847,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6138107181,"difficulty":1.6138107181}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Audrey's card is shown to Audrey. Helen's card is shown to Audrey. Maria's card is shown to Audrey. Helen's card is shown to James. Maria's card is shown to James. Helen's card is shown to Helen. Maria's card is shown to Helen. Audrey's card is shown to Maria. 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. It is publicly announced that Maria picked a black card. It is publicly announced that Audrey picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Audrey can now know that Helen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Audrey","James","Helen","Maria"],"index":52728,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983735085,"difficulty":0.0016264915}
{"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. Jill's card is shown to Jennifer. David's card is shown to Lona. Lona's card is shown to Lona. David's card is shown to Jill. Jill's card is shown to Jill. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Lona picked a red card. It is publicly announced that Jill picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] 0","hypothesis":"Jennifer can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Jennifer","Lona","Jill"],"index":62331,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997242093,"difficulty":0.0002757907}
{"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. Rebecca's card is shown to Edward. Twila's card is shown to Edward. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Twila can now know that Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rebecca","Twila","Edward"],"index":5830,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998277545,"difficulty":0.001722455}
{"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 Margaret. Jacqueline's card is shown to Margaret. Margaret's card is shown to Clara. It is publicly announced that someone picked a red card. It is publicly announced that Clara knows whether or not nobody 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 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":"Clara can now know that Margaret can know that Jacqueline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Clara","Jacqueline"],"index":21054,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977205396,"difficulty":0.0022794604}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delores's card is shown to Kathleen. Dana's card is shown to Kathleen. Delores's card is shown to Delores. Kathleen's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen knows whether Delores 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) ] (Agentc 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":"Dana can now know that Delores picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Delores","Dana"],"index":31,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965023994,"difficulty":0.0034976006}
{"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. Donna's card is shown to Norma. Donna's card is shown to Donna. Jeremy's card is shown to Donna. Donna's card is shown to Jeremy. 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:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeremy can now know that Donna can know that Donna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norma","Donna","Jeremy"],"index":47672,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9911007285,"difficulty":0.0088992715}
{"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 Eugene. Eugene's card is shown to Mark. Eugene's card is shown to Debra. Mark's card is shown to Debra. Debra's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Debra can now know whether Eugene can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","Mark","Debra"],"index":30151,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997698665,"difficulty":0.0002301335}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edna's card is shown to Edna. Edna's card is shown to Marisa. Marisa's card is shown to Marisa. Marisa's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Ralph knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Marisa can now know whether Ralph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edna","Marisa","Ralph"],"index":36946,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9095412493,"difficulty":0.0904587507}
{"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. Margaret's card is shown to Peter. Peter's card is shown to Margaret. Margaret's card is shown to Margaret. Joshua's card is shown to Margaret. Margaret's card is shown to Joshua. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Margaret 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:2,3 Agentb:2,3,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Thomas can now know that Peter can know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Peter","Margaret","Joshua"],"index":62483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9283671975,"difficulty":0.0716328025}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wynona's card is shown to Carol. Jeanna's card is shown to Wynona. Jeanna's card is shown to Andrew. Jeanna's card is shown to Jeanna. It is publicly announced that someone picked a red card. It is publicly announced that Andrew does not know whether Wynona picked a red card. It is publicly announced that Carol knows whether Wynona picked a red card. It is publicly announced that Jeanna 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:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Carol can now know that Wynona can know whether Wynona picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Wynona","Andrew","Jeanna"],"index":34426,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7537146211,"difficulty":1.7537146211}
{"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 Roberta. Jennifer's card is shown to Jennifer. Kelly's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer 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 Jennifer does not know whether Roberta 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) ] Agentc knows whether (Agentb knows whether 2)","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":"Kelly can now know whether Jennifer can know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roberta","Jennifer","Kelly"],"index":39473,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9969283938,"difficulty":0.0030716062}
{"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 Andrew. Ernestina's card is shown to Antoinette. Antoinette's card is shown to Tracy. Andrew's card is shown to Ernestina. It is publicly announced that someone picked a red card. It is publicly announced that Ernestina does not know whether or not everyone picked a red card. It is publicly announced that Antoinette picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Tracy can now know that Antoinette can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrew","Antoinette","Tracy","Ernestina"],"index":5070,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981979728,"difficulty":0.0018020272}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Arlene. Michael's card is shown to Arlene. Arlene'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 Michael picked a black card. It is publicly announced that Arlene 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) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Arlene can now know that Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Arlene","Michael"],"index":48719,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5221546888,"difficulty":1.5221546888}
{"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 Manuel. Manuel's card is shown to Kathleen. Kathleen's card is shown to Kathleen. Richard's card is shown to Kathleen. Kathleen's card is shown to Richard. Richard's card is shown to Richard. 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 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know whether Kathleen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Manuel","Kathleen","Richard"],"index":66743,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994226694,"difficulty":0.0005773306}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Kathleen's card is shown to Bryan. Bryan's card is shown to Bryan. Kathleen's card is shown to Sherry. Bryan's card is shown to Sherry. 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: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:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bryan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathleen","Bryan","Sherry"],"index":43015,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997753501,"difficulty":0.0002246499}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Richard. Elaine's card is shown to David. David's card is shown to Elaine. It is publicly announced that someone picked a red card. It is publicly announced that Rachel does not know whether Richard picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card. It is publicly announced that Rachel knows whether someone picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rachel can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","David","Rachel","Elaine"],"index":26086,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985995889,"difficulty":0.0014004111}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Bryan. Dennis's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Dennis does not know whether 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Bryan can now know whether Bryan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bryan","Dennis"],"index":36473,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8801625371,"difficulty":1.8801625371}
{"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. Shayne's card is shown to Shayne. It is publicly announced that someone picked a red card. It is publicly announced that Danielle knows whether or not everyone picked a red card. It is publicly announced that Danielle picked a black card. It is publicly announced that someone 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)) ] [ ! ~(1) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Danielle can now know that April can know that Shayne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Danielle","April","Shayne"],"index":24302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.68873173,"difficulty":0.31126827}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chrissy's card is shown to Julio. Julio's card is shown to Lynn. Chrissy's card is shown to Lynn. It is publicly announced that someone picked a red card. It is publicly announced that Julio does not know whether or not everyone picked a red card. It is publicly announced that Julio does not know whether Julio 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 whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Julio can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julio","Lynn","Chrissy"],"index":25313,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8395824432,"difficulty":1.8395824432}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmon's card is shown to Jacob. James's card is shown to Jacob. James's card is shown to Carmon. Jacob'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 Jacob does not know whether Jacob picked a red card. It is publicly announced that Carmon does not know whether or not everyone picked a red card. It is publicly announced that James picked a red card. It is publicly announced that Carmon 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)) ] Agenta knows that (Agentc 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":"Jacob can now know that James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jacob","Carmon","James"],"index":19044,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972831011,"difficulty":0.0027168989}
{"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 Allen. Walter's card is shown to Allen. Walter's card is shown to Walter. Tim's card is shown to Tim. 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 that 2)","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":"Allen can now know that Walter can know that Walter picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Allen","Walter","Tim"],"index":33334,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953599572,"difficulty":0.0046400428}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cliff's card is shown to Mindy. Ricardo's card is shown to Ricardo. Mindy's card is shown to Judith. Cliff's card is shown to Judith. Mindy's card is shown to Cliff. 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 whether (~(1|2|3|4)))","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":"Ricardo can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mindy","Ricardo","Judith","Cliff"],"index":24380,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997242093,"difficulty":0.0002757907}
{"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 Leo. Angelica's card is shown to Leo. Leo's card is shown to Ruth. Angelica's card is shown to Ruth. Leo's card is shown to Angelica. Angelica's card is shown to Angelica. 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:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1,4 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":["Leo","John","Ruth","Angelica"],"index":19910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997265935,"difficulty":0.0002734065}
{"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 Karen. Karen's card is shown to Amy. Douglas's card is shown to Amy. Karen's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Douglas 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) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Amy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Amy","Douglas"],"index":34144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997233748,"difficulty":0.0002766252}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacey's card is shown to Stacey. Stacey's card is shown to Adrianne. It is publicly announced that someone picked a red card. It is publicly announced that Stacey does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (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&2&3)) ] 0","hypothesis":"Stacey can now know that Adrianne can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stacey","Adrianne","Beverly"],"index":65662,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997072816,"difficulty":0.0002927184}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kay's card is shown to Susan. Susan's card is shown to Kay. It is publicly announced that someone picked a red card. It is publicly announced that Kay does not know whether or not everyone picked a red card. It is publicly announced that Kay 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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Kay can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Susan","Kay"],"index":13961,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9927099943,"difficulty":0.0072900057}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Miranda's card is shown to Miranda. Ivette's card is shown to Ivette. Leanna's card is shown to Anne. Ivette's card is shown to Leanna. 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:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leanna can now know whether Anne can know that Leanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Miranda","Ivette","Anne","Leanna"],"index":25976,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7447493076,"difficulty":1.7447493076}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elmer's card is shown to Elmer. Eugene's card is shown to Callie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elmer can now know that Elmer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elmer","Callie","Clayton","Eugene"],"index":186,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954413176,"difficulty":0.0045586824}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angie's card is shown to Angie. Angie's card is shown to Debra. Debra's card is shown to Debra. Debra's card is shown to Leon. It is publicly announced that someone picked a red card. It is publicly announced that Leon does not know whether Angie picked a red card. It is publicly announced that Angie does not know whether Leon picked a red card. It is publicly announced that Leon knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Debra can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angie","Debra","Leon"],"index":64284,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986096621,"difficulty":0.0013903379}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Scott. Jack's card is shown to Scott. Scott's card is shown to Alice. Alice's card is shown to Alice. Jack's card is shown to Alice. Alice's card is shown to Peter. Jack's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Peter knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alice can now know that Scott can know that Jack picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Alice","Peter","Jack"],"index":37485,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969929457,"difficulty":0.0030070543}
{"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 Carolyn. Jean's card is shown to Catherine. Catherine's card is shown to Paris. 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 (~(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":"Jean can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jean","Carolyn","Catherine","Paris"],"index":8156,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997211099,"difficulty":0.0002788901}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rita's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know whether Jose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rita","David","Jose","Thelma"],"index":64055,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9744819999,"difficulty":0.0255180001}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margarette's card is shown to John. Margarette's card is shown to James. 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:2,3 VALID? [ ! (1|2|3) ] (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":"John can now know that Margarette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Margarette","James"],"index":11879,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982913136,"difficulty":0.0017086864}
{"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 Alice. Alice's card is shown to Lindsy. William's card is shown to Lindsy. Lindsy'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 Alice does not know whether or not everyone picked a red card. It is publicly announced that William 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 whether 2)","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":"Lindsy can now know whether Alice can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Donald","Lindsy","William"],"index":52060,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984017015,"difficulty":0.0015982985}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to James. James's card is shown to Victoria. Victoria's card is shown to Victoria. It is publicly announced that someone picked a red card. It is publicly announced that Victoria picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"James can now know that Victoria can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Victoria"],"index":67388,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973976612,"difficulty":0.0026023388}
{"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. Rita's card is shown to Thomas. Rita's card is shown to Rita. Gina's card is shown to Gina. 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 (Agentc knows that 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":"Thomas can now know that Gina can know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Rita","Gina"],"index":58516,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959563613,"difficulty":0.0040436387}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cecil's card is shown to Nellie. Troy's card is shown to Troy. Tracey's card is shown to Troy. Tracey's card is shown to Cecil. 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: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:4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tracey can now know whether Nellie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nellie","Troy","Tracey","Cecil"],"index":5893,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997116923,"difficulty":0.0002883077}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Claudine's card is shown to Elizabeth. Claudine's card is shown to Helen. Paul's card is shown to Helen. Helen's card is shown to Claudine. 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 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Helen","Claudine","Paul"],"index":50878,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983533621,"difficulty":0.0016466379}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Clarence. Clarence's card is shown to Joanne. It is publicly announced that someone picked a red card. It is publicly announced that Joanne picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Clarence can now know whether Joanne can know whether Clarence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Clarence","Joanne"],"index":32659,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9974395037,"difficulty":0.0025604963}
{"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 Kara. Kara's card is shown to Mary. Mary's card is shown to Ana. It is publicly announced that someone picked a red card. It is publicly announced that Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 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 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Inez can now know that Ana picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kara","Mary","Inez","Ana"],"index":62414,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8955286741,"difficulty":0.1044713259}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julio's card is shown to Tara. Tara's card is shown to Glenn. Julio's card is shown to Glenn. Tara's card is shown to Marshall. Tara's card is shown to Julio. Glenn's card is shown to Julio. It is publicly announced that someone picked a red card. It is publicly announced that Glenn picked a black card. It is publicly announced that Julio does not know whether Julio picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentd knows whether 4) ] Agentc knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Marshall can now know whether Glenn can know that Glenn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tara","Glenn","Marshall","Julio"],"index":33922,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9736390114,"difficulty":0.0263609886}
{"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. Mary's card is shown to Mary. David's card is shown to Mary. Mary's card is shown to David. Mary's card is shown to Nina. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Mary picked a red card. It is publicly announced that Mary 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) ] (Agenta 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":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Mary","David","Nina"],"index":22688,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8214262724,"difficulty":1.8214262724}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronnie's card is shown to Roger. Sylvia's card is shown to Roger. Ronnie's card is shown to Cecile. Cecile's card is shown to Cecile. Cecile's card is shown to Sylvia. Sylvia's card is shown to Sylvia. It is publicly announced that someone picked a red card. It is publicly announced that Ronnie 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) ] (Agentc knows that 3)","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":"Cecile can now know that Cecile picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roger","Ronnie","Cecile","Sylvia"],"index":63413,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9860617518,"difficulty":0.0139382482}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Moises's card is shown to Moises. Sylvia's card is shown to Jason. Sylvia's card is shown to James. Moises's card is shown to Sylvia. Sylvia's card is shown to Sylvia. 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 whether 3)","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":"James can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Moises","Jason","James","Sylvia"],"index":55941,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9001586437,"difficulty":0.0998413563}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raul's card is shown to Joseph. Joseph's card is shown to Raul. Raul's card is shown to Raul. Michael's card is shown to Raul. Raul's card is shown to Christopher. 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) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Raul can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Raul","Christopher","Michael"],"index":17747,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973842502,"difficulty":0.0026157498}
{"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 Adrienne. Helen's card is shown to Adrienne. Helen's card is shown to Helen. Albert's card is shown to Helen. Albert'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:1,2 Agentb:2,3 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:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Adrienne can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adrienne","Helen","Albert"],"index":5008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983853102,"difficulty":0.0016146898}
{"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 Nina. Nina's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Esther picked a black card. It is publicly announced that Nina knows 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) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Esther can now know that Nina can know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Esther","Nina","Jennifer"],"index":6885,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5879947543,"difficulty":1.5879947543}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evangeline's card is shown to Joanne. John's card is shown to John. Joanne's card is shown to Joel. Joanne's card is shown to Evangeline. John's card is shown to Evangeline. 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 (~(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":"Joanne can now know that Joel can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joanne","John","Joel","Evangeline"],"index":31346,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984586239,"difficulty":0.0015413761}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chastity's card is shown to John. Chastity's card is shown to Chastity. Christina's card is shown to Gregory. Christina's card is shown to Christina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Chastity can now know that Chastity picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Chastity","Gregory","Christina"],"index":40150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973632693,"difficulty":0.0026367307}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmen's card is shown to Georgia. Kristine's card is shown to Georgia. Carmen's card is shown to Kristine. Dennis's card is shown to Kristine. Kristine's card is shown to Dennis. 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:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristine can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Georgia","Carmen","Kristine","Dennis"],"index":23348,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999776423,"difficulty":0.000223577}
{"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. Brett's card is shown to Michael. Pete's card is shown to Michael. Brett's card is shown to Brett. Pete's card is shown to Pete. 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 whether (1&2&3))","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":"Pete can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Brett","Pete"],"index":29163,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917884469,"difficulty":0.0082115531}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alma's card is shown to Alma. Alma's card is shown to Marguerite. Marguerite's card is shown to Marguerite. Alyssa's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Alma does not know whether John picked a red card. It is publicly announced that Alyssa picked a red card. It is publicly announced that Marguerite 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)) ] (Agenta knows whether 3)","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":"Alma can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alma","Marguerite","John","Alyssa"],"index":37006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5529891849,"difficulty":0.4470108151}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Leonard. Leonard's card is shown to Corliss. Judith's card is shown to Nancy. Leonard's card is shown to Judith. Corliss's card is shown to Judith. Judith's card is shown to Judith. 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) ] (Agentb knows that 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":"Corliss can now know that Judith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leonard","Corliss","Nancy","Judith"],"index":61117,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979091287,"difficulty":0.0020908713}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nannie's card is shown to Nannie. Vickie's card is shown to Nannie. Alison's card is shown to Nannie. Vickie's card is shown to Vickie. Alison's card is shown to Vickie. Vickie's card is shown to Alison. 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) ] (Agentb knows that (~(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":"Vickie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nannie","Vickie","Alison"],"index":48260,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983770847,"difficulty":0.0016229153}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leroy's card is shown to Leroy. Leroy's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Carolyn's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Leroy picked a red card. It is publicly announced that Leroy does not know whether Susan picked a red card. It is publicly announced that Susan knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Carolyn can now know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leroy","Carolyn","Susan"],"index":505,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.71732831,"difficulty":0.28267169}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mavis's card is shown to Mavis. Tiffaney's card is shown to Tiffaney. Robin's card is shown to Tiffaney. Mavis's card is shown to Nathan. Mavis's card is shown to Robin. Robin's card is shown to Robin. It is publicly announced that someone picked a red card. It is publicly announced that Tiffaney does not know whether Mavis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mavis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mavis","Tiffaney","Nathan","Robin"],"index":30150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985961318,"difficulty":0.0014038682}
{"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. Joe's card is shown to Joe. Carl's card is shown to Joe. Edward's card is shown to Carl. Edward's card is shown to Margaret. Joe's card is shown to Margaret. 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:1 Agentd:1,2 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:1 Agentb:2,3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edward can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","Joe","Carl","Margaret"],"index":31341,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997732043,"difficulty":0.0002267957}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Dorothy. Dorothy's card is shown to Duane. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether or not everyone picked a red card. It is publicly announced that Duane knows whether Duane 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 whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dorothy can now know whether Duane can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Duane"],"index":37895,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994712472,"difficulty":0.0005287528}
{"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 Mable. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Mable knows whether or not everyone picked a red card. It is publicly announced that Mable knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Mable can now know whether Joseph can know that Susan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mable","Joseph","Susan"],"index":1505,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9771651626,"difficulty":0.0228348374}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frederick's card is shown to Frederick. Miguel's card is shown to Miguel. It is publicly announced that someone picked a red card. It is publicly announced that Miguel knows whether Miguel 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:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(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 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Miguel can now know that Frederick can know that Miguel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Frederick","Miguel"],"index":43484,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9810468554,"difficulty":0.0189531446}
{"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 Vance. Maria'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 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know whether Vance can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vance","Maria","Joseph"],"index":26673,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997701049,"difficulty":0.0002298951}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dave's card is shown to Alvin. Alvin's card is shown to Dave. Alvin's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not everyone picked a red card. It is publicly announced that Dave knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alvin","Dave","Robert"],"index":56496,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Ann. Maranda's card is shown to Ann. Ann's card is shown to Eric. Eric's card is shown to Eric. Maranda's card is shown to Maranda. It is publicly announced that someone picked a red card. It is publicly announced that Eric does not know whether Maranda picked a red card. It is publicly announced that Eric 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 3) ] [ ! 2 ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Eric can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ann","Eric","Maranda"],"index":58854,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997288585,"difficulty":0.0002711415}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jamie's card is shown to Jamie. Wayne's card is shown to Wayne. It is publicly announced that someone picked a red card. It is publicly announced that Jamie knows whether or not nobody picked a red card. It is publicly announced that Jamie does not know whether Wayne 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 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jamie can now know whether Wayne can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jamie","Wayne"],"index":41330,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99948138,"difficulty":0.00051862}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barry's card is shown to Ruben. Barry's card is shown to Ray. Ruben's card is shown to Dennis. Dennis's card is shown to Dennis. Barry's card is shown to Dennis. Ray's card is shown to Barry. It is publicly announced that someone picked a red card. It is publicly announced that Ruben picked a red card. It is publicly announced that Ruben knows whether Ruben picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ruben can now know whether Dennis can know that Ruben picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruben","Ray","Dennis","Barry"],"index":5466,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9103255272,"difficulty":0.0896744728}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Evelyn. Martha's card is shown to Martha. 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) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Martha can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Evelyn","Martha"],"index":38801,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997584224,"difficulty":0.0002415776}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Jody's card is shown to Bonnie. Jody's card is shown to Jody. 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) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darlene can now know whether Bonnie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlene","Valerie","Bonnie","Jody"],"index":8765,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999620676,"difficulty":0.000379324}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Laura. Barbara's card is shown to Cherie. Margaret'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:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know that Cherie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Cherie","Margaret","Barbara"],"index":11302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983703494,"difficulty":0.0016296506}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Joseph. Joseph's card is shown to Joseph. Ruth's card is shown to Ruth. Sherri's card is shown to Sherri. 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 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arlene","Joseph","Ruth","Sherri"],"index":66283,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983600974,"difficulty":0.0016399026}
{"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. Christina's card is shown to Josephine. Christina's card is shown to Christina. Josephine's card is shown to Patrick. Patrick's card is shown to Patrick. It is publicly announced that someone picked a red card. It is publicly announced that Christina does not know whether Josephine picked a red card. It is publicly announced that Christina knows whether Christina picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Josephine can now know that Christina can know that Patrick picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Josephine","Christina","Patrick"],"index":45850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9399958849,"difficulty":0.0600041151}
{"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. Lenora's card is shown to Lenora. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Nada 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) ] (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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Nada can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nada","Kenneth","Lenora"],"index":21493,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9854194522,"difficulty":0.0145805478}
{"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 Barbara. Jean's card is shown to Elliot. Barbara's card is shown to Patricia. Patricia'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:4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Elliot can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Elliot","Patricia","Jean"],"index":40732,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983599782,"difficulty":0.0016400218}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pam's card is shown to Pam. Pam's card is shown to Betsy. It is publicly announced that someone picked a red card. It is publicly announced that Pam does not know whether Betsy 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 (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":"Pam can now know whether Betsy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pam","Betsy"],"index":10218,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9957662821,"difficulty":0.0042337179}
{"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 Karie. Kim's card is shown to Kim. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kim can now know that Karie can know that Kim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karie","Kim","Carolyn"],"index":17495,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975121021,"difficulty":0.0024878979}
{"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 Derek. Derek's card is shown to Bob. Derek's card is shown to Jeffrey. Bob's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Derek can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Derek","Bob","Jeffrey"],"index":44785,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985200763,"difficulty":0.0014799237}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alyce's card is shown to Lois. Julia's card is shown to Lois. Lois's card is shown to Alyce. Julia's card is shown to Alyce. Jeffrey's card is shown to Alyce. Alyce's card is shown to Julia. Julia's card is shown to Julia. Jeffrey's card is shown to Julia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3,4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3,4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alyce can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lois","Alyce","Julia","Jeffrey"],"index":38213,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997754693,"difficulty":0.0002245307}
{"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 Jim. Richard's card is shown to Jim. David's card is shown to Jim. Richard's card is shown to Richard. Jim'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:2 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:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jim","Richard","David"],"index":11233,"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). Irene's card is shown to Patricia. Irene's card is shown to Jacob. Beatrice's card is shown to Beatrice. 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 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jacob can now know whether Patricia can know that Beatrice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Jacob","Beatrice","Irene"],"index":45861,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9317244887,"difficulty":0.0682755113}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Adam. Adam's card is shown to Fay. Fay's card is shown to Luis. 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) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Luis can now know that Fay can know that Adam picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Adam","Fay","Luis"],"index":36727,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979966283,"difficulty":0.0020033717}
{"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 Calvin. Mary's card is shown to Mary. Herman's card is shown to Mary. Calvin's card is shown to Herman. Mary's card is shown to Herman. Herman's card is shown to Herman. It is publicly announced that someone picked a red card. It is publicly announced that Mary 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:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know whether Calvin can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Calvin","Mary","Herman"],"index":16965,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.996460259,"difficulty":0.003539741}
{"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. Bryan's card is shown to David. David's card is shown to Bryan. Bryan's card is shown to Bryan. Jeffrey's card is shown to Bryan. Bryan's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc: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:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bryan can now know that David can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Bryan","Jeffrey"],"index":5833,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997816682,"difficulty":0.0002183318}
{"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 Brian. Esther's card is shown to Esther. James's card is shown to Jeffrey. Esther'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:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know whether James can know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Esther","Jeffrey","James"],"index":39444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986579418,"difficulty":0.0013420582}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nina's card is shown to Earline. Earline's card is shown to Ryan. Nina's card is shown to Nina. Ryan's card is shown to Natalie. Nina's card is shown to Natalie. Natalie's card is shown to Natalie. 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 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Natalie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earline","Ryan","Nina","Natalie"],"index":15600,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985530972,"difficulty":0.0014469028}
{"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 Robert. Kimberly's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn does not know whether Evelyn 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:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Evelyn can now know that Evelyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Robert","Mary","Kimberly"],"index":1382,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9635331035,"difficulty":0.0364668965}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Albert. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Albert knows whether or not nobody picked a red card. It is publicly announced that Joseph does not know whether Albert 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) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Joseph can now know whether Albert can know that Albert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Albert","Joseph"],"index":6435,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8612189293,"difficulty":1.8612189293}
{"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 Jami. Sophie's card is shown to Jami. Jami's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Harry does not know whether Harry picked a red card. It is publicly announced that Jami 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))) ] (Agenta knows whether 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":"Jami can now know whether Jami picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jami","Harry","Sophie"],"index":49032,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9955829978,"difficulty":1.9955829978}
{"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 Maureen. Maureen's card is shown to Regenia. It is publicly announced that someone picked a red card. It is publicly announced that Regenia knows whether Maureen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Maureen can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maureen","Regenia","Elizabeth"],"index":55204,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966198206,"difficulty":0.0033801794}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irma's card is shown to Gary. George's card is shown to George. Irma's card is shown to Anthony. Irma's card is shown to Irma. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether Anthony picked a red card. It is publicly announced that George picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] 0","hypothesis":"George can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","George","Anthony","Irma"],"index":52674,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8093301058,"difficulty":0.1906698942}
{"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 Janice. Janice's card is shown to Anne. Janice's card is shown to Josephine. Deloris's card is shown to Josephine. Anne's card is shown to Josephine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deloris can now know whether Josephine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Deloris","Anne","Josephine"],"index":4245,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5705230236,"difficulty":1.5705230236}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Toni's card is shown to Toni. John's card is shown to Toni. Toni's card is shown to Luz. Toni's card is shown to John. Luz's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Toni does not know whether Luz picked a red card. It is publicly announced that Luz knows whether or not everyone picked a red card. It is publicly announced that John 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 2)","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":"Luz can now know that John can know whether Luz picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Toni","Luz","John"],"index":14522,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7882193327,"difficulty":0.2117806673}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arvilla's card is shown to Jose. Lindsey's card is shown to Jose. Gerald's card is shown to Gerald. Lindsey's card is shown to Gerald. Gerald's card is shown to Arvilla. Lindsey's card is shown to Arvilla. Gerald's card is shown to Lindsey. Lindsey's card is shown to Lindsey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:2,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:2,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Arvilla can now know that Arvilla picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Gerald","Arvilla","Lindsey"],"index":39614,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965205193,"difficulty":0.0034794807}
{"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 Mary. Arthur's card is shown to Mary. Mary's card is shown to Jason. Jason's card is shown to Jason. Betty's card is shown to Jason. Betty's card is shown to Betty. Mary's card is shown to Arthur. Betty'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:3,4 Agentb:1,2,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Arthur can now know that Betty can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Jason","Betty","Arthur"],"index":7391,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981911778,"difficulty":0.0018088222}
{"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 Richard. Scott's card is shown to Scott. Scott's card is shown to Joseph. Joseph's card is shown to Joseph. Joseph's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 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:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Scott","Joseph","Mary"],"index":23306,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984163046,"difficulty":0.0015836954}
{"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 Alex. Dan's card is shown to Alex. Rose's card is shown to Rose. Alex's card is shown to Dan. Dan's card is shown to Dan. 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:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dan can now know whether Dan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alex","Rose","Dan"],"index":8112,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9781211019,"difficulty":0.0218788981}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Dawn. Stephan's card is shown to Dawn. Dawn's card is shown to Brian. Brian's card is shown to Brian. Stephan's card is shown to Brian. Dawn's card is shown to Stephan. Stephan's card is shown to Stephan. 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:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dawn can now know that Stephan can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dawn","Brian","Stephan"],"index":7915,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983265996,"difficulty":0.0016734004}
{"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. Earlie's card is shown to Nicole. Roseanne's card is shown to Nicole. Earlie's card is shown to Earlie. Juan's card is shown to Earlie. Roseanne's card is shown to Roseanne. Juan's card is shown to Roseanne. Earlie's card is shown to Juan. 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) ] (Agentd knows that 1)","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":"Juan can now know that Nicole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicole","Earlie","Roseanne","Juan"],"index":29659,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978487492,"difficulty":0.0021512508}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ted's card is shown to James. Eleanor's card is shown to Eleanor. Eleanor's card is shown to Ted. It is publicly announced that someone picked a red card. It is publicly announced that Ted picked a red card. It is publicly announced that Alexis knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Alexis can now know whether James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Eleanor","Alexis","Ted"],"index":18627,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8144222498,"difficulty":0.1855777502}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Gary. Laura's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Gary 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)) ] Agenta knows that (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":"Gary can now know that Laura can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gary","Laura"],"index":66543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983304143,"difficulty":0.0016695857}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Gladys. Gladys's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that Judith does not know whether or not everyone picked a red card. It is publicly announced that Judith knows whether or not nobody picked a red card. It is publicly announced that Gladys 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 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 1 ] 0","hypothesis":"Judith can now know whether Gladys can know that Judith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gladys","Judith"],"index":14996,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9350215197,"difficulty":1.9350215197}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyler's card is shown to Thomas. Thomas's card is shown to Bernice. Thomas's card is shown to Tyler. 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 Loretta does not know whether Bernice 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 whether (~(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":"Thomas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Bernice","Loretta","Tyler"],"index":296,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997138381,"difficulty":0.0002861619}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ebony's card is shown to Ebony. Michelle's card is shown to Ebony. Lorraine's card is shown to Ebony. Lorraine's card is shown to Michelle. Michelle's card is shown to Lorraine. Lorraine's card is shown to Lorraine. 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) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ramona can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ramona","Ebony","Michelle","Lorraine"],"index":40636,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9832633734,"difficulty":0.0167366266}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Ruth. Ruth's card is shown to Jesse. Jesse's card is shown to Jesse. Jesse's card is shown to Jeremy. 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 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeremy can now know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Jesse","Jeremy","Matilda"],"index":19710,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974761605,"difficulty":0.0025238395}
{"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 Norma. Kyle's card is shown to Kyle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kyle can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norma","Kyle","Irene","Barb"],"index":56488,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983666539,"difficulty":0.0016333461}
{"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. Patrice's card is shown to James. Patrice's card is shown to Patrice. It is publicly announced that someone picked a red card. It is publicly announced that Patrice 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)","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":"Anthony can now know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anthony","James","Patrice"],"index":57104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9862809181,"difficulty":0.0137190819}
{"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 Rodney. Charles's card is shown to Evonne. Rodney's card is shown to Charles. Mariano's card is shown to Mariano. 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) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Mariano can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rodney","Evonne","Charles","Mariano"],"index":62883,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9846108556,"difficulty":0.0153891444}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lanny's card is shown to Lanny. Robin's card is shown to Lanny. Robert's card is shown to Lanny. Robert's card is shown to Robin. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Robin does not know whether Robin picked a red card. It is publicly announced that Lanny 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))) ] (Agentc knows whether 1)","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":"Robert can now know whether Lanny picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lanny","Robin","Robert"],"index":6119,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7439305782,"difficulty":1.7439305782}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Pauline. Pauline's card is shown to Walter. Patricia's card is shown to Walter. Walter'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:1 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:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pauline can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pauline","Patricia","Walter"],"index":66464,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997716546,"difficulty":0.0002283454}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harriett's card is shown to Delphia. Harriett's card is shown to Alma. Alma's card is shown to Harriett. Harriett's card is shown to Harriett. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alma can now know that Delphia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Delphia","Alma","Harriett"],"index":20096,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981081486,"difficulty":0.0018918514}
{"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 Sharon. Rita's card is shown to Sharon. Carl's card is shown to Carl. Rita's card is shown to Carl. Sharon's card is shown to Jerry. Carl's card is shown to Rita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 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:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know whether Carl can know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Carl","Jerry","Rita"],"index":38327,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8999449015,"difficulty":0.1000550985}
{"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 Timothy. Delilah's card is shown to Delilah. Linda's card is shown to Delilah. Delilah's card is shown to Eugene. Timothy's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Delilah picked a black card. It is publicly announced that Delilah does not know whether Timothy picked a red card. It is publicly announced that Delilah knows whether someone picked a red card. It is publicly announced that Delilah does not know whether Timothy 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) ] Agenta knows that (Agentb knows whether (1|2|3|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":"Timothy can now know that Delilah can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Delilah","Eugene","Linda"],"index":36847,"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). Ashley's card is shown to Rex. Bradley's card is shown to Ashley. Tamara's card is shown to Ashley. Rex's card is shown to Bradley. Ashley's card is shown to Bradley. Ashley's card is shown to Tamara. Bradley's card is shown to Tamara. 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 (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:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bradley can now know that Tamara can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rex","Ashley","Bradley","Tamara"],"index":26521,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997139573,"difficulty":0.0002860427}
{"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 Virginia. Florence's card is shown to Clarence. Florence's card is shown to Florence. Virginia's card is shown to Renee. 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 Agentd: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 Agentb:3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Virginia can now know that Clarence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Clarence","Florence","Renee"],"index":11581,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980917573,"difficulty":0.0019082427}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caren's card is shown to Kathryn. Kathryn's card is shown to Bessie. Bessie's card is shown to Bessie. Kathryn's card is shown to Margaret. Bessie's card is shown to Margaret. Kathryn's card is shown to Caren. Caren's card is shown to Caren. It is publicly announced that someone picked a red card. It is publicly announced that Bessie picked a black card. It is publicly announced that Bessie does not know whether Caren 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)) ] Agentb knows that (Agentc knows whether 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":"Bessie can now know that Margaret can know whether Caren picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathryn","Bessie","Margaret","Caren"],"index":30300,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9215990305,"difficulty":1.9215990305}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Lois. Lois's card is shown to Juliette. Jeffrey's card is shown to Juliette. Jeffrey's card is shown to Frank. Lois's card is shown to Jeffrey. Juliette's card is shown to Jeffrey. Frank's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juliette can now know whether Jeffrey can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lois","Juliette","Frank","Jeffrey"],"index":21544,"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). Octavia's card is shown to Robert. Victor's card is shown to Victor. Robert's card is shown to Octavia. Octavia's card is shown to Octavia. It is publicly announced that someone picked a red card. It is publicly announced that Victor does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Victor","Octavia","Helen"],"index":18440,"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). Catalina's card is shown to Robert. Robert's card is shown to Catalina. Catalina's card is shown to Catalina. Catalina'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 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Catalina can now know whether Sheila picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Catalina","Sheila"],"index":47218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7283701301,"difficulty":0.2716298699}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ken's card is shown to Ken. Ken's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Ken knows whether or not nobody picked a red card. It is publicly announced that Ken 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 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ken","Robert","Marcia","John"],"index":13114,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6395909786,"difficulty":0.3604090214}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lindsey's card is shown to Matthew. Bernadine's card is shown to Matthew. Lindsey's card is shown to Lindsey. It is publicly announced that someone picked a red card. It is publicly announced that Matthew does not know whether Paige picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Matthew can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Lindsey","Bernadine","Paige"],"index":48203,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9920626283,"difficulty":0.0079373717}
{"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 Richard. Richard's card is shown to Douglas. Douglas's card is shown to Douglas. 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 whether (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":"Douglas can now know whether Richard can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Douglas"],"index":34569,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.996049583,"difficulty":0.003950417}
{"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 Christopher. Marianne's card is shown to Christopher. Marianne's card is shown to Marianne. It is publicly announced that someone picked a red card. It is publicly announced that Marianne knows whether or not nobody picked a red card. It is publicly announced that Marianne does not know whether Christopher picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Christopher can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Marianne"],"index":41379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9890489578,"difficulty":0.0109510422}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Imelda's card is shown to Juan. Marcella's card is shown to Thomas. Thomas's card is shown to Imelda. Marcella's card is shown to Imelda. Juan's card is shown to Marcella. Thomas's card is shown to Marcella. 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 (Agenta knows whether 2)","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":"Marcella can now know that Juan can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juan","Thomas","Imelda","Marcella"],"index":11459,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6766174436,"difficulty":1.6766174436}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. David's card is shown to David. 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 Brenda does not know whether David picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Brenda can now know whether David can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brenda","David"],"index":45662,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994910955,"difficulty":0.0005089045}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anita's card is shown to Carol. Caleb's card is shown to Caleb. John's card is shown to John. John's card is shown to Anita. 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) ] Agentc knows that (Agentb knows that (1|2|3|4))","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":"John can now know that Caleb can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Caleb","John","Anita"],"index":57628,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. William's card is shown to Anthony. Anthony's card is shown to Bennie. Bennie's card is shown to Bennie. Bennie's card is shown to Tracy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bennie can now know that Anthony can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","William","Bennie","Tracy"],"index":65118,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976434112,"difficulty":0.0023565888}
{"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. Herbert's card is shown to William. Ruth'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:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Herbert","Ruth","Dominick"],"index":64669,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9887825847,"difficulty":0.0112174153}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marina's card is shown to Gaylene. Marina's card is shown to David. Marina's card is shown to Marina. Herbert'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:3 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd 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":"David can now know that Herbert can know whether Herbert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gaylene","David","Marina","Herbert"],"index":32319,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7261019349,"difficulty":1.7261019349}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hazel's card is shown to Robert. Loretta's card is shown to Hattie. Robert's card is shown to Loretta. Hattie's card is shown to Loretta. Loretta's card is shown to Loretta. Hazel's card is shown to Loretta. 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:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3,4 VALID? [ ! (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":0,"names":["Robert","Hattie","Loretta","Hazel"],"index":11881,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8492438197,"difficulty":1.8492438197}
{"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 Mary. Terry's card is shown to Terry. Terry's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Terry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc 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) ] [ ! 2 ] 0","hypothesis":"Timothy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Terry","Timothy"],"index":8167,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997262359,"difficulty":0.0002737641}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alvaro's card is shown to Richard. Richard's card is shown to Karen. Karen's card is shown to Karen. Carla's card is shown to Karen. Alvaro's card is shown to Karen. Karen's card is shown to Carla. Richard's card is shown to Alvaro. It is publicly announced that someone picked a red card. It is publicly announced that Carla does not know whether Richard picked a red card. It is publicly announced that Richard knows whether 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:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Karen can now know whether Alvaro can know that Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Karen","Carla","Alvaro"],"index":13177,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9522621632,"difficulty":0.0477378368}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Marilyn. Sarah's card is shown to Marilyn. Marilyn's card is shown to Sarah. 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 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Katherine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marilyn","Katherine","Sarah"],"index":23304,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984429479,"difficulty":0.0015570521}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eduardo's card is shown to Eduardo. Russell's card is shown to Lois. Lois's card is shown to Russell. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc: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 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Russell can now know whether Lois can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eduardo","Lois","Russell"],"index":55059,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9135151505,"difficulty":0.0864848495}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carrie's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether Carrie picked a red card. It is publicly announced that Jeffrey does not know whether Jeffrey picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jeffrey can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jeffrey","Carrie"],"index":53033,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986079335,"difficulty":0.0013920665}
{"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 Terry. Larry's card is shown to Kathy. Terry's card is shown to Larry. 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. It is publicly announced that Kathy knows whether Larry 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 (1&2&3)) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Larry can now know whether Larry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Terry","Kathy","Larry"],"index":48641,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9877912998,"difficulty":0.0122087002}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Magdalena's card is shown to Elton. Elton's card is shown to Erick. Erick's card is shown to Erick. Magdalena's card is shown to Erick. It is publicly announced that someone picked a red card. It is publicly announced that Magdalena picked a black card. It is publicly announced that Magdalena picked a black card. It is publicly announced that Elton does not know whether Erick picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Elton can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elton","Erick","Magdalena"],"index":32316,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979012012,"difficulty":0.0020987988}
{"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. Cindy's card is shown to Michael. Alfred's card is shown to Michael. Ralph's card is shown to Michael. Cindy's card is shown to Cindy. Michael's card is shown to Alfred. Michael's card is shown to Ralph. Alfred's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Alfred does not know whether Alfred picked a red card. It is publicly announced that Michael knows whether Alfred picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Alfred can now know that Alfred picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Cindy","Alfred","Ralph"],"index":22782,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9604175687,"difficulty":0.0395824313}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Joanne. Joanne's card is shown to Scott. Scott's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Scott knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joanne does not know whether Scott 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 whether (Agentb knows that 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":"Joanne can now know whether Scott can know that Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joanne","Scott"],"index":25170,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9447675347,"difficulty":1.9447675347}
{"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 Gladys. Gladys's card is shown to Jose. Gladys's card is shown to Gregory. Jose's card is shown to Gregory. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jose can now know that Gladys can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gladys","Jose","Gregory"],"index":14578,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
{"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 Carole. Carole'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 Karen knows whether Karen picked a red card. It is publicly announced that Carole does not know whether Karen 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 whether 2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Carole can now know whether Carole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Carole","Karen"],"index":46585,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9936170578,"difficulty":0.0063829422}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dina's card is shown to Dina. Robert's card is shown to Dina. Dina'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 everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Robert can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dina","Robert"],"index":18972,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9972533584,"difficulty":0.0027466416}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Silvia's card is shown to Leo. Leo's card is shown to Charles. Silvia's card is shown to Charles. Leo's card is shown to Silvia. It is publicly announced that someone picked a red card. It is publicly announced that Leo does not know whether Leo 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) ] (Agentb knows that (1&2&3))","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":"Charles can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leo","Charles","Silvia"],"index":29992,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986311793,"difficulty":0.0013688207}
{"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 Lonnie. Pedro's card is shown to Pedro. Kenneth's card is shown to Pedro. Bert's card is shown to Bert. Lonnie's card is shown to Kenneth. Pedro'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 Bert picked a red card. It is publicly announced that Pedro picked a black card. It is publicly announced that Pedro knows whether Kenneth picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Bert can now know that Pedro can know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lonnie","Pedro","Bert","Kenneth"],"index":19071,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7950390577,"difficulty":1.7950390577}
{"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 Lesley. Lesley'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 someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Ray can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lesley","Ray"],"index":25688,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997534156,"difficulty":0.0002465844}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilma's card is shown to Wilma. Steve's card is shown to Wilma. Wilma's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Wilma knows whether Wilma 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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Steve can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wilma","Steve"],"index":32645,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9451220036,"difficulty":0.0548779964}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Richard. Kevin's card is shown to Kevin. Michael's card is shown to Kevin. Richard'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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Kevin can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Kevin","Michael"],"index":36413,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.996776998,"difficulty":0.003223002}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Andrew. Andrew's card is shown to Sherry. Helen's card is shown to Sherry. Sherry's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Sherry 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 whether (Agentb knows whether (~(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":"Andrew can now know whether Sherry can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Sherry","Helen"],"index":33937,"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). Jeffery's card is shown to Jeffery. Jeffery's card is shown to Ralph. Samantha's card is shown to Ralph. Ralph's card is shown to Samantha. Jeffery's card is shown to Stanley. Samantha's card is shown to Stanley. 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:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffery can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffery","Ralph","Samantha","Stanley"],"index":56174,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
{"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 Antoinette. Rita's card is shown to Antoinette. Antoinette's card is shown to Claudine. Michael's card is shown to Claudine. Michael's card is shown to Michael. Antoinette's card is shown to Rita. Michael's card is shown to Rita. 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 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Claudine can now know whether Rita can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Antoinette","Claudine","Michael","Rita"],"index":2447,"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). Guadalupe's card is shown to Guadalupe. Guadalupe's card is shown to Katherine. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that Guadalupe knows whether Katherine 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 (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":"Katherine can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Guadalupe","Katherine"],"index":32108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Travis's card is shown to Elena. Elena's card is shown to Doris. Doris's card is shown to Doris. Elena's card is shown to Travis. It is publicly announced that someone picked a red card. It is publicly announced that Elena does not know whether Doris picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Doris can now know that Travis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elena","Doris","Travis"],"index":59124,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958586097,"difficulty":0.0041413903}
{"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. Doris's card is shown to Michael. Doris's card is shown to Doris. It is publicly announced that someone picked a red card. It is publicly announced that Doris knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Doris can now know that Michael can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Doris"],"index":59558,"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). Elizabeth's card is shown to Harold. Elsie's card is shown to Elsie. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 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":"Elizabeth can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harold","Elsie","Elizabeth"],"index":29886,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971151352,"difficulty":0.0028848648}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michele's card is shown to Michele. Fernando's card is shown to Fernando. Michele'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:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Fernando can now know whether Maria can know that Maria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michele","Fernando","Maria"],"index":50180,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7283283472,"difficulty":1.7283283472}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Genia's card is shown to Genia. Janet's card is shown to Genia. Genia's card is shown to Janet. Rickey's card is shown to Janet. 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:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rickey can now know that Genia can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Genia","Rickey","Janet"],"index":17253,"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). Nicole's card is shown to Marco. Nelida's card is shown to Nicole. Nicole's card is shown to Nicole. Nelida's card is shown to Philip. Marco's card is shown to Philip. It is publicly announced that someone picked a red card. It is publicly announced that Marco knows whether or not everyone picked a red card. It is publicly announced that Nelida 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) ] (Agentb 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":"Marco can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nelida","Marco","Nicole","Philip"],"index":26060,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997230172,"difficulty":0.0002769828}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Mattie. Mattie's card is shown to April. April's card is shown to April. Mattie's card is shown to Marlene. Marlene's card is shown to Marlene. It is publicly announced that someone picked a red card. It is publicly announced that April knows whether Mattie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"April can now know that Marlene can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mattie","April","Marlene"],"index":12325,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
{"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 Lorenzo. Matthew's card is shown to Shelly. Shelly's card is shown to James. James's card is shown to James. Lorenzo's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Lorenzo does not know whether Matthew picked a red card. It is publicly announced that Shelly 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) ] (Agenta knows whether 1)","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":"Lorenzo can now know whether Lorenzo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorenzo","Shelly","James","Matthew"],"index":12452,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9941097498,"difficulty":1.9941097498}
{"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 Patricia. James's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(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":["Patricia","Robert","James"],"index":64836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deana's card is shown to Deana. Tammy's card is shown to Tammy. 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:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Deana can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Deana","Tammy"],"index":51666,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Loretta's card is shown to Loretta. Michelle's card is shown to Loretta. Michelle's card is shown to Michelle. Letha's card is shown to Michelle. Shirley's card is shown to Letha. Letha's card is shown to Letha. 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) ] (Agenta 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:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Loretta can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Loretta","Michelle","Shirley","Letha"],"index":14114,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997242093,"difficulty":0.0002757907}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Lewis. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Lewis 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))) ] Agentb knows whether (Agenta knows that 1)","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":"Barbara can now know whether Lewis can know that Lewis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lewis","Barbara"],"index":41985,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6026719809,"difficulty":1.6026719809}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Marilyn. Marilyn's card is shown to Carlos. Carlos'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:1 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marilyn can now know that Betty can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Marilyn","Carlos"],"index":48337,"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). Sam's card is shown to Fred. Sam's card is shown to Sam. Joann's card is shown to Sam. Fred's card is shown to Joann. Sam's card is shown to Joann. Joann's card is shown to Joann. It is publicly announced that someone picked a red card. It is publicly announced that Sam picked a red card. It is publicly announced that Sam does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Fred can now know that Sam can know whether Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Fred","Sam","Joann"],"index":40922,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8397435546,"difficulty":1.8397435546}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Violet's card is shown to Violet. Violet's card is shown to Brenda. Brenda's card is shown to Brett. Helen's card is shown to Brett. Helen's card is shown to Helen. 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 Brett 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 that (Agentb knows that 2)","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":"Violet can now know that Brenda can know that Brenda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Violet","Brenda","Brett","Helen"],"index":52040,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9214017987,"difficulty":0.0785982013}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Maureen. Sara's card is shown to Sara. It is publicly announced that someone picked a red card. It is publicly announced that Maureen does not know whether Maureen 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 that (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 1) ] 0","hypothesis":"Maureen can now know that Sara can know that Sara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maureen","Sara"],"index":47017,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9870266318,"difficulty":1.9870266318}
{"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 Constance. Gregory's card is shown to Constance. Constance's card is shown to Lois. Jean's card is shown to Lois. Lois's card is shown to Jean. Jean's card is shown to Jean. Gregory's card is shown to Jean. Constance's card is shown to Gregory. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2,3,4 Agentd:1 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:1,3 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know whether Lois can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Constance","Lois","Jean","Gregory"],"index":38739,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997109771,"difficulty":0.0002890229}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to Martha. Barbara's card is shown to Martha. Barbara's card is shown to Barbara. 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:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Martha can now know whether Barbara can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Martha","Barbara"],"index":15515,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997672439,"difficulty":0.0002327561}
{"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 Brandy. Brandy's card is shown to Norma. Carlton's card is shown to Stacy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 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":"Carlton can now know that Stacy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carlton","Brandy","Norma","Stacy"],"index":19083,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984742999,"difficulty":0.0015257001}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 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":"Charles can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Gregory"],"index":14936,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947196245,"difficulty":0.0052803755}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheri's card is shown to Sheri. Aaron's card is shown to Andrea. Sheri's card is shown to Andrea. Harry's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Sheri 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 whether 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":"Aaron can now know whether Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aaron","Sheri","Andrea","Harry"],"index":16684,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7409079075,"difficulty":1.7409079075}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erwin's card is shown to Erwin. Erwin's card is shown to Richard. Richard's card is shown to Richard. Linda's card is shown to Richard. Erwin'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:1,2,3 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 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Erwin","Richard","Linda"],"index":44677,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to June. Linda's card is shown to June. Richard's card is shown to June. Linda's card is shown to Linda. June's card is shown to Richard. Linda's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Linda can now know whether June can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["June","Linda","Richard"],"index":63814,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980254173,"difficulty":0.0019745827}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Salvador's card is shown to Salvador. Salvador's card is shown to Pamela. 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) ] Agenta knows that (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":"Salvador can now know that Pamela can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Salvador","Pamela"],"index":64450,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.987896204,"difficulty":0.012103796}
{"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 Tina. Donald's card is shown to Patricia. Tina's card is shown to Donald. Patricia's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether Donald picked a red card. It is publicly announced that Tina 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 that 1)","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":"Tina can now know that Tina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tina","Patricia","Donald"],"index":50811,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9792732,"difficulty":0.0207268}
{"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 Mirta. Marjorie's card is shown to Marie. Tina's card is shown to Tina. Marie's card is shown to Marjorie. Tina's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Tina does not know whether Marie picked a red card. It is publicly announced that Mirta knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marie can now know whether Marjorie can know whether Marie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mirta","Marie","Tina","Marjorie"],"index":18609,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9969789982,"difficulty":0.0030210018}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vito's card is shown to Vito. Mable's card is shown to Vito. Mable's card is shown to Mable. Vivian's card is shown to Vivian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vivian can now know that Mable can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vito","Mable","Vivian"],"index":63741,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997180104,"difficulty":0.0002819896}
{"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 Robert. William's card is shown to William. William's card is shown to Luis. Luis's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Nicholas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Nicholas","William","Luis"],"index":19777,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8349634409,"difficulty":0.1650365591}
{"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 Robert. Maurice's card is shown to Jeffrey. Edward's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Robert does not know whether Maurice 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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Maurice can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Jeffrey","Maurice","Edward"],"index":1265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.991887033,"difficulty":0.008112967}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karl's card is shown to Karl. Susan's card is shown to Karl. Susan's card is shown to Susan. Karl's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Susan 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 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":"Karl can now know whether Harold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Karl","Susan","Harold"],"index":19930,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6304668784,"difficulty":0.3695331216}
{"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. Monica's card is shown to Anthony. Anthony's card is shown to Cheryl. Monica's card is shown to Cheryl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb: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:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know that Monica can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Monica","Cheryl"],"index":25546,"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). Jared's card is shown to Jared. Jared's card is shown to Misti. Misti's card is shown to Misti. It is publicly announced that someone picked a red card. It is publicly announced that Jared knows whether Aaron 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) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Aaron can now know that Jared can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Aaron","Jared","Misti"],"index":45342,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9427565336,"difficulty":1.9427565336}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Patricia. Patricia's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card. It is publicly announced that Patricia knows whether Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Patricia can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Michael"],"index":56879,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99967134,"difficulty":0.00032866}
{"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 Andrea. Jared's card is shown to Andrea. Andrea's card is shown to Larry. Larry's card is shown to Larry. Jared's card is shown to Larry. Larry's card is shown to Elizabeth. Jared's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Andrea can now know whether Elizabeth can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrea","Larry","Elizabeth","Jared"],"index":10703,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996334314,"difficulty":0.0003665686}
{"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 Doris. Jay's card is shown to Martha. Doris's card is shown to Jay. Jay's card is shown to Jay. 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:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Martha can now know whether Martha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doris","Martha","Jay","Lydia"],"index":26577,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.838283062,"difficulty":0.161716938}
{"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. Eric's card is shown to Lisa. James's card is shown to Eric. Latonya's card is shown to Eric. Eric's card is shown to Latonya. It is publicly announced that someone picked a red card. It is publicly announced that Lisa 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:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Eric","James","Latonya"],"index":39758,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7247262597,"difficulty":1.7247262597}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. Harry's card is shown to Cindy. Cindy's card is shown to Harry. Harry's card is shown to Dorothy. 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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Cindy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cindy","Harry","Dorothy"],"index":48526,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7503051162,"difficulty":1.7503051162}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyler's card is shown to Tyler. Patrick's card is shown to Tyler. Edith's card is shown to Patrick. Edith's card is shown to Edith. Michelle's card is shown to Michelle. 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 that 3)","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":"Patrick can now know that Edith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tyler","Patrick","Edith","Michelle"],"index":5691,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982126951,"difficulty":0.0017873049}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alanna's card is shown to Alanna. George's card is shown to Alanna. Alanna's card is shown to Jeff. Paul's card is shown to Paul. Alanna'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:1,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alanna can now know whether George can know whether Alanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alanna","Jeff","Paul","George"],"index":49576,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980260134,"difficulty":0.0019739866}
{"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 Donna. Donna's card is shown to Scot. Scot's card is shown to Scot. Dorothy's card is shown to Scot. Donna's card is shown to Dorothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 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 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Scot can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Scot","Dorothy"],"index":37332,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984967709,"difficulty":0.0015032291}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Catherine. Barbara's card is shown to Carol. Carol's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Catherine picked a red card. It is publicly announced that Catherine does not know whether Carol picked a red card. It is publicly announced that Barbara knows whether Carol picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Catherine can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Catherine","Barbara","Carol"],"index":4423,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997156262,"difficulty":0.0002843738}
{"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 Stacy. Ashley's card is shown to Stacy. Charles's card is shown to Charles. Calvin's card is shown to Charles. Stacy's card is shown to Calvin. Charles's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that Stacy does not know whether Calvin picked a red card. It is publicly announced that Charles picked a black card. It is publicly announced that Stacy does not know whether Stacy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Calvin can now know whether Stacy can know that Stacy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stacy","Charles","Calvin","Ashley"],"index":5565,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9435238242,"difficulty":0.0564761758}
{"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 Ethan. Ethan's card is shown to Ethan. Dana's card is shown to Ethan. Matthew's card is shown to Margaret. Margaret's card is shown to Margaret. Dana's card is shown to Margaret. Matthew's card is shown to Dana. Margaret'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:1,2,4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ethan can now know that Matthew can know that Ethan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Matthew","Ethan","Margaret","Dana"],"index":60864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962905645,"difficulty":0.0037094355}
{"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 Matthew. Elsie's card is shown to Matthew. Elsie's card is shown to Elsie. It is publicly announced that someone picked a red card. It is publicly announced that Elsie knows whether or not nobody picked a red card. It is publicly announced that Elsie does not know whether Matthew picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Elsie can now know that Elsie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Matthew","Elsie"],"index":48854,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8452242613,"difficulty":1.8452242613}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rufus's card is shown to Florence. Victor's card is shown to Florence. Juliette's card is shown to Juliette. Rufus's card is shown to Victor. Florence'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:1,4 Agentb:3 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:1,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juliette can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rufus","Florence","Juliette","Victor"],"index":7606,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985185266,"difficulty":0.0014814734}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adolfo's card is shown to Dan. Adolfo's card is shown to Mary. Geoffrey's card is shown to Mary. Dan's card is shown to Adolfo. It is publicly announced that someone picked a red card. It is publicly announced that Dan knows whether someone 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agenta knows whether 2)","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) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Dan can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dan","Mary","Adolfo","Geoffrey"],"index":45444,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9723204374,"difficulty":0.0276795626}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynne's card is shown to Lynne. Lynne'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 Christopher picked a red card. It is publicly announced that Christopher 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) ] Agenta knows whether (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":"Lynne can now know whether Christopher can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lynne","Christopher"],"index":36746,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
{"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 Phyllis. Sue's card is shown to Sue. Joshua's card is shown to Joshua. Phyllis's card is shown to Jeanie. It is publicly announced that someone picked a red card. It is publicly announced that Phyllis picked a red card. It is publicly announced that Jeanie does not know whether Jeanie picked a red card. It is publicly announced that Sue knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Phyllis can now know that Jeanie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phyllis","Sue","Joshua","Jeanie"],"index":5526,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996980429,"difficulty":0.0003019571}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Robert. Robert's card is shown to Adam. Adam's card is shown to Adam. It is publicly announced that someone picked a red card. It is publicly announced that Adam knows whether or not everyone 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 that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Robert can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Adam"],"index":44746,"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). Patricia's card is shown to Frances. David's card is shown to Frances. David's card is shown to Patricia. 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:2,3 Agentb:3 Agentc:3 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:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"David can now know that Frances can know that Frances picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frances","Patricia","David"],"index":6988,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6733557582,"difficulty":0.3266442418}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dolores's card is shown to John. John's card is shown to Dolores. Dolores's card is shown to Stefanie. 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 Dolores knows whether Dolores picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know whether Dolores picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Dolores","Stefanie"],"index":20909,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9934784174,"difficulty":0.0065215826}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janelle's card is shown to Janelle. Berniece's card is shown to Janelle. Janelle's card is shown to Daniel. Janelle's card is shown to Berniece. 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 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":"Daniel can now know that Berniece picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janelle","Daniel","Berniece"],"index":65368,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981895089,"difficulty":0.0018104911}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmy's card is shown to Jimmy. Helen's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Jimmy knows 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 whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Helen can now know whether Jimmy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jimmy","Helen"],"index":8151,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996885061,"difficulty":0.0003114939}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terry's card is shown to Angie. Sandy's card is shown to Sandy. Sandy's card is shown to Terry. Angie's card is shown to Gladys. 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:2 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gladys can now know that Angie can know whether Gladys picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angie","Sandy","Terry","Gladys"],"index":43910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9148259163,"difficulty":0.0851740837}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Mattie. Tom's card is shown to Tom. It is publicly announced that someone picked a red card. It is publicly announced that Mattie does not know whether Mattie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Tom can now know that Mattie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mattie","Tom"],"index":53370,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985938668,"difficulty":0.0014061332}
{"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. Eva's card is shown to Jamie. Eva's card is shown to William. Jamie's card is shown to Victor. William's card is shown to Eva. Eva's card is shown to Eva. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether Jamie 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":"William can now know whether Victor can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jamie","William","Victor","Eva"],"index":26394,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5532009006,"difficulty":1.5532009006}
{"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 Mary. Frederick's card is shown to Mary. Troy's card is shown to Troy. Troy'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:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","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":"Mary can now know whether Troy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Troy","Frederick"],"index":43485,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.569485724,"difficulty":1.569485724}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernardo's card is shown to Lana. Lana's card is shown to Lana. It is publicly announced that someone picked a red card. It is publicly announced that Lana picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Bernardo can now know whether Bernardo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bernardo","Lana"],"index":625,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9852924943,"difficulty":0.0147075057}
{"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 Timothy. Valerie's card is shown to Timothy. Timothy's card is shown to Valerie. It is publicly announced that someone picked a red card. It is publicly announced that Valerie 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)) ] Agenta knows that (Agentb knows whether (~(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":"Timothy can now know that Valerie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Timothy","Valerie"],"index":10333,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997001886,"difficulty":0.0002998114}
{"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 Shirley. Patsy's card is shown to Shirley. Shirley's card is shown to Kimberly. Shirley's card is shown to Patsy. It is publicly announced that someone picked a red card. It is publicly announced that Shirley picked a red card. It is publicly announced that Kimberly knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Shirley knows whether Patsy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Patsy can now know that Shirley can know that Patsy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shirley","Kimberly","Patsy"],"index":52489,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8898383975,"difficulty":0.1101616025}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cruz's card is shown to Cruz. Maria's card is shown to John. Cruz's card is shown to Maria. John's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria 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 (Agentb knows that 2)","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":"Cruz can now know whether John can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cruz","John","Maria"],"index":42022,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6670017838,"difficulty":0.3329982162}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwardo's card is shown to George. Michael's card is shown to George. George's card is shown to Edwardo. Edwardo's card is shown to Edwardo. Phillip'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: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:2,3 Agentb:1,2 Agentc:4 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":["George","Edwardo","Michael","Phillip"],"index":53976,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984856248,"difficulty":0.0015143752}
{"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 Eugenia. Marjorie's card is shown to Helen. Helen's card is shown to David. Helen's card is shown to Marjorie. Marjorie's card is shown to Marjorie. 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 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eugenia","Helen","David","Marjorie"],"index":9881,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997246861,"difficulty":0.0002753139}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roberta's card is shown to Gertrude. Angela's card is shown to Gertrude. Gertrude's card is shown to Roberta. Gertrude's card is shown to Gloria. Roberta's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Gertrude does not know whether Gertrude picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gertrude can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gertrude","Roberta","Gloria","Angela"],"index":57608,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997108579,"difficulty":0.0002891421}
{"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 Clemente. Nona's card is shown to Nona. Carolyn's card is shown to Nona. Clemente's card is shown to Carolyn. Nona's card is shown to Carolyn. It is publicly announced that someone picked a red card. It is publicly announced that Nona does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Clemente can now know whether Nona can know whether Evelyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clemente","Nona","Evelyn","Carolyn"],"index":17867,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997972548,"difficulty":0.002027452}
{"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 Steven. Raquel's card is shown to David. Doris's card is shown to Doris. 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 that 1)","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":"Raquel can now know that David can know that Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","David","Raquel","Doris"],"index":11857,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983546138,"difficulty":0.0016453862}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Natasha's card is shown to Natasha. Natasha's card is shown to Manuel. Manuel's card is shown to Michael. Michael's card is shown to Michael. Natasha's card is shown to Carol. Carol's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Natasha does not know whether or not everyone picked a red card. It is publicly announced that Natasha picked a red card. It is publicly announced that Natasha 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)) ] Agentb knows that (Agenta knows whether 2)","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":"Manuel can now know that Natasha can know whether Manuel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Natasha","Manuel","Michael","Carol"],"index":45394,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8639174104,"difficulty":1.8639174104}
{"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. Lena's card is shown to Richard. Gussie's card is shown to Richard. Richard's card is shown to Homer. Homer's card is shown to Gussie. Gussie's card is shown to Gussie. 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 Agentc:2,4 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:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Homer can now know whether Lena can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Homer","Lena","Gussie"],"index":44215,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Patrick. Ann's card is shown to Ann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lee can now know that Patrick can know whether Ann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patrick","Lee","Ann"],"index":5904,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5710164309,"difficulty":1.5710164309}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Veronica's card is shown to Patricia. Patricia's card is shown to Veronica. Veronica's card is shown to Veronica. Stephen's card is shown to Veronica. Patricia's card is shown to Stephen. Stephen's card is shown to Stephen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Veronica can now know whether Stephen can know whether Veronica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Veronica","Stephen"],"index":45290,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979419112,"difficulty":0.0020580888}
{"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 Timothy. Marc's card is shown to Marc. It is publicly announced that someone picked a red card. It is publicly announced that Marc knows whether Marc 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:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Marc can now know whether Timothy can know that Marc picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Timothy","Marc"],"index":36017,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.85994941,"difficulty":0.14005059}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernest's card is shown to Ernest. Shannon's card is shown to Ernest. Ernest's card is shown to Shannon. Emily's card is shown to Shannon. Shannon's card is shown to Emily. Ernest's card is shown to Adam. It is publicly announced that someone picked a red card. It is publicly announced that Shannon knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Shannon picked a black card. It is publicly announced that Ernest does not know whether Adam 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) ] Agenta knows that (Agentb knows that 1)","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":"Ernest can now know that Shannon can know that Ernest picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ernest","Shannon","Emily","Adam"],"index":28215,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8530004025,"difficulty":0.1469995975}
{"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 Susan. Carolyn's card is shown to Carolyn. Susan's card is shown to Sandra. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn does not know whether Sandra picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Sandra can now know that Susan can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Carolyn","Sandra"],"index":35445,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9372344017,"difficulty":0.0627655983}
{"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. Rudy's card is shown to James. Steven's card is shown to Steven. James's card is shown to Rudy. 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:3 Agentd: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:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know that James can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","James","Steven","Rudy"],"index":19986,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997151494,"difficulty":0.0002848506}
{"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 Richard. Albertina's card is shown to Albertina. Viola's card is shown to Albertina. Richard's card is shown to Victor. Victor's card is shown to Victor. Viola's card is shown to Victor. Richard's card is shown to Viola. Viola's card is shown to Viola. 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) ] Agentc knows that (Agenta knows whether 2)","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":"Victor can now know that Richard can know whether Albertina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Albertina","Victor","Viola"],"index":45149,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5696917772,"difficulty":1.5696917772}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Katherine. Robin's card is shown to Robin. Rhonda's card is shown to Rhonda. It is publicly announced that someone picked a red card. It is publicly announced that Robin 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 Robin does not know whether Katherine 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 that (Agentb knows whether (1&2&3))","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":"Katherine can now know that Robin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katherine","Robin","Rhonda"],"index":61990,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6961627007,"difficulty":0.3038372993}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keith's card is shown to Daisy. Judi's card is shown to Raymond. Daisy's card is shown to Judi. Raymond's card is shown to Judi. Judi's card is shown to Judi. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know that Raymond can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Daisy","Raymond","Judi"],"index":66482,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerri's card is shown to Jerri. Jerri's card is shown to Sophia. Sophia's card is shown to Sophia. 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) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Jerri can now know whether Sophia can know whether Jerri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jerri","Sophia"],"index":34876,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979900122,"difficulty":0.0020099878}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erick's card is shown to Erick. Charlene's card is shown to Erick. Erick's card is shown to Charlene. Charlene's card is shown to Charlene. Erick's card is shown to Jackie. Charlene's card is shown to Jackie. Stacy's card is shown to Stacy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Erick can now know that Jackie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erick","Charlene","Jackie","Stacy"],"index":55518,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981201291,"difficulty":0.0018798709}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myung's card is shown to Kevin. Abel's card is shown to Kevin. Myung's card is shown to Myung. Kevin's card is shown to Abel. Abel's card is shown to Abel. Abel'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 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Myung can now know whether Abel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Myung","Abel","Douglas"],"index":55166,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7965758443,"difficulty":1.7965758443}
{"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 Joseph. Stephen's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Stephen picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Stephen can now know whether Joseph can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Stephen"],"index":2221,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7717943192,"difficulty":0.2282056808}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynda's card is shown to Lynda. Stewart's card is shown to Lynda. Lynda's card is shown to Donald. Donald's card is shown to Donald. Bradley's card is shown to Bradley. Lynda's card is shown to Stewart. Donald's card is shown to Stewart. 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 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether Stewart can know whether Bradley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lynda","Donald","Bradley","Stewart"],"index":19862,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998455286,"difficulty":0.001544714}
{"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 Kevin. Diane's card is shown to Marsha. Kevin's card is shown to Christina. Marsha's card is shown to Christina. Kevin's card is shown to Diane. Marsha's card is shown to Diane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know whether Marsha can know that Marsha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Marsha","Christina","Diane"],"index":41087,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.914968133,"difficulty":0.085031867}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stanley's card is shown to Kathryn. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathryn can now know whether Kathryn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathryn","Joshua","Stanley"],"index":57742,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8562967777,"difficulty":0.1437032223}
{"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 James. Mary's card is shown to James. James's card is shown to Jessica. Jessica's card is shown to Jessica. James's card is shown to Nancy. Mary's card is shown to Nancy. James's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Nancy can know whether Nancy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Jessica","Nancy","Mary"],"index":29591,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8289880753,"difficulty":0.1710119247}
{"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 Benjamin. Roger's card is shown to Benjamin. Benjamin's card is shown to Laura. Laura's card is shown to William. William's card is shown to William. Laura's card is shown to Roger. William's card is shown to Roger. 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:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know whether Roger picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Benjamin","Laura","William","Roger"],"index":34397,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9473828673,"difficulty":1.9473828673}
{"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 Howard. Danny's card is shown to Howard. Howard's card is shown to Bonnie. Bonnie's card is shown to Bonnie. Bonnie'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:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bonnie can now know that Danny can know that Howard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Howard","Danny","Bonnie","Norman"],"index":33867,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978049397,"difficulty":0.0021950603}
{"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 Nicole. Doris's card is shown to Nicole. Emma's card is shown to Doris. Nicole's card is shown to Emma. Emma's card is shown to Emma. It is publicly announced that someone picked a red card. It is publicly announced that Emma 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)) ] Agentb knows that (Agenta knows that 2)","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":"Doris can now know that Nicole can know that Doris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicole","Doris","Emma"],"index":15313,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6280497313,"difficulty":0.3719502687}
{"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 Karen. Michelle's card is shown to Paul. Karen's card is shown to Michelle. Paul's card is shown to Michelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta 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":"Paul can now know whether Karen can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Paul","Michelle"],"index":51865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978947043,"difficulty":0.0021052957}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jorge's card is shown to Jorge. Corey's card is shown to Jorge. Heather's card is shown to Heather. Corey's card is shown to Corey. It is publicly announced that someone picked a red card. It is publicly announced that Corey does not know whether Jorge 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) ] Agentb knows that (Agentc knows whether (1&2&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":"Heather can now know that Corey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jorge","Heather","Corey"],"index":55914,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9369118214,"difficulty":0.0630881786}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Megan's card is shown to Sharon. Rosa's card is shown to Sharon. Sharon's card is shown to Megan. Megan's card is shown to Megan. Rosa's card is shown to Megan. Rosa's card is shown to Rosa. 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 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rosa can now know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Megan","Rosa"],"index":18097,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977532029,"difficulty":0.0022467971}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sammy's card is shown to Charles. Charles's card is shown to Sammy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Sammy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Sammy"],"index":15533,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997176528,"difficulty":0.0002823472}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leon's card is shown to Cassandra. Doris's card is shown to Judy. Leon's card is shown to Judy. Doris's card is shown to Doris. Doris's card is shown to Leon. It is publicly announced that someone picked a red card. It is publicly announced that Cassandra does not know whether Doris picked a red card. It is publicly announced that Doris picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Judy can now know that Doris can know whether Cassandra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cassandra","Judy","Doris","Leon"],"index":20989,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7829595208,"difficulty":0.2170404792}
{"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 Maurice. Mary's card is shown to Maurice. Maurice's card is shown to Maria. Maria's card is shown to Maria. Maurice's card is shown to Mary. Matthew's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Maurice does not know whether Matthew picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Matthew can now know that Maurice can know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maurice","Maria","Matthew","Mary"],"index":14060,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932431579,"difficulty":0.0067568421}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Wanda. Wanda's card is shown to Janice. Janice's card is shown to Miguel. Miguel's card is shown to Miguel. Miguel's card is shown to Theodore. It is publicly announced that someone picked a red card. It is publicly announced that Theodore does not know whether Wanda picked a red card. It is publicly announced that Wanda does not know whether Janice picked a red card. It is publicly announced that Miguel knows whether Miguel 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 3)","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":"Theodore can now know whether Miguel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wanda","Janice","Miguel","Theodore"],"index":51126,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5444802642,"difficulty":0.4555197358}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stuart's card is shown to Wanda. Minnie's card is shown to Wanda. Stuart's card is shown to Stuart. Minnie's card is shown to Stuart. Minnie's card is shown to Claudia. Stuart's card is shown to Minnie. It is publicly announced that someone picked a red card. It is publicly announced that Claudia does not know whether Stuart 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 that (Agentb knows whether (1&2&3&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":"Minnie can now know that Stuart can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wanda","Stuart","Claudia","Minnie"],"index":5063,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9375711083,"difficulty":0.0624288917}
{"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 Marisa. Bebe's card is shown to Marisa. Judy's card is shown to Sandra. Bebe's card is shown to Sandra. 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 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:2,3 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Marisa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marisa","Judy","Bebe","Sandra"],"index":46976,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982008934,"difficulty":0.0017991066}
{"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 Anthony. Earl's card is shown to Anthony. Earl's card is shown to Cristina. Kelly's card is shown to Kelly. Cristina's card is shown to Earl. Earl's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Kelly knows whether someone picked a red card. It is publicly announced that Anthony picked a red card. It is publicly announced that Cristina does not know whether Kelly 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 (Agentd knows whether 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":"Kelly can now know that Earl can know whether Earl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Cristina","Kelly","Earl"],"index":47559,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.919166863,"difficulty":0.080833137}
{"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 Jacqueline. Jacqueline's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Jesus does not know whether John 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 4) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jacqueline can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacqueline","Jesus","Carl","John"],"index":53617,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
{"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 Ignacio. Emily's card is shown to Judy. Emily'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 everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Judy can now know that Ignacio picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ignacio","Judy","Emily","Michael"],"index":51989,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.995408833,"difficulty":0.004591167}
{"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 Donald. Mary's card is shown to Donald. Robin's card is shown to Gary. Donald's card is shown to Gary. 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:3,4 Agentb:1,2 Agentc:4 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:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robin","Donald","Gary","Mary"],"index":6717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6223440766,"difficulty":0.3776559234}
{"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 David. David's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that Heather knows whether Heather picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Heather can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Heather"],"index":65124,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9059901237,"difficulty":1.9059901237}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricardo's card is shown to Della. Della's card is shown to Ricardo. Ricardo's card is shown to Ricardo. Della's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Ricardo knows whether Ricardo 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 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ricardo can now know whether Della can know that Della picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Della","Ricardo","Stephen"],"index":64776,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7800415158,"difficulty":0.2199584842}
{"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 Marie. Marie's card is shown to Amber. Amber's card is shown to Amber. Suzanne's card is shown to Amber. Suzanne's card is shown to Suzanne. 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:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amber can now know that Suzanne can know whether Suzanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marie","Amber","Suzanne"],"index":417,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6510472894,"difficulty":0.3489527106}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marc's card is shown to Michael. Michael's card is shown to Kelli. Kelli's card is shown to Marc. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Kelli","Marc"],"index":17595,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953917265,"difficulty":0.0046082735}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jolene's card is shown to Jolene. Dorothy's card is shown to Jolene. Daniel's card is shown to Dorothy. Dorothy'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:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Daniel can now know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jolene","Dorothy","Daniel"],"index":2492,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.977822721,"difficulty":1.977822721}
{"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 Amy. Beatrice's card is shown to Ernest. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb: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:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amy","Daniel","Ernest","Beatrice"],"index":56498,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985161424,"difficulty":0.0014838576}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Sophia. Sophia's card is shown to Danielle. It is publicly announced that someone picked a red card. It is publicly announced that Danielle picked a red card. It is publicly announced that Sophia 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) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Sophia can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sophia","Danielle"],"index":12407,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8928956985,"difficulty":1.8928956985}
{"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. Carol's card is shown to Michael. Carol's card is shown to Carol. Janet's card is shown to Carol. Michael's card is shown to Lucas. Carol's card is shown to Lucas. Michael's card is shown to Janet. Janet's card is shown to Janet. 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 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carol can now know that Janet can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Carol","Lucas","Janet"],"index":64362,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carla's card is shown to Bryan. Jamie's card is shown to Robert. Robert's card is shown to Carla. Carla's card is shown to Carla. Bryan's card is shown to Jamie. It is publicly announced that someone picked a red card. It is publicly announced that Bryan does not know whether Jamie picked a red card. It is publicly announced that Robert 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) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Bryan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bryan","Robert","Carla","Jamie"],"index":61309,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998588264,"difficulty":0.001411736}
{"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. Anthony's card is shown to Carol. Carol's card is shown to Bill. Anthony's card is shown to Bill. Bill's card is shown to Anthony. 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 1)","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":"Anthony can now know that Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carol","Bill","Anthony"],"index":18105,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980789423,"difficulty":0.0019210577}
{"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 Benjamin. Elizabeth's card is shown to Elizabeth. Benjamin'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 Elizabeth does not know whether Benjamin 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 (Agenta 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":"Robert can now know that Benjamin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Benjamin","Elizabeth","Robert"],"index":9554,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997065663,"difficulty":0.0002934337}
{"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 Julian. Julian's card is shown to Gerald. Julian's card is shown to Karen. Gerald's card is shown to Karen. James's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Julian does not know whether Julian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Julian can now know that James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julian","Gerald","James","Karen"],"index":9272,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.988522768,"difficulty":0.011477232}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kurt's card is shown to Yuki. Yuki's card is shown to Kurt. Kurt's card is shown to Kurt. It is publicly announced that someone picked a red card. It is publicly announced that Kurt picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Kurt can now know whether Yuki can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Yuki","Kurt"],"index":16197,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
{"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. Edward's card is shown to Michael. Michael's card is shown to Cheryl. Jane's card is shown to Cheryl. Michael's card is shown to Jane. Edward's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Jane 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) ] Agenta knows whether (Agentc knows that 3)","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":"Michael can now know whether Jane can know that Jane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Cheryl","Jane","Edward"],"index":13257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9261645079,"difficulty":0.0738354921}
{"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 Francis. Virginia's card is shown to Todd. Francis's card is shown to Virginia. 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 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:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Francis can now know that Francis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francis","Todd","Virginia","Melissa"],"index":30362,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945462942,"difficulty":0.0054537058}
{"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. Tracey's card is shown to Steven. Tracey's card is shown to Tracey. It is publicly announced that someone picked a red card. It is publicly announced that Tracey 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) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Steven can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Steven","Tracey"],"index":9144,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979327917,"difficulty":0.0020672083}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brad's card is shown to Brad. Brad's card is shown to Jacalyn. Jacalyn's card is shown to Jacalyn. John's card is shown to Jacalyn. Brad's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card. It is publicly announced that Brad picked a black card. It is publicly announced that Jacalyn knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Brad can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brad","Jacalyn","John"],"index":24399,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985608459,"difficulty":0.0014391541}
{"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 Victoria. Joshua's card is shown to Joshua. Victoria's card is shown to Rosemary. Joshua's card is shown to Rosemary. Joshua's card is shown to Kent. 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:4 Agentb:2 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Joshua can now know that Kent can know whether Rosemary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victoria","Joshua","Rosemary","Kent"],"index":16433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6514199376,"difficulty":0.3485800624}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lyle's card is shown to Lyle. Lyle's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason 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 that 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":"Jason can now know that Lyle can know that Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lyle","Jason"],"index":16806,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962064028,"difficulty":0.0037935972}
{"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 Jason. James's card is shown to Jason. Shawn's card is shown to Susan. Jason's card is shown to Shawn. Susan's card is shown to Shawn. 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 Jason picked a red card. It is publicly announced that Shawn 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)) ] Agentb knows whether (Agentc knows whether 1)","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":"Susan can now know whether Shawn can know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Susan","Shawn","James"],"index":31175,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985780716,"difficulty":0.0014219284}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelo's card is shown to Angelo. Angelo's card is shown to Carmen. Carmen's card is shown to Carmen. Alicia's card is shown to Carmen. Angelo's card is shown to David. David's card is shown to David. David's card is shown to Alicia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 Agentc:1,3 Agentd: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 Agentb:1,2,4 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Angelo can now know that Carmen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angelo","Carmen","David","Alicia"],"index":16541,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981466532,"difficulty":0.0018533468}
{"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 Greg. John's card is shown to Greg. Greg's card is shown to Linda. John's card is shown to Linda. Kevin's card is shown to Kevin. Linda's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Greg knows whether or not nobody picked a red card. It is publicly announced that Greg 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 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":"Greg can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Greg","Linda","Kevin","John"],"index":65365,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977037311,"difficulty":0.0022962689}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Austin's card is shown to Angel. Angel's card is shown to Austin. 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:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Angel can now know that Angel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angel","Annette","Austin"],"index":20027,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9564601779,"difficulty":0.0435398221}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nila's card is shown to Nila. Gloria's card is shown to Nila. Gloria's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that Gloria picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 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) ] [ ! 2 ] 0","hypothesis":"Nila can now know that Gloria can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nila","Gloria"],"index":42937,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984813333,"difficulty":0.0015186667}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Gerald. Sheila's card is shown to Gerald. Gerald's card is shown to Sheila. Elizabeth's card is shown to Sheila. Sheila's card is shown to Elizabeth. Gerald's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Sheila knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Sheila picked a black card. It is publicly announced that Gerald does not know whether Laura 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) ] Agenta knows whether (Agentb knows that 3)","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":"Gerald can now know whether Sheila can know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gerald","Sheila","Elizabeth","Laura"],"index":15580,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.96001333,"difficulty":1.96001333}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Denise. Harold's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Harold knows whether or not nobody picked a red card. It is publicly announced that Harold 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))) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Denise can now know whether Harold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Denise","Harold"],"index":31607,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9804172516,"difficulty":0.0195827484}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rochelle's card is shown to Rochelle. Lora's card is shown to Lora. Rochelle's card is shown to Jack. Lora'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 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lora can now know whether Lora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rochelle","Lora","Jack"],"index":14484,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9014885426,"difficulty":0.0985114574}
{"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. Meghan's card is shown to William. Sara's card is shown to Sara. Meghan's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb: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:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sara can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Sara","Meghan"],"index":40751,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943766594,"difficulty":0.0056233406}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Jeremy. Jeremy's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Jeremy does not know whether Jeremy 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":"Jeremy can now know that Walter can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeremy","Walter"],"index":1813,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9193685055,"difficulty":1.9193685055}
{"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 Suzanne. Suzanne's card is shown to Joseph. Suzanne's card is shown to Rhonda. Joseph's card is shown to Rhonda. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Willie picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Willie can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Suzanne","Willie","Joseph","Rhonda"],"index":27984,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.662130475,"difficulty":1.662130475}
{"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 Joseph. Joseph'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 Joseph knows whether or not nobody picked a red card. It is publicly announced that Joseph knows whether Mary picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card. It is publicly announced that Mary knows whether Mary 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 whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":4,"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) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joseph can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Mary"],"index":15846,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997854829,"difficulty":0.0002145171}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Amanda. Keisha's card is shown to Gayla. Ann's card is shown to Gayla. Ann's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Amanda knows whether or not nobody picked a red card. It is publicly announced that Ann 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:4 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Gayla can now know whether Amanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amanda","Gayla","Keisha","Ann"],"index":50733,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9403377175,"difficulty":1.9403377175}
{"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 Luis. Luis's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Luis 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)) ] (Agentb 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":"Shannon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Luis","Shannon"],"index":15448,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997184873,"difficulty":0.0002815127}
{"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 Larry. Thomas's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Thomas can now know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Larry","John"],"index":9548,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9953676462,"difficulty":1.9953676462}
{"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 Danielle. Gladys's card is shown to Billy. Gladys's card is shown to Gladys. Vincent's card is shown to Vincent. 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:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gladys can now know that Billy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danielle","Billy","Gladys","Vincent"],"index":6721,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983293414,"difficulty":0.0016706586}
{"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 Teresa picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Teresa can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Teresa","Bernard"],"index":2977,"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). Diane's card is shown to Gary. Gary's card is shown to Diane. Gary's card is shown to Erin. 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) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","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":"Diana can now know whether Gary can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Diana","Diane","Erin"],"index":7393,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997710586,"difficulty":0.0002289414}
{"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 Ellen. Mark's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Ellen knows whether Mark picked a red card. It is publicly announced that Ellen does not know whether Jeff 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:3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Jeff can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeff","Ellen","Mark","David"],"index":44419,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985877275,"difficulty":0.0014122725}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Alan. Kevin's card is shown to Kevin. Jon's card is shown to Kevin. Alan's card is shown to Jon. Kevin's card is shown to Jon. It is publicly announced that someone picked a red card. It is publicly announced that Kevin picked a black card. It is publicly announced that Alan knows whether Alan 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)) ] (Agentc knows whether (1|2|3))","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":"Jon can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alan","Kevin","Jon"],"index":29061,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
{"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 Cecilia. Benjamin's card is shown to Cecilia. Benjamin's card is shown to Stephen. Cecilia's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Cecilia picked a red card. It is publicly announced that Benjamin does not know whether or not everyone picked a red card. It is publicly announced that Benjamin does not know whether Stephen 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 (~(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":"Stephen can now know that Cecilia can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cecilia","Stephen","Benjamin"],"index":9539,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980137348,"difficulty":0.0019862652}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Mildred. Savannah's card is shown to Mildred. Eva's card is shown to Savannah. Eva's card is shown to Lester. It is publicly announced that someone picked a red card. It is publicly announced that Eva does not know whether Mildred picked a red card. It is publicly announced that Savannah picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Savannah can now know that Mildred can know whether Eva picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mildred","Eva","Savannah","Lester"],"index":3185,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5005304217,"difficulty":1.5005304217}
{"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. Dennis's card is shown to Joy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Joy","Dennis"],"index":30617,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966729879,"difficulty":0.0033270121}
{"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 Florence. Michael's card is shown to Michael. Michael's card is shown to Kathryn. Russel's card is shown to Kathryn. Florence's card is shown to Russel. Michael's card is shown to Russel. 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 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":"Kathryn can now know whether Russel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Florence","Michael","Kathryn","Russel"],"index":32329,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9744707942,"difficulty":0.0255292058}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Louise. Arthur's card is shown to Lois. Arthur's card is shown to Eileen. Lois's card is shown to Eileen. 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 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louise can now know that Lois picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arthur","Louise","Lois","Eileen"],"index":62747,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982892871,"difficulty":0.0017107129}
{"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. Hazel's card is shown to James. John's card is shown to Hazel. Hazel's card is shown to Hazel. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 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:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"John can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","James","Hazel"],"index":42761,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984912872,"difficulty":0.0015087128}
{"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 Beulah. Beulah's card is shown to Sandra. It is publicly announced that someone picked a red card. It is publicly announced that Beulah does not know whether Norma picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 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:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Norma can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Beulah","Norma","Sandra"],"index":15245,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9862357974,"difficulty":0.0137642026}
{"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 Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] 0","hypothesis":"Jennifer can now know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jennifer","Willie"],"index":54039,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8090672493,"difficulty":1.8090672493}
{"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 Richard. Timothy's card is shown to Timothy. Michael's card is shown to Michael. Michael's card is shown to Dana. Dana's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Dana does not know whether Richard picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Dana can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Timothy","Michael","Dana"],"index":29476,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983386993,"difficulty":0.0016613007}
{"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 Katherine. Timothy's card is shown to Katherine. Susan's card is shown to Susan. Timothy's card is shown to Joseph. Katherine's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susan can now know that Joseph can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katherine","Susan","Joseph","Timothy"],"index":44015,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997162223,"difficulty":0.0002837777}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mitchell's card is shown to Alice. Victoria's card is shown to Alice. Alice's card is shown to Mitchell. Mitchell's card is shown to Mitchell. Victoria's card is shown to Mitchell. Alice's card is shown to Victoria. It is publicly announced that someone picked a red card. It is publicly announced that Mitchell knows whether or not nobody picked a red card.","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))) ] Agenta 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":"Alice can now know that Mitchell can know that Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alice","Mitchell","Victoria"],"index":16893,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954727292,"difficulty":0.0045272708}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felice's card is shown to Thomas. Thomas's card is shown to Zina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Zina","Felice"],"index":26008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998380661,"difficulty":0.001619339}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Emma. Clifton's card is shown to Clifton. Thelma's card is shown to Clifton. Thelma's card is shown to Pamela. Pamela's card is shown to Thelma. 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) ] Agentb knows that (Agentd 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":"Clifton can now know that Thelma can know whether Emma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emma","Clifton","Pamela","Thelma"],"index":45853,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8804495335,"difficulty":0.1195504665}
{"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 Evelyn. Kenneth's card is shown to Evelyn. Linda's card is shown to Linda. Kenneth's card is shown to Linda. Kenneth's card is shown to Kenneth. Lisa's card is shown to Kenneth. Lisa's card is shown to Lisa. 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 everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Evelyn can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Evelyn","Linda","Kenneth","Lisa"],"index":16768,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848333001,"difficulty":0.0151666999}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Sharon. Joanne's card is shown to Joanne. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether Sharon 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) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(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) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Sharon can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sharon","Joanne"],"index":32866,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985960126,"difficulty":0.0014039874}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ladonna's card is shown to Pedro. Pedro's card is shown to Ladonna. Harry's card is shown to Ladonna. Pedro's card is shown to Harry. 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 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:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pedro can now know whether Ladonna can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pedro","Ladonna","Harry"],"index":32587,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997118115,"difficulty":0.0002881885}
{"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 Joshua. Joshua's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donna can now know that Joshua can know whether Donna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Donna","Madge"],"index":37177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9384871125,"difficulty":0.0615128875}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Enid's card is shown to Enid. Enid'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:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Enid can now know whether John can know whether Enid picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Enid","John"],"index":11563,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988695979,"difficulty":0.0011304021}
{"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 Jean. Elizabeth's card is shown to Jean. Jean's card is shown to Regina. Regina's card is shown to Regina. Elizabeth's card is shown to Regina. David's card is shown to Regina. Regina's card is shown to Elizabeth. David's card is shown to Elizabeth. Jean's card is shown to David. Elizabeth'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 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd 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:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Regina can now know that Jean can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jean","Regina","Elizabeth","David"],"index":36809,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5916931033,"difficulty":1.5916931033}
{"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 Joann. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"David can now know whether Joann can know whether Joann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joann","David"],"index":22343,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9950187206,"difficulty":0.0049812794}
{"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 Doris. Andrew's card is shown to Melissa. Doris's card is shown to Andrew. Melissa's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Andrew knows whether or not everyone picked a red card. It is publicly announced that Doris 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)) ] Agenta knows that (Agentc knows that 1)","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":"Doris can now know that Andrew can know that Doris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Doris","Melissa","Andrew"],"index":12232,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6045072675,"difficulty":0.3954927325}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gene's card is shown to Gene. Joseph's card is shown to Gene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Gene can now know that Gene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gene","Joseph"],"index":20814,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9924824834,"difficulty":0.0075175166}
{"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 Rose. Rose's card is shown to Norene. Kerri's card is shown to Norene. It is publicly announced that someone picked a red card. It is publicly announced that Rose knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Norene can now know whether Rose can know whether Rose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rose","Norene","Kerri"],"index":12077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997192204,"difficulty":0.002807796}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Vivian. Brian's card is shown to Brian. Vivian's card is shown to Thomas. Brian's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Vivian does not know whether or not everyone picked a red card. It is publicly announced that Brian knows whether Brian picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Vivian can now know whether Thomas can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vivian","Brian","Thomas"],"index":639,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997732043,"difficulty":0.0002267957}
{"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 George. Judy's card is shown to George. Magnolia's card is shown to George. Magnolia's card is shown to Magnolia. 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 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gregory can now know whether Magnolia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Gregory","Judy","Magnolia"],"index":17619,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6888420582,"difficulty":0.3111579418}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dustin's card is shown to Dustin. Lance's card is shown to Dustin. Kathleen's card is shown to Dustin. Dustin's card is shown to Lance. Kathleen's card is shown to Lance. Lauren's card is shown to Lance. Dustin's card is shown to Lauren. Lance's card is shown to Lauren. Kathleen's card is shown to Lauren. It is publicly announced that someone picked a red card. It is publicly announced that Lance does not know whether Lance picked a red card. It is publicly announced that Lauren picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,3,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,3,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Kathleen can now know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dustin","Lance","Kathleen","Lauren"],"index":43513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7111709118,"difficulty":0.2888290882}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Casey's card is shown to Edith. Michael's card is shown to Edith. Edith's card is shown to Michael. Edith's card is shown to John. Casey's card is shown to John. Michael'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 Edith 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)) ] (Agenta knows whether (1&2&3&4))","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":"Edith can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edith","Casey","Michael","John"],"index":44489,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7458631992,"difficulty":1.7458631992}
{"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 Sierra. Denise's card is shown to Tracey. Tracey's card is shown to Tracey. Dianna's card is shown to Tracey. Dianna's card is shown to Dianna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Denise can now know that Sierra can know that Denise picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sierra","Denise","Tracey","Dianna"],"index":37381,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967018962,"difficulty":0.0032981038}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kerry's card is shown to Jeffrey. Sheryl's card is shown to Kerry. Kerry's card is shown to Sheryl. Sheryl's card is shown to Sheryl. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey 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)) ] Agentb knows that (Agenta knows whether 2)","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":"Kerry can now know that Jeffrey can know whether Kerry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeffrey","Kerry","Sheryl"],"index":46558,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9266192317,"difficulty":0.0733807683}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorcas's card is shown to Carolyn. Kimberly's card is shown to Dorcas. Catherine's card is shown to Catherine. Kimberly's card is shown to Catherine. Catherine'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:2 Agentb:4 Agentc:3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberly can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carolyn","Dorcas","Catherine","Kimberly"],"index":2373,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olivia's card is shown to Olivia. Michael's card is shown to Olivia. Olivia's card is shown to Wanda. Michael's card is shown to Wanda. Wanda's card is shown to Leona. Leona's card is shown to Leona. Wanda's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Wanda 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 that (Agentd knows that 1)","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":"Olivia can now know that Michael can know that Olivia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Olivia","Wanda","Leona","Michael"],"index":65259,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967097044,"difficulty":0.0032902956}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bertha's card is shown to Joseph. Joseph's card is shown to Joseph. Adam's card is shown to Joseph. Craig's card is shown to Joseph. Adam's card is shown to Adam. Craig's card is shown to Adam. Joseph's card is shown to Craig. 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:1,2,3,4 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joseph can now know whether Bertha can know that Bertha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bertha","Joseph","Adam","Craig"],"index":54455,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6361852884,"difficulty":1.6361852884}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Nicholas. Evan's card is shown to Evan. Kim's card is shown to Evan. Evan's card is shown to Kim. 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) ] (Agentc 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":"Kim can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nicholas","Evan","Kim"],"index":44146,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997273088,"difficulty":0.0002726912}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Annie. Barbara's card is shown to Annie. Douglas's card is shown to Apryl. Apryl's card is shown to Douglas. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Annie does not know whether Douglas picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Douglas can now know whether Annie can know that Apryl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annie","Apryl","Douglas","Barbara"],"index":55021,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9406459332,"difficulty":0.0593540668}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to Alberta. Priscilla's card is shown to Carey. Carey'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 Priscilla picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Priscilla can now know whether Carey can know that Carey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alberta","Carey","Priscilla","Martha"],"index":7370,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8101632595,"difficulty":0.1898367405}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Willis. Mary's card is shown to Willis. Mary's card is shown to Elaine. Willis's card is shown to Patrick. 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:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patrick can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willis","Elaine","Patrick","Mary"],"index":48276,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985571504,"difficulty":0.0014428496}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Alexander. Alexander's card is shown to Alexander. Jose's card is shown to Melody. Eric's card is shown to Jose. Alexander's card is shown to Jose. Melody's card is shown to Jose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2,3 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:1,2 Agentb:4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melody can now know whether Eric can know that Jose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Alexander","Melody","Jose"],"index":47167,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9298086166,"difficulty":0.0701913834}
{"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 Robert. Ashley's card is shown to Eugene. Robert's card is shown to James. Eugene's card is shown to James. Eugene's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know whether Ashley can know that Ashley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Eugene","James","Ashley"],"index":57160,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9701828957,"difficulty":0.0298171043}
{"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 Timothy. Timothy's card is shown to Jeffrey. Daniel's card is shown to Jeffrey. 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:3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Timothy can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Timothy","Darlene","Daniel","Jeffrey"],"index":1148,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mae's card is shown to Ruben. Mae's card is shown to Mae. Amelia's card is shown to Amelia. 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:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mae can now know that Alan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruben","Alan","Mae","Amelia"],"index":17889,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983335137,"difficulty":0.0016664863}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Robert. Robert's card is shown to Katherine. Katherine'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 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Katherine can now know that Robert can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Katherine"],"index":41697,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.973605454,"difficulty":0.026394546}
{"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 Joslyn. Joslyn's card is shown to Catherine. Catherine's card is shown to Catherine. David's card is shown to Catherine. Catherine'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 Joslyn 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:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joslyn can now know that David can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joslyn","Catherine","David"],"index":7161,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9931628704,"difficulty":0.0068371296}
{"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. Joycelyn's card is shown to Florence. Florence's card is shown to Brittany. James's card is shown to Joycelyn. James'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:1,3 Agentb:1 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Joycelyn can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florence","Brittany","Joycelyn","James"],"index":37506,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974796176,"difficulty":0.0025203824}
{"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 Coy. Kerry's card is shown to Coy. Coy's card is shown to Michelle. 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)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michelle can now know whether Coy can know whether Coy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Coy","Michelle","Kerry"],"index":35144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970217347,"difficulty":0.0029782653}
{"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 William. William's card is shown to Philip. Diana's card is shown to Philip. Kristina's card is shown to Diana. Diana's card is shown to Diana. 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) ] (Agentc knows whether (~(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":"Philip can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Kristina","Philip","Diana"],"index":66545,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997271895,"difficulty":0.0002728105}
{"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. Bertha'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 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:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sharon","John","James","Bertha"],"index":17099,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9912310243,"difficulty":1.9912310243}
{"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. Bradley's card is shown to Antonio. Antonio's card is shown to Bradley. Bradley's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Bradley 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 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Bradley can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Antonio","Bradley","Jane"],"index":33149,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771893,"difficulty":0.000228107}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Kimberly. Todd's card is shown to Lucy. Kimberly's card is shown to Todd. Louise's card is shown to Todd. Kimberly's card is shown to Louise. 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 Agentd:1 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:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberly can now know whether Lucy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Lucy","Todd","Louise"],"index":52383,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997738004,"difficulty":0.0002261996}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Austin's card is shown to Miles. Miles's card is shown to Austin. Austin's card is shown to Austin. It is publicly announced that someone picked a red card. It is publicly announced that Austin picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Austin can now know whether Miles can know that Miles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Miles","Austin"],"index":25113,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.859811306,"difficulty":0.140188694}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. Lamonica's card is shown to Cindy. Brian's card is shown to Cindy. Sean's card is shown to Cindy. Lamonica's card is shown to Lamonica. Cindy's card is shown to Brian. Cindy's card is shown to Sean. Brian's card is shown to Sean. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether Brian picked a red card. It is publicly announced that Cindy knows whether Brian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Sean can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cindy","Lamonica","Brian","Sean"],"index":10423,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997263551,"difficulty":0.0002736449}
{"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 Angela. Richard's card is shown to Richard. Richard's card is shown to Susie. Susie's card is shown to Susie. It is publicly announced that someone picked a red card. It is publicly announced that Richard picked a black card. It is publicly announced that Susie 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 ] Agenta knows whether (Agentc knows whether (1|2|3))","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":"Angela can now know whether Susie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Richard","Susie"],"index":21686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
{"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. Scott's card is shown to Scott. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Janet picked a red card. It is publicly announced that Scott 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) ] Agentc knows that (Agenta knows that 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":"Mary can now know that Janet can know that Gilbert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Scott","Mary","Gilbert"],"index":22754,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9781858921,"difficulty":0.0218141079}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alta's card is shown to Robert. Alta's card is shown to George. George'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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 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:1 Agentb:1 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know that Robert can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alta","Robert","George","Maria"],"index":25265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9854387045,"difficulty":0.0145612955}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugenia's card is shown to Erik. Erik's card is shown to Eugenia. Eugenia's card is shown to Eugenia. It is publicly announced that someone picked a red card. It is publicly announced that Eugenia knows whether someone picked a red card. It is publicly announced that Erik knows whether someone picked a red card. It is publicly announced that Eugenia knows whether Erik picked a red card. It is publicly announced that Eugenia 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 whether 1)","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":"Eugenia can now know whether Erik picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Erik","Eugenia"],"index":47366,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6383838058,"difficulty":0.3616161942}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kayla's card is shown to Kayla. Tonya's card is shown to Tonya. Marie's card is shown to Tonya. Kayla's card is shown to Marie. Tonya's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Tonya picked a black card. It is publicly announced that Kayla knows whether Kayla 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)) ] (Agentc 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":"Marie can now know that Tonya picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kayla","Tonya","Marie"],"index":14451,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9132278562,"difficulty":0.0867721438}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caroline's card is shown to Caroline. Caroline's card is shown to Tatiana. Caroline's card is shown to Elinor. 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) ] (Agenta 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) ] [ ! (1&2&3) ] 0","hypothesis":"Caroline can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Caroline","Tatiana","Elinor"],"index":12303,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997100234,"difficulty":0.0002899766}
{"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 Donald. Donald's card is shown to David. David's card is shown to David. Rose's card is shown to David. Donald'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 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether Donald can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","David","Rose"],"index":15461,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7856598496,"difficulty":0.2143401504}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Brian. Brian's card is shown to Bianca. 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 that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know whether Karen can know that Karen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Karen","Bianca"],"index":59263,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.530318737,"difficulty":0.469681263}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darren's card is shown to Russell. Russell's card is shown to Darren. Russell's card is shown to Nelda. Darren's card is shown to Nelda. Nelda's card is shown to Nelda. It is publicly announced that someone picked a red card. It is publicly announced that Nelda knows whether Darren 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) ] (Agentb 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":"Darren can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Russell","Darren","Nelda"],"index":35790,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984511137,"difficulty":0.0015488863}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keitha's card is shown to Keitha. It is publicly announced that someone picked a red card. It is publicly announced that Keitha knows whether someone picked a red card. It is publicly announced that Keitha does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Keitha can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Keitha","Andrew"],"index":34733,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.920984149,"difficulty":1.920984149}
{"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 Joshua. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Joshua picked a red card. It is publicly announced that Joshua 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) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"David can now know whether Joshua can know that Joshua picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Joshua"],"index":42806,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8432079554,"difficulty":0.1567920446}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Thomas. Carmen's card is shown to Carmen. Carmen's card is shown to Judy. It is publicly announced that someone picked a red card. It is publicly announced that Thomas picked a red card. It is publicly announced that Thomas 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)) ] Agentb knows whether (Agentc knows whether (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":"Carmen can now know whether Judy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Carmen","Judy"],"index":8893,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
{"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. Angelita's card is shown to Angelita. Isela's card is shown to Angelita. Jennifer's card is shown to Isela. Angelita's card is shown to Isela. It is publicly announced that someone picked a red card. It is publicly announced that Angelita picked a black card. It is publicly announced that Jennifer knows whether Jennifer 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)) ] (Agentc knows that (1&2&3))","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":"Isela can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Angelita","Isela"],"index":5829,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982178807,"difficulty":0.0017821193}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bradley's card is shown to Joseph. Joseph's card is shown to Carl. 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 Joseph does not know whether Carl picked a red card. It is publicly announced that Carl does not know whether Bradley picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Joseph can now know whether Carl can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Carl","Bradley"],"index":64748,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.942825377,"difficulty":1.942825377}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tamika's card is shown to Lori. Lori's card is shown to Douglas. Tamika's card is shown to Douglas. Lori's card is shown to Tamika. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows 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":"Douglas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lori","Douglas","Tamika"],"index":30142,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997263551,"difficulty":0.0002736449}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carol. Rita's card is shown to Carol. Carol's card is shown to Rita. Rita's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Rita 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 (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Rita can now know whether Carol can know that Rita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carol","Rita"],"index":4877,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9201204181,"difficulty":0.0798795819}
{"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 Teodoro. Carlos's card is shown to Alicia. 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:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Teodoro can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carlos","Teodoro","Alicia"],"index":23257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7831429839,"difficulty":0.2168570161}
{"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 Robert. Linda's card is shown to Linda. Gregory's card is shown to Linda. Linda's card is shown to Mark. Mark's card is shown to Mark. 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:4 Agentb:2,4 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Linda","Mark","Gregory"],"index":24417,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6357839108,"difficulty":0.3642160892}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherill's card is shown to Betty. William's card is shown to Betty. Charles's card is shown to Sherill. 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:2,3 Agentb:4 Agentc:3 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:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Betty can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Sherill","William","Charles"],"index":63504,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9625682235,"difficulty":0.0374317765}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Christopher. Christopher's card is shown to Lois. Julie's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Lois 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) ] [ ! 3 ] (Agenta 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) ] [ ! 3 ] 0","hypothesis":"Julie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Christopher","Lois","Scott"],"index":24619,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982497096,"difficulty":0.0017502904}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rafaela's card is shown to Barbara. Barbara's card is shown to Corrine. Barbara's card is shown to Rafaela. It is publicly announced that someone picked a red card. It is publicly announced that Corrine does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Rafaela can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Corrine","Rafaela"],"index":4917,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7504850626,"difficulty":1.7504850626}
{"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. Lois's card is shown to Christine. Christine's card is shown to Lois. It is publicly announced that someone picked a red card. It is publicly announced that Christine knows whether Lois 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&2))","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":"Christine can now know that Lois can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Christine","Lois"],"index":57426,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983329177,"difficulty":0.0016670823}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Claude's card is shown to Claude. Jeff's card is shown to Mae. Mae's card is shown to Jeff. Jeff's card is shown to Jeff. 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 that (1&2&3&4))","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":"Claude can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Claude","Mae","Jeff"],"index":6891,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985710382,"difficulty":0.0014289618}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ethel's card is shown to Nancy. Martha's card is shown to Martha. Nancy's card is shown to Ethel. 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) ] (Agentb knows whether (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":"Martha can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Martha","Ethel","David"],"index":3411,"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). Donald's card is shown to Corey. Michael's card is shown to Donald. Michael's card is shown to Christine. 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 Donald 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 ] (Agenta 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":"Corey can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Corey","Donald","Michael","Christine"],"index":65386,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982649684,"difficulty":0.0017350316}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susanna's card is shown to David. Donald's card is shown to David. Patrick's card is shown to Susanna. David's card is shown to Susanna. Donald'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:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susanna can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","David","Susanna","Donald"],"index":63091,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6298699379,"difficulty":1.6298699379}
{"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 Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Joseph can now know whether Suzette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joseph","Suzette"],"index":39123,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9763145447,"difficulty":0.0236854553}
{"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 George. Christopher's card is shown to Christopher. George's card is shown to Connie. It is publicly announced that someone picked a red card. It is publicly announced that Connie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether (~(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":"Connie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Christopher","Connie"],"index":54287,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997237325,"difficulty":0.0002762675}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harrison's card is shown to Harrison. Anne's card is shown to Anne. Harrison's card is shown to Miguel. Anne's card is shown to Miguel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 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 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anne can now know whether Harrison can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harrison","Anne","Miguel"],"index":36460,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9926395416,"difficulty":0.0073604584}
{"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 Willie. Ruby's card is shown to Willie. Willie's card is shown to Rick. Arlene's card is shown to Ruby. Arlene's card is shown to Arlene. 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 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rick can now know whether Willie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Rick","Ruby","Arlene"],"index":9854,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9930576086,"difficulty":0.0069423914}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernard's card is shown to Paul. Paul's card is shown to Bernard. It is publicly announced that someone picked a red card. It is publicly announced that Bernard does not know whether Bernard picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Bernard can now know whether Paul can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Bernard"],"index":43212,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Amy's card is shown to Jessie. Jessie's card is shown to Jessie. It is publicly announced that someone picked a red card. It is publicly announced that Jessie knows whether Jessie 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&2))","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":"Amy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Amy","Jessie"],"index":7797,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986280203,"difficulty":0.0013719797}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Viola's card is shown to Barbara. Kristel's card is shown to Kristel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","John","Kristel","Viola"],"index":22400,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962278605,"difficulty":0.0037721395}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maude's card is shown to Maude. Maude's card is shown to Pamela. Bertram's card is shown to Pamela. Maude's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Maude does not know whether Bertram picked a red card. It is publicly announced that Gregory knows whether or not everyone picked a red card. It is publicly announced that Maude does not know whether Pamela 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 (Agentc knows that 3)","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":"Pamela can now know that Gregory can know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maude","Pamela","Gregory","Bertram"],"index":12875,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.727339685,"difficulty":0.272660315}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phyllis's card is shown to William. Krystal's card is shown to Krystal. Phyllis's card is shown to Krystal. Krystal's card is shown to Phyllis. Phyllis's card is shown to Phyllis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Krystal can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Krystal","Phyllis"],"index":58003,"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). Gerri's card is shown to Gerri. Gary's card is shown to Gerri. Gerri's card is shown to Wanita. Gerri's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gerri can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gerri","Wanita","Gary"],"index":4628,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997729659,"difficulty":0.0002270341}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Violet's card is shown to David. David's card is shown to Joseph. Violet's card is shown to Joseph. Joseph's card is shown to Velma. David's card is shown to Violet. Velma's card is shown to Violet. It is publicly announced that someone picked a red card. It is publicly announced that Violet does not know whether Violet picked a red card. It is publicly announced that David knows whether or not nobody picked a red card. It is publicly announced that Velma 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 whether (Agentb knows whether 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":"Velma can now know whether Joseph can know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Joseph","Velma","Violet"],"index":28006,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9952924252,"difficulty":1.9952924252}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wesley's card is shown to Bernard. Bernard's card is shown to Vaughn. Charles's card is shown to Vaughn. Wesley's card is shown to Wesley. 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 Agentc:4 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:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernard","Charles","Vaughn","Wesley"],"index":37296,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977887869,"difficulty":0.0022112131}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Patricia's card is shown to Douglas. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Douglas knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Douglas 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) ] Agentb knows whether (Agenta knows that 1)","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":"Douglas can now know whether Patricia can know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Douglas"],"index":46651,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9475482702,"difficulty":0.0524517298}
{"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 Peggy. Rachel's card is shown to Peggy. Peggy's card is shown to Rachel. 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 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Peggy can now know that Peggy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peggy","Gerald","Rachel"],"index":21479,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9407271743,"difficulty":0.0592728257}
{"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. Gertrude's card is shown to Barbara. Barbara's card is shown to Gertrude. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Alice 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 3)","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":"Barbara can now know whether Clarence can know that Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clarence","Barbara","Alice","Gertrude"],"index":32101,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9422849417,"difficulty":0.0577150583}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. Yesenia's card is shown to Andrea. Yesenia's card is shown to Yesenia. Robert's card is shown to Yesenia. Evelyn's card is shown to Robert. Yesenia'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:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrea can now know that Robert can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrea","Yesenia","Robert","Evelyn"],"index":47880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962383509,"difficulty":0.0037616491}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linwood's card is shown to Linwood. Alice's card is shown to Linwood. Dustin's card is shown to Alice. Alice's card is shown to Dustin. Dustin's card is shown to Dustin. It is publicly announced that someone picked a red card. It is publicly announced that Linwood 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:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Latasha can now know whether Alice can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Latasha","Linwood","Alice","Dustin"],"index":30623,"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). Mary's card is shown to Angelica. Troy's card is shown to Angelica. Angelica's card is shown to Mary. Troy's card is shown to Mary. Mary's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that Angelica does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Angelica can now know that Mary can know that Troy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angelica","Mary","Troy"],"index":31857,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6703234911,"difficulty":1.6703234911}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matilda's card is shown to Clifton. Raymond's card is shown to Clifton. Matilda's card is shown to Matilda. Raymond's card is shown to Matilda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clifton can now know whether Matilda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clifton","Matilda","Raymond"],"index":58943,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9566532373,"difficulty":0.0433467627}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Jason. Scot's card is shown to Jason. Jason's card is shown to Scot. It is publicly announced that someone picked a red card. It is publicly announced that Cecil 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)) ] 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) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Cecil can now know that Jason can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cecil","Jason","Scot"],"index":42945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983091354,"difficulty":0.0016908646}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Dalton. Dalton's card is shown to Daniel. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Daniel knows whether or not everyone 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 that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Dalton can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dalton","Daniel"],"index":472,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981289506,"difficulty":0.0018710494}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Estela's card is shown to Fran. Crystal's card is shown to Fran. Fran's card is shown to Donald. Donald's card is shown to Estela. Estela's card is shown to Estela. Donald's card is shown to Crystal. Estela's card is shown to Crystal. 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:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Crystal can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fran","Donald","Estela","Crystal"],"index":60602,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983482361,"difficulty":0.0016517639}
{"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 Theresa. William's card is shown to Theresa. Dorothy's card is shown to Dorothy. Dorothy'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 Theresa 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 1) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"William can now know whether Theresa can know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Theresa","Dorothy","William"],"index":16416,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986467957,"difficulty":0.0013532043}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to Darryl. Paula's card is shown to Brenda. Jesus's card is shown to Paula. Paula'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:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","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":"Darryl can now know whether Brenda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darryl","Jesus","Brenda","Paula"],"index":50039,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8025647402,"difficulty":0.1974352598}
{"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 Robert. Lane's card is shown to Robert. Willie's card is shown to Robert. Robert's card is shown to Willard. Willard's card is shown to Willard. Willard's card is shown to Willie. Willie's card is shown to Willie. 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:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Lane can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Lane","Willard","Willie"],"index":58733,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8495690823,"difficulty":0.1504309177}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlene's card is shown to Marlene. James's card is shown to Marlene. Betsy's card is shown to Woodrow. Woodrow'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:1,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Betsy can now know whether Marlene can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marlene","Betsy","Woodrow","James"],"index":15839,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985845089,"difficulty":0.0014154911}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Micheal's card is shown to Stuart. Stuart's card is shown to Julie. Julie's card is shown to Julie. Sarah's card is shown to Julie. Micheal's card is shown to Julie. Julie's card is shown to Sarah. Stuart's card is shown to Micheal. It is publicly announced that someone picked a red card. It is publicly announced that Sarah does not know whether Stuart picked a red card. It is publicly announced that Stuart knows whether 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:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Stuart can now know whether Micheal can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stuart","Julie","Sarah","Micheal"],"index":1076,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lula's card is shown to Lula. Anthony's card is shown to Lula. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether Lula picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Lula can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lula","Anthony"],"index":56124,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Alan. Margaret's card is shown to Alan. Alan's card is shown to Hazel. Hazel's card is shown to Hazel. Margaret's card is shown to Hazel. Alan's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Hazel knows whether or not nobody picked a red card. It is publicly announced that Alan does not know whether Hazel 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 whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alan","Hazel","Margaret"],"index":64021,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9755772352,"difficulty":0.0244227648}
{"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 Mary. Frank's card is shown to Mary. Judy's card is shown to Michael. Michael's card is shown to Judy. Judy's card is shown to Judy. Mary'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:2,4 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Judy can now know whether Frank can know that Judy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Michael","Judy","Frank"],"index":30787,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9230240583,"difficulty":0.0769759417}
{"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 Catherine. James's card is shown to James. Catherine's card is shown to Susan. James'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:3 Agentb:2 Agentc:1 Agentd:2 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:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susan can now know whether Catherine can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","James","Susan","Howard"],"index":52162,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9119984508,"difficulty":0.0880015492}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ja's card is shown to Ja. Amy's card is shown to Ja. Tiffany's card is shown to Ja. Amy's card is shown to Amy. Tiffany's card is shown to Tiffany. It is publicly announced that someone picked a red card. It is publicly announced that Amy does not know whether Tiffany 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) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Ja can now know whether Tiffany can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ja","Amy","Tiffany"],"index":23990,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997039437,"difficulty":0.0002960563}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Troy's card is shown to Troy. Tiffany's card is shown to Antone. Troy's card is shown to Tiffany. Tiffany's card is shown to Tiffany. 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:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Antone can now know whether Tiffany can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Troy","Antone","Tiffany"],"index":23234,"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). Andres's card is shown to Andres. Andres's card is shown to James. Andres's card is shown to Timothy. James's card is shown to Timothy. Timothy'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 Agentb:1 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:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Andres picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andres","James","Timothy"],"index":19688,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6465066075,"difficulty":0.3534933925}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Ramon. Kevin's card is shown to Paul. Ramon's card is shown to Kevin. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that Kevin can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ramon","Paul","Kevin"],"index":58131,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9344931841,"difficulty":0.0655068159}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to Amber. Heather's card is shown to Heather. Ryan's card is shown to Heather. Heather's card is shown to Ryan. Ryan's card is shown to Ryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ryan can now know that Amber can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amber","Heather","Ryan"],"index":51127,"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). Maria's card is shown to Maria. Percy's card is shown to Maria. Maria's card is shown to Dexter. Percy's card is shown to Dexter. Maria's card is shown to Percy. Dexter's card is shown to Percy. 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 Maria picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Dexter knows whether Percy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Maria can now know whether Percy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maria","Dexter","Percy"],"index":47563,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7200214863,"difficulty":0.2799785137}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Conrad's card is shown to Conrad. Conrad's card is shown to Amy. Conrad's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Debra does not know whether Amy 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) ] (Agenta knows whether 2)","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":"Conrad can now know whether Amy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Conrad","Amy","Debra"],"index":10962,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.941513896,"difficulty":0.058486104}
{"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 Emmett. Christopher's card is shown to Michele. Christopher's card is shown to Christopher. Catherine'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:3 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michele can now know that Emmett can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emmett","Michele","Christopher","Catherine"],"index":40841,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997178912,"difficulty":0.0002821088}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gertrude's card is shown to Gertrude. Raymond's card is shown to Gertrude. Gertrude's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Elvin does not know whether Elvin 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) ] (Agentb 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 2) ] 0","hypothesis":"Elvin can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gertrude","Elvin","Raymond"],"index":58938,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984931946,"difficulty":0.0015068054}
{"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 Pamela. Walter's card is shown to Walter. Leon's card is shown to Walter. Walter's card is shown to Leon. Leon's card is shown to Leon. It is publicly announced that someone picked a red card. It is publicly announced that Pamela does not know whether Walter picked a red card. It is publicly announced that Leon knows whether Walter picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Pamela can now know whether Walter can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Walter","Leon"],"index":52016,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7632947564,"difficulty":1.7632947564}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roberta's card is shown to Roberta. Jonathan'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 Roberta picked a red card. It is publicly announced that Roberta picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] (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) ] [ ! 1 ] 0","hypothesis":"Roberta can now know that Jonathan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roberta","Jonathan"],"index":29331,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6906194687,"difficulty":1.6906194687}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delia's card is shown to Delia. Rachel's card is shown to Delia. Lisa's card is shown to Rachel. Shirley's card is shown to Shirley. Shirley'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 Rachel does not know whether Shirley picked a red card. It is publicly announced that Shirley does not know whether Rachel picked a red card. It is publicly announced that Shirley does not know whether Rachel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Delia can now know whether Delia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Delia","Rachel","Shirley","Lisa"],"index":65825,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8246149421,"difficulty":0.1753850579}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennie's card is shown to Tiffany. Jennie's card is shown to Jennie. 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 that (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Jennie can now know that Tiffany can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tiffany","Jennie"],"index":9557,"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). Janet's card is shown to Janet. Janet's card is shown to Tuyet. Tuyet's card is shown to Tuyet. Janet's card is shown to Julianne. Julianne's card is shown to Julianne. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Tuyet picked a red card. It is publicly announced that Tuyet 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:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Tuyet can now know that Jo can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Tuyet","Jo","Julianne"],"index":65145,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976494908,"difficulty":0.0023505092}
{"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 Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] 0","hypothesis":"Joseph can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Patrick"],"index":49151,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997629523,"difficulty":0.0002370477}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nina's card is shown to Nina. David's card is shown to Nina. David's card is shown to Colleen. Nina's card is shown to David. Connie's card is shown to David. Connie's card is shown to Connie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that Nina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nina","Colleen","David","Connie"],"index":33359,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979842901,"difficulty":0.0020157099}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Lilia. Charles's card is shown to Lilia. Lilia's card is shown to Doris. Doris's card is shown to Doris. Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Doris 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)) ] (Agentb knows that (1&2&3))","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":"Doris can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lilia","Doris","Charles"],"index":21195,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984989166,"difficulty":0.0015010834}
{"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 Elias. Elias's card is shown to Elias. Eric's card is shown to Matthew. Elias'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 Eric does not know whether Matthew picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Elias can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Elias","Leigh","Matthew"],"index":14671,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932268262,"difficulty":0.0067731738}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristi's card is shown to Beryl. Beryl's card is shown to Joann. Kristi's card is shown to Joann. Beryl'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:3 Agentb:1,3 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:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beryl can now know whether Beryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beryl","Joann","Kristi","Walter"],"index":16996,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9073963761,"difficulty":1.9073963761}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Kyle. Donald's card is shown to Kyle. George's card is shown to Valerie. Donald's card is shown to Valerie. Valerie'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 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether Valerie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kyle","Valerie","George","Donald"],"index":25305,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995644689,"difficulty":0.0004355311}
{"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 Sharon. Leonard's card is shown to Carl. Sharon'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:1 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know whether Leonard can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leonard","Sharon","Carl","Yvonne"],"index":5554,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995824695,"difficulty":0.0004175305}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ida's card is shown to Ida. Donald's card is shown to Ida. Timothy's card is shown to Jeanette. Ida's card is shown to Jeanette. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Ida does not know whether Donald picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Ida can now know that Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Ida","Jeanette","Donald"],"index":26338,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946684241,"difficulty":0.0053315759}
{"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 Dave. Dave's card is shown to Kenneth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Dave can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dave","Kenneth"],"index":12014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997672439,"difficulty":0.0002327561}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vicky's card is shown to Vicky. Jacquelyn's card is shown to Vicky. Arthur's card is shown to Vicky. Jacquelyn's card is shown to Jacquelyn. Robert's card is shown to Jacquelyn. Arthur's card is shown to Arthur. Robert's card is shown to Arthur. Jacquelyn'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:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Arthur can now know that Jacquelyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vicky","Jacquelyn","Arthur","Robert"],"index":27556,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976246953,"difficulty":0.0023753047}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leroy's card is shown to Elizabeth. Michelle's card is shown to Elizabeth. Elizabeth's card is shown to Leroy. It is publicly announced that someone picked a red card. It is publicly announced that Leroy does not know whether Michelle picked a red card. It is publicly announced that Elizabeth does not know whether Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Leroy can now know that Elizabeth can know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","Leroy","Michelle"],"index":35000,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9813162088,"difficulty":0.0186837912}
{"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. Jose's card is shown to Rosemary. Rosemary's card is shown to Rosemary. Hershel's card is shown to Rosemary. Rosemary's card is shown to Hershel. Dewayne's card is shown to Dewayne. It is publicly announced that someone picked a red card. It is publicly announced that Dewayne picked a red card. It is publicly announced that Jose 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) ] (Agenta knows whether (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":"Jose can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Rosemary","Hershel","Dewayne"],"index":55863,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5286673903,"difficulty":0.4713326097}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Darlene. It is publicly announced that someone picked a red card. It is publicly announced that Darlene does not know whether Darlene picked a red card. It is publicly announced that Darlene 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 that (1&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":"Darlene can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Darlene","Mattie"],"index":33750,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986076951,"difficulty":0.0013923049}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glen's card is shown to Glen. Norma's card is shown to Glen. Jennifer's card is shown to Glen. Glen's card is shown to Norma. Glen's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Norma can now know whether Norma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glen","Norma","Jennifer"],"index":20995,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9758415222,"difficulty":1.9758415222}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Mary. Guadalupe's card is shown to Guadalupe. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card. It is publicly announced that Guadalupe does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Guadalupe can now know that Mary can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Guadalupe"],"index":53409,"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). Victoria's card is shown to Kenneth. Gregory's card is shown to Kenneth. Frank's card is shown to Victoria. Frank's card is shown to Gregory. Kenneth's card is shown to Frank. Victoria's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Kenneth can now know whether Gregory can know that Frank picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Victoria","Gregory","Frank"],"index":31561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9229015112,"difficulty":0.0770984888}
{"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 Brandon. Christopher's card is shown to Brandon. Christopher's card is shown to John. Christopher's card is shown to Orlando. It is publicly announced that someone picked a red card. It is publicly announced that Orlando does not know whether Brandon 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) ] Agentc knows that (Agentb knows that 4)","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":"Orlando can now know that John can know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brandon","John","Orlando","Christopher"],"index":51822,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949937463,"difficulty":0.0050062537}
{"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 Kevin. Joseph's card is shown to Joseph. Kevin's card is shown to Lynn. Lynn's card is shown to Lynn. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Kevin 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 whether (Agenta 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":"Lynn can now know whether Kevin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Joseph","Lynn"],"index":44520,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5872446299,"difficulty":1.5872446299}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shawn's card is shown to Robert. Robert's card is shown to Shawn. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 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 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shawn can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Shawn","Anthony"],"index":54623,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985221028,"difficulty":0.0014778972}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dolores's card is shown to Michael. Michael's card is shown to Dolores. It is publicly announced that someone picked a red card. It is publicly announced that Dolores picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Dolores"],"index":45436,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997285008,"difficulty":0.0002714992}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Albert. Katherine's card is shown to Albert. Marie's card is shown to Marie. Katherine's card is shown to Marie. Albert's card is shown to Sheila. Marie's card is shown to Sheila. Katherine's card is shown to Sheila. Sheila's card is shown to Katherine. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1,2,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1,2,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sheila can now know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Albert","Marie","Sheila","Katherine"],"index":15456,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975205064,"difficulty":0.0024794936}
{"premise":"There are two 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 Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether Andrew 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) ] (Agenta knows whether (~(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":"Andrew can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Andrew","Mary"],"index":36221,"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). Petra's card is shown to James. James's card is shown to Julia. Petra's card is shown to Julia. Julia's card is shown to Petra. Petra's card is shown to Petra. It is publicly announced that someone picked a red card. It is publicly announced that Julia knows whether or not everyone picked a red card. It is publicly announced that Julia knows whether Petra picked a red card. It is publicly announced that Julia 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)) ] Agenta knows that (Agentc knows whether 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":"James can now know that Petra can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Julia","Petra"],"index":41954,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6401252151,"difficulty":1.6401252151}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernest's card is shown to Alan. Alan's card is shown to Ernest. Alan's card is shown to David. Ernest'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 David picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Alan can now know that Ernest picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alan","Ernest","David"],"index":26316,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953243732,"difficulty":0.0046756268}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeanette's card is shown to Jeanette. Kim's card is shown to Jeanette. Jeanette's card is shown to Arron. Jeanette's card is shown to Kim. Kim's card is shown to Kim. 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 that (Agenta knows whether 2)","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":"Arron can now know that Jeanette can know whether Arron picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeanette","Arron","Kim"],"index":39693,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8512917757,"difficulty":0.1487082243}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Joseph. Joseph's card is shown to Thelma. It is publicly announced that someone picked a red card. It is publicly announced that Thelma picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Thelma can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Thelma"],"index":56504,"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). Hazel's card is shown to Lillian. Dorothy's card is shown to Curtis. Hazel's card is shown to Dorothy. Dorothy's card is shown to Hazel. 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) ] Agentb knows that (Agenta knows that 1)","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":"Curtis can now know that Lillian can know that Lillian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lillian","Curtis","Dorothy","Hazel"],"index":59499,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980024695,"difficulty":0.0019975305}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Norman. Shaun's card is shown to Shaun. William's card is shown to Shaun. Norman's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Shaun does not know whether Michael picked a red card. It is publicly announced that Michael does not know whether Michael 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 that 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":"Shaun can now know whether Michael can know that Shaun picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Norman","Michael","Shaun","William"],"index":54045,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9188594818,"difficulty":1.9188594818}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernice's card is shown to Bernice. Bernice'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 Bernice does not know whether Barbara 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 (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":"Barbara can now know whether Bernice can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bernice","Barbara"],"index":19605,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995125532,"difficulty":0.0004874468}
{"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 Julia. Julia's card is shown to Darrell. Julia's card is shown to Bertha. Darrell's card is shown to Bertha. It is publicly announced that someone picked a red card. It is publicly announced that Julia knows 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 whether (Agentc knows whether 2)","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":"Julia can now know whether Bertha can know whether Darrell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julia","Darrell","Bertha"],"index":21537,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983897209,"difficulty":0.0016102791}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terrell's card is shown to Patricia. Patricia'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 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Terrell can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Terrell","Patricia","John"],"index":49530,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983489513,"difficulty":0.0016510487}
{"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 Ray. Willie's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Willie knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Ray can now know that Willie can know that Willie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ray","Willie"],"index":40057,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9544275403,"difficulty":0.0455724597}
{"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 Louis. Cheryl's card is shown to Teresa. Teresa's card is shown to Teresa. Lucy's card is shown to Teresa. Lucy's card is shown to Lucy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louis can now know that Teresa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Cheryl","Teresa","Lucy"],"index":61521,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997810721,"difficulty":0.0002189279}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Janet. Aurelia's card is shown to Janet. Janet's card is shown to Aurelia. It is publicly announced that someone picked a red card. It is publicly announced that Janet knows whether Janet 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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Aurelia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Janet","Aurelia"],"index":35576,"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). James's card is shown to Marion. James's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 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:2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marion can now know that James can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marion","James","Maria"],"index":33152,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996980429,"difficulty":0.0003019571}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Pauline. Pauline's card is shown to Gregory. Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Pauline knows whether Gregory picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Gregory can now know whether Pauline can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pauline","Gregory"],"index":29053,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9961498976,"difficulty":0.0038501024}
{"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 William. Josephine's card is shown to Josephine. Roy'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:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Josephine can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Josephine","Roy"],"index":64434,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983421564,"difficulty":0.0016578436}
{"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 Deborah. Maria's card is shown to Deborah. Maria's card is shown to Janet. Deborah's card is shown to Rose. Janet's card is shown to Maria. Rose's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janet can now know that Deborah can know that Deborah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Janet","Rose","Maria"],"index":28619,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969409108,"difficulty":0.0030590892}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Celia. Celia's card is shown to Janice. Janice's card is shown to Janice. Gregory's card is shown to Gregory. 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:3 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:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gregory can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Celia","Janice","Gregory"],"index":10050,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983812571,"difficulty":0.0016187429}
{"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 Eduardo. Eduardo's card is shown to Michelle. Michelle's card is shown to Michelle. John's card is shown to Michelle. Michelle's card is shown to Kathleen. Eduardo'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:4 Agentb:1,2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eduardo","Michelle","Kathleen","John"],"index":26975,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979617596,"difficulty":0.0020382404}
{"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 Jason. Tammie's card is shown to Tammie. Tammie's card is shown to Richard. Jason's card is shown to Tifany. 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 whether 3)","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":"Tifany can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Tammie","Richard","Tifany"],"index":60133,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.718083322,"difficulty":0.281916678}
{"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 Leonard. Leonard's card is shown to Gloria. Leonard's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leonard can now know that Leonard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leonard","Gloria","Nancy"],"index":21043,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967926145,"difficulty":0.0032073855}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Miles's card is shown to Jackie. Betty's card is shown to Jackie. Jackie'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 Jackie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Miles can now know whether Jackie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","Miles","Betty"],"index":41576,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roman's card is shown to William. Madelene's card is shown to William. William's card is shown to Roman. Roman's card is shown to Roman. William's card is shown to James. Madelene's card is shown to James. William's card is shown to Madelene. 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) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Madelene can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Roman","James","Madelene"],"index":5628,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983960986,"difficulty":0.0016039014}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robbie's card is shown to Ernest. Ruth's card is shown to Ruth. Laurie's card is shown to Robbie. Ernest's card is shown to Robbie. 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:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ruth can now know whether Laurie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laurie","Ernest","Ruth","Robbie"],"index":66004,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997705817,"difficulty":0.0002294183}
{"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. William's card is shown to John. John's card is shown to Janis. John'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:1 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that William can know that Janis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Janis","William"],"index":43890,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981354475,"difficulty":0.0018645525}
{"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 Juanita. Robert's card is shown to Juanita. Juanita's card is shown to Abigail. Robert's card is shown to Abigail. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juanita can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Anna","Robert","Abigail"],"index":65728,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5763085485,"difficulty":1.5763085485}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Jerry. Jerry's card is shown to Katelyn. Katelyn's card is shown to Katelyn. Jerry's card is shown to Ida. 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:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jerry can now know whether Ida can know whether Katelyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jerry","Katelyn","Ida"],"index":65182,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985995889,"difficulty":0.0014004111}
{"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 Timothy. Dana's card is shown to Timothy. Dorothy's card is shown to Margaret. Margaret's card is shown to Dana. Timothy's card is shown to Dorothy. 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 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd 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":"Dorothy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Margaret","Dana","Dorothy"],"index":37927,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6912122965,"difficulty":1.6912122965}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gisele's card is shown to Gisele. Margarita's card is shown to Gisele. Gisele's card is shown to Margarita. 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) ] 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) ] [ ! (1|2) ] 0","hypothesis":"Margarita can now know that Gisele can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gisele","Margarita"],"index":55948,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985381365,"difficulty":0.0014618635}
{"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. Mary's card is shown to Millie. Wanda's card is shown to Millie. Wanda's card is shown to Wanda. Candace's card is shown to Wanda. Millie's card is shown to Candace. It is publicly announced that someone picked a red card. It is publicly announced that Candace does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Wanda can now know that Millie can know whether Wanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Millie","Wanda","Candace"],"index":44101,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6392011046,"difficulty":0.3607988954}
{"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 Rhonda. Ann's card is shown to Rhonda. Ann's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Rhonda knows whether Rhonda picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Rhonda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rhonda","Michael","Ann"],"index":45190,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9961723685,"difficulty":1.9961723685}
{"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 Brian. Heather's card is shown to Brian. Pete's card is shown to Brian. Heather's card is shown to Christopher. Heather's card is shown to Heather. Heather's card is shown to Pete. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether Christopher 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 (Agenta 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":"Christopher can now know that Brian can know that Brian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Christopher","Heather","Pete"],"index":42704,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8851546645,"difficulty":0.1148453355}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wesley's card is shown to Ruth. Tim's card is shown to Tim. James's card is shown to Tim. Ruth's card is shown to Wesley. Wesley's card is shown to Wesley. James's card is shown to Wesley. Ruth'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 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 whether (Agentb knows that (~(1|2|3|4)))","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":"Ruth can now know whether Tim can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Tim","Wesley","James"],"index":27466,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996047616,"difficulty":0.0003952384}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Phillip. Phillip's card is shown to Geraldine. Therese's card is shown to Geraldine. Phillip's card is shown to Therese. Therese's card is shown to Therese. 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:1,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Therese can now know whether Geraldine can know whether Geraldine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phillip","Geraldine","Therese"],"index":63449,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9862902761,"difficulty":0.0137097239}
{"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 Raymond. Don's card is shown to Don. Juan's card is shown to Don. Keri's card is shown to Juan. Keri's card is shown to Keri. It is publicly announced that someone picked a red card. It is publicly announced that Raymond does not know whether Keri picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Raymond can now know whether Juan can know that Don picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Don","Juan","Keri"],"index":66967,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.981380403,"difficulty":0.018619597}
{"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 Tracey. Deborah's card is shown to Tracey. Tracey's card is shown to Nancy. Tracey's card is shown to Deborah. 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 whether (~(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":"Nancy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tracey","Nancy","Deborah"],"index":23003,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997244477,"difficulty":0.0002755523}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlon's card is shown to James. Larry's card is shown to James. Marlon's card is shown to Marlon. James's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Larry can now know whether James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Marlon","Larry"],"index":13390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9954624772,"difficulty":0.0045375228}
{"premise":"There are two 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 Willard. 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:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Charles can now know that Willard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Willard"],"index":42762,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975761771,"difficulty":0.0024238229}
{"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 Gerald. Nicole's card is shown to Gerald. Nicole's card is shown to Nicole. Anna's card is shown to Nicole. Nicole's card is shown to Anna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anna can now know whether Gerald can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gerald","Nicole","Anna"],"index":30892,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. Carly's card is shown to Carly. It is publicly announced that someone picked a red card. It is publicly announced that Cindy does not know whether Carly picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Cindy can now know that Carly can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cindy","Carly"],"index":62347,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997106194,"difficulty":0.0002893806}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Norman. Janet's card is shown to Janet. Laurie's card is shown to Carla. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Carla 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) ] [ ! ~(Agentc knows whether 4) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Janet can now know that Norman can know that Carla picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laurie","Norman","Janet","Carla"],"index":57163,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958608747,"difficulty":0.0041391253}
{"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. Betsy's card is shown to Andrew. Andrew's card is shown to Betsy. 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) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lynda can now know whether Andrew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lynda","Andrew","Betsy"],"index":170,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997742772,"difficulty":0.0002257228}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sylvia's card is shown to Sylvia. Sylvia's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Sylvia does not know whether Ruth picked a red card. It is publicly announced that Sylvia 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))) ] (Agentb 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 (~(1|2))) ] 0","hypothesis":"Ruth can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sylvia","Ruth"],"index":59865,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9774000049,"difficulty":0.0225999951}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Serena's card is shown to James. William's card is shown to Gregory. Serena's card is shown to Gregory. William's card is shown to Serena. Serena's card is shown to Serena. 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:4 Agentb:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Gregory can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","James","Gregory","Serena"],"index":53952,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9603019357,"difficulty":0.0396980643}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. Betty's card is shown to Steven. Steven's card is shown to Aurelia. Aurelia's card is shown to Aurelia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know that Betty can know that Betty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Steven","Aurelia"],"index":21423,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9808005691,"difficulty":0.0191994309}
{"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 Diane. Margaret's card is shown to Margaret. 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 Margaret does not know whether Diane 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 1) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Margaret can now know that Diane can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Diane","Margaret"],"index":35728,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998188436,"difficulty":0.001811564}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to William. Laura's card is shown to Laura. Jennifer's card is shown to Laura. William's card is shown to Hubert. Hubert's card is shown to Hubert. William's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Laura","Hubert","Jennifer"],"index":55336,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
{"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 Eva. Catherine's card is shown to Eva. Eva's card is shown to Mark. Mark's card is shown to Mark. Catherine's card is shown to Mark. Eva's card is shown to Catherine. 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:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mark can now know that Eva can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eva","Mark","Catherine"],"index":51766,"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). Gretchen's card is shown to Gretchen. Bethany's card is shown to Gretchen. Janice's card is shown to Gretchen. Shawn's card is shown to Bethany. Shawn's card is shown to Janice. Janice's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 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:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shawn can now know whether Janice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gretchen","Bethany","Shawn","Janice"],"index":34693,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6734692454,"difficulty":0.3265307546}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nick's card is shown to Nick. Chad's card is shown to Chad. 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 that (~(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":"Tina can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tina","Nicholas","Nick","Chad"],"index":24446,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983434677,"difficulty":0.0016565323}
{"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 George. Matthew's card is shown to George. George's card is shown to Jonathan. Jonathan's card is shown to Jonathan. George's card is shown to Matthew. 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 Matthew knows whether Matthew 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 that (1|2|3))","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":"Jonathan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Jonathan","Matthew"],"index":28407,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
{"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 Carla. Carla's card is shown to Carla. Carla's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Karen picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Carla can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Carla","Karen"],"index":30783,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998287499,"difficulty":0.001712501}
{"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 Alice. Juan's card is shown to Mary. Gary's card is shown to Juan. Juan's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Juan does not know whether or not everyone picked a red card. It is publicly announced that Alice does not know whether Alice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Juan can now know whether Mary can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Mary","Juan","Gary"],"index":52122,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
{"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 James. Cassandra's card is shown to Cassandra. 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 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","James","Cassandra","Vickie"],"index":56852,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7002394199,"difficulty":1.7002394199}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Charles. Charles's card is shown to Virginia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that Maryanne can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Maryanne","Virginia"],"index":471,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997687936,"difficulty":0.0002312064}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Lisa. Willie's card is shown to Willie. Lisa'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:3 Agentb:2 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:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Doris can now know whether Willie can know that Willie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","Willie","Doris"],"index":11683,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7409775853,"difficulty":1.7409775853}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Nadia. Frances's card is shown to Frances. Frances's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Nadia does not know whether or 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Frances can now know whether Melissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nadia","Frances","Melissa"],"index":47752,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5314434171,"difficulty":1.5314434171}
{"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 Margaret. Margaret's card is shown to Maria. Stephanie's card is shown to Maria. Maria's card is shown to Stephanie. Margaret's card is shown to Betty. Stephanie's card is shown to Betty. 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:2 Agentd: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:1 Agentb:1,3 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stephanie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margaret","Maria","Stephanie","Betty"],"index":48616,"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). Steven's card is shown to Mary. Elena's card is shown to Mary. Steven's card is shown to Steven. Elena's card is shown to Steven. Trey's card is shown to Steven. Steven's card is shown to Elena. Trey's card is shown to Trey. It is publicly announced that someone picked a red card. It is publicly announced that Steven knows whether Trey picked a red card. It is publicly announced that Trey does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Elena can now know whether Elena picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Steven","Elena","Trey"],"index":2531,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8124821186,"difficulty":1.8124821186}
{"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 Lorraine. Joy's card is shown to Lorraine. Joshua's card is shown to Betty. Joy's card is shown to Betty. Joy's card is shown to Joshua. Lorraine's card is shown to Joy. It is publicly announced that someone picked a red card. It is publicly announced that Betty knows whether Joshua picked a red card. It is publicly announced that Betty knows whether someone picked a red card. It is publicly announced that Betty picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 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:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Betty can now know that Joy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lorraine","Betty","Joshua","Joy"],"index":53602,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997836947,"difficulty":0.0002163053}
{"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. Ida's card is shown to Paul. Paul's card is shown to Ida. Paul's card is shown to Ruben. It is publicly announced that someone picked a red card. It is publicly announced that Ruben knows whether Paul 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) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Paul can now know that Ida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Ida","Ruben","Laurie"],"index":54880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966456294,"difficulty":0.0033543706}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Michael. Michael's card is shown to Jerry. Jerry's card is shown to Jerry. Jerry's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Jerry","Joseph"],"index":44612,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985386133,"difficulty":0.0014613867}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Roseann. Roseann's card is shown to Gloria. Fred's card is shown to Gloria. Benjamin's card is shown to Fred. Roseann's card is shown to Benjamin. Gloria's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Roseann does not know whether Benjamin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Fred can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roseann","Gloria","Fred","Benjamin"],"index":46987,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997242093,"difficulty":0.0002757907}
{"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 Stacia. Stacia's card is shown to Stacia. Elizabeth's card is shown to Stacia. Stacia's card is shown to Floyd. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Stacia can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Stacia","Floyd","Elizabeth"],"index":5748,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995648265,"difficulty":0.0004351735}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Scott. John's card is shown to Scott. Scott's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Scott 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 whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Scott 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":["Scott","John"],"index":24905,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997029901,"difficulty":0.0002970099}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Travis's card is shown to Travis. Travis's card is shown to Frankie. Frankie's card is shown to Frankie. Donna's card is shown to Frankie. Travis's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Donna does not know whether Donna picked a red card. It is publicly announced that Travis picked a black card. It is publicly announced that Frankie knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Frankie can now know whether Travis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Travis","Frankie","Donna"],"index":60173,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.675029099,"difficulty":0.324970901}
{"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 Jesse. Gerald's card is shown to Joseph. Gerald's card is shown to Gerald. Darren's card is shown to Gerald. Gerald's card is shown to Darren. Darren's card is shown to Darren. 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) ] Agentb knows whether (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know whether Darren can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesse","Joseph","Gerald","Darren"],"index":21321,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997742772,"difficulty":0.0002257228}
{"premise":"There are three 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 Jason. Rose's card is shown to Jason. Jason's card is shown to Rose. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jason can now know that Rose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eric","Jason","Rose"],"index":23694,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7696608901,"difficulty":1.7696608901}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittany's card is shown to Brittany. Timothy's card is shown to Brittany. Eric's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Eric picked a red card. It is publicly announced that Diane does not know whether or not everyone picked a red card. It is publicly announced that Timothy picked a red card. It is publicly announced that Brittany does not know whether Diane 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 2)","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":"Diane can now know that Diane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brittany","Diane","Eric","Timothy"],"index":28749,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5180197954,"difficulty":1.5180197954}
{"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. Paul's card is shown to Elsa. Elsa's card is shown to Elsa. Nancy's card is shown to Elsa. Mitchell's card is shown to Nancy. Nancy'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 Agentb:1,2,4 Agentc:3,4 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:1,2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paul can now know whether Elsa can know that Mitchell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Elsa","Mitchell","Nancy"],"index":34893,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9041082263,"difficulty":1.9041082263}
{"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 Thomas. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Thomas does not know whether Thomas picked a red card. It is publicly announced that Jackson picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Thomas can now know that Jackson can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jackson","Thomas","Dorothy","Jenifer"],"index":38354,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997832179,"difficulty":0.0002167821}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Tiffany. Tiffany's card is shown to Lacy. Craig's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tiffany can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tiffany","Craig","Lacy","Laura"],"index":7198,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955726862,"difficulty":0.0044273138}
{"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. Maria's card is shown to Jennifer. Kimberly's card is shown to Jennifer. Kimberly's card is shown to Kimberly. Saul'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:1 Agentb:1,3 Agentc:3,4 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:1 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Kimberly can know that Kimberly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Jennifer","Kimberly","Saul"],"index":47291,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917969704,"difficulty":0.0082030296}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Leslie. Ted's card is shown to Leslie. Michelle's card is shown to Leslie. Michelle's card is shown to Ted. Ted's card is shown to Michelle. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Leslie picked a red card. It is publicly announced that Linda does not know whether or not everyone picked a red card. It is publicly announced that Leslie knows whether Michelle picked a red card. It is publicly announced that Ted 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:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Linda can now know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leslie","Linda","Ted","Michelle"],"index":34266,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8324131966,"difficulty":0.1675868034}
{"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 Timothy. Timothy's card is shown to Patricia. George's card is shown to Patricia. Timothy's card is shown to George. Patricia's card is shown to George. George's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"George can now know whether Patricia can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Patricia","George"],"index":63352,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jackie's card is shown to Jackie. Janis's card is shown to Janis. It is publicly announced that someone picked a red card. It is publicly announced that Jackie does not know whether Pedro picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (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 2) ] 0","hypothesis":"Jackie can now know whether Pedro can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","Pedro","Janis"],"index":21997,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9958843589,"difficulty":0.0041156411}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alvin's card is shown to Mae. Mae's card is shown to Mae. Mae's card is shown to Mona. It is publicly announced that someone picked a red card. It is publicly announced that Alvin 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 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:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mae can now know whether Alvin can know whether Mona picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alvin","Mae","Mona"],"index":38835,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99766469,"difficulty":0.00233531}
{"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 Daniel. John's card is shown to Thomas. Daniel's card is shown to Anne. Anne's card is shown to Anne. 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 that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that John can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Thomas","John","Anne"],"index":55372,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
{"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. Gregory's card is shown to Paul. Michael's card is shown to Paul. Gregory's card is shown to Gregory. Gregory's card is shown to Michael. Paul's card is shown to Cheryl. It is publicly announced that someone picked a red card. It is publicly announced that Paul picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Paul can now know that Michael can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Gregory","Michael","Cheryl"],"index":43388,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963012934,"difficulty":0.0036987066}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Diane. Diane's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","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":"Diane can now know that Francis can know whether Heather picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Francis","Diane","Heather"],"index":15209,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8325568438,"difficulty":1.8325568438}
{"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 Albert. Erwin's card is shown to Albert. Albert's card is shown to Mark. Erwin's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Albert does not know whether Albert picked a red card. It is publicly announced that Albert 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:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Albert can now know that Albert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Albert","Emma","Erwin","Mark"],"index":37881,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8283738494,"difficulty":1.8283738494}
{"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 Brenda. Brenda's card is shown to Janice. Stephanie's card is shown to Stephanie. Janice's card is shown to Keith. Stephanie'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:3 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janice can now know whether Brenda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brenda","Janice","Stephanie","Keith"],"index":64056,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6476959586,"difficulty":1.6476959586}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Eric. Ginger's card is shown to Eric. Eric's card is shown to Sheila. Sheila's card is shown to Sheila. Ginger's card is shown to Ginger. 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) ] 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:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ginger can now know whether Eric can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Sheila","Ginger"],"index":14773,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999582231,"difficulty":0.000417769}
{"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 Dorothy. Jennifer's card is shown to Harry. Jennifer's card is shown to Jennifer. 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:4 Agentb:3 Agentc:3 Agentd: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:4 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harry can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dorothy","Harry","Jennifer","Peter"],"index":40022,"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). Beverly's card is shown to Stanley. Ronald's card is shown to Stanley. Beverly's card is shown to Beverly. Dorothy's card is shown to Beverly. Ronald's card is shown to Dorothy. Dorothy's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Ronald does not know whether Beverly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Beverly can now know whether Stanley can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stanley","Beverly","Dorothy","Ronald"],"index":26883,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999778688,"difficulty":0.000221312}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Sheila. Sharon's card is shown to Sharon. Debra's card is shown to Sharon. Sharon's card is shown to Debra. Debra's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Sheila does not know whether Sharon picked a red card. It is publicly announced that Debra knows whether Sharon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Sheila can now know whether Debra can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sheila","Sharon","Debra"],"index":10992,"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). Christopher's card is shown to Judith. Robert's card is shown to Judith. Judith's card is shown to Christopher. Christopher's card is shown to Christopher. Judith's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether Judith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Judith","Christopher","Robert"],"index":31552,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5399266481,"difficulty":1.5399266481}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emmanuel's card is shown to Clara. William's card is shown to Clara. Clara's card is shown to Kimberly. William's card is shown to Emmanuel. 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: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:3,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberly can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clara","Kimberly","Emmanuel","William"],"index":57805,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985387325,"difficulty":0.0014612675}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Robert. Juanita's card is shown to Robert. Robert's card is shown to Juanita. Juanita's card is shown to Juanita. Dennis's card is shown to Juanita. Nancy's card is shown to Dennis. Dennis's card is shown to Dennis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nancy can now know that Nancy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Robert","Juanita","Dennis"],"index":1393,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959642887,"difficulty":0.0040357113}
{"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 Henry. Christopher's card is shown to Randy. Randy's card is shown to Randy. Harold's card is shown to Randy. Harold's card is shown to Harold. 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 Harold picked a red card. It is publicly announced that Christopher knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 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 whether (Agentb knows whether 2)","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":"Randy can now know whether Henry can know whether Henry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Henry","Randy","Harold"],"index":13706,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9925185442,"difficulty":0.0074814558}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandi's card is shown to Brandi. Beverly's card is shown to Megan. Phyllis's card is shown to Megan. Brandi's card is shown to Beverly. Brandi's card is shown to Phyllis. It is publicly announced that someone picked a red card. It is publicly announced that Phyllis does not know whether Phyllis picked a red card. It is publicly announced that Beverly 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 (~(1|2|3|4)))","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":"Phyllis can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brandi","Megan","Beverly","Phyllis"],"index":2961,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997238517,"difficulty":0.0002761483}
{"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 Aaron. Debra's card is shown to Debra. Beatrice's card is shown to Debra. Debra'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 Beatrice does not know whether or not everyone picked a red card. It is publicly announced that Aaron does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Beatrice can now know that Aaron can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Aaron","Debra","Beatrice"],"index":16627,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9554393888,"difficulty":0.0445606112}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bob's card is shown to Bob. Edith's card is shown to Bob. Edith's card is shown to Glen. Bob's card is shown to Andrea. Andrea's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Andrea does not know whether Edith picked a red card. It is publicly announced that Glen does not know whether Andrea 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 that (~(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":"Glen can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bob","Glen","Andrea","Edith"],"index":46225,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985622764,"difficulty":0.0014377236}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vickie's card is shown to Vickie. Inell's card is shown to Vickie. John's card is shown to Vickie. Vickie's card is shown to Inell. Inell's card is shown to Inell. Vickie'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:1,2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Inell can now know whether John can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vickie","Inell","John"],"index":37056,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
{"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. Ricardo'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:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know that Michael can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Michael","Ricardo"],"index":25528,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9483143687,"difficulty":0.0516856313}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelby's card is shown to Jeffrey. Brandon's card is shown to Jeffrey. Jeffrey's card is shown to Brandon. Jeffrey's card is shown to Ryan. Shelby's card is shown to Ryan. Brandon's card is shown to Ryan. Ryan's card is shown to Ryan. 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.","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 that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Shelby can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffrey","Shelby","Brandon","Ryan"],"index":39170,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999769032,"difficulty":0.000230968}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shane's card is shown to Margaret. Shane's card is shown to Norman. Jesus's card is shown to Shane. Norman's card is shown to Shane. Shane's card is shown to Shane. 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:1,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know whether Norman can know that Norman picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jesus","Margaret","Norman","Shane"],"index":21095,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7951841354,"difficulty":1.7951841354}
{"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. Jennifer's card is shown to Jennifer. Shelton's card is shown to Jennifer. Jennifer's card is shown to Shelton. 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) ] (Agentc 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":"Shelton can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Jennifer","Shelton"],"index":57330,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucille's card is shown to Sonia. Sonia's card is shown to Gary. Lucille's card is shown to Courtney. It is publicly announced that someone picked a red card. It is publicly announced that Sonia picked a red card. It is publicly announced that Sonia does not know whether Gary picked a red card. It is publicly announced that Gary does not know whether Courtney picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Sonia can now know that Lucille can know whether Lucille picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucille","Sonia","Gary","Courtney"],"index":34722,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9859316349,"difficulty":0.0140683651}
{"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. James's card is shown to William. William's card is shown to William. James's card is shown to Stephanie. William's card is shown to Stephanie. Stephanie's card is shown to Stephanie. 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:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Stephanie can now know whether Stephanie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","William","Stephanie"],"index":15725,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9756778479,"difficulty":0.0243221521}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to John. John's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Amanda can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Amanda"],"index":61956,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976154566,"difficulty":0.0023845434}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. Betty's card is shown to Gregory. Gregory's card is shown to Irene. Betty's card is shown to Irene. 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 Gregory knows whether or not nobody picked a red card. It is publicly announced that Betty knows whether Irene 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&2&3))","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":"Gregory can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gregory","Betty","Irene"],"index":53639,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9917308688,"difficulty":0.0082691312}
{"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 Paula. Paula's card is shown to Maria. Gussie's card is shown to Maria. Gussie's card is shown to Neil. Paula's card is shown to Gussie. Maria's card is shown to Gussie. Neil's card is shown to Gussie. 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:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gussie can now know that Paula can know that Paula picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paula","Maria","Neil","Gussie"],"index":39991,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9927499294,"difficulty":0.0072500706}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Rebecca. Diane's card is shown to Diane. Diane's card is shown to Lonna. 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 (Agentc knows that 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":"Rebecca can now know that Lonna can know that Lonna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebecca","Diane","Lonna"],"index":34830,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976900816,"difficulty":0.0023099184}
{"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 Essie. Gloria's card is shown to Essie. Essie's card is shown to Eugene. Essie'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:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eugene can now know whether Essie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronald","Essie","Eugene","Gloria"],"index":34529,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7360391617,"difficulty":0.2639608383}
{"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. Ricky's card is shown to Robert. Robert's card is shown to Ricky. 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) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ricky can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Robert","Ricky"],"index":56553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983363748,"difficulty":0.0016636252}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Casey's card is shown to Casey. Kristen's card is shown to Kristen. Kristen's card is shown to Marian. It is publicly announced that someone picked a red card. It is publicly announced that Casey does not know whether Lien 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) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lien can now know that Kristen can know that Marian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Casey","Kristen","Lien","Marian"],"index":34091,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960173965,"difficulty":0.0039826035}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Saundra's card is shown to Rosie. Rosie's card is shown to Saundra. It is publicly announced that someone picked a red card. It is publicly announced that Saundra does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Saundra can now know whether Rosie can know that Rosie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rosie","Saundra"],"index":18009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9103563428,"difficulty":0.0896436572}
{"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 Nettie. Jeanna's card is shown to Jeanna. Carolyn's card is shown to Jeanna. Carolyn's card is shown to Carolyn. 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) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","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":"Nettie can now know that Jeanna can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nettie","Jeanna","Carolyn"],"index":60674,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997209907,"difficulty":0.0002790093}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Micheal's card is shown to Mary. Mary's card is shown to Micheal. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Micheal can now know that Mary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Micheal"],"index":64838,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983124733,"difficulty":0.0016875267}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Ruth. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Clarence does not know whether or not everyone picked a red card. It is publicly announced that Ruth knows whether Clarence picked a red card. It is publicly announced that Clarence does not know whether Ruth picked a red card. It is publicly announced that Clarence knows whether or not nobody 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 2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Clarence can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ruth","Clarence"],"index":56781,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
{"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 Joseph. Karen's card is shown to Joseph. Xavier's card is shown to Xavier. Karen's card is shown to Xavier. Joseph's card is shown to Eric. Xavier'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:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Karen can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Xavier","Eric","Karen"],"index":52152,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9749364853,"difficulty":0.0250635147}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Alice. Nicholas's card is shown to Alice. Michael's card is shown to Nicholas. Alice's card is shown to Michael. Nicholas'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 Alice does not know whether Robbie picked a red card. It is publicly announced that Nicholas knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robbie can now know that Nicholas can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Nicholas","Robbie","Michael"],"index":27084,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5585314035,"difficulty":0.4414685965}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicky's card is shown to Darlena. Kenneth's card is shown to Kenneth. Nicky's card is shown to Nicky. 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 Nicky picked a red card. It is publicly announced that Darlena does not know whether Darlena picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Darlena","Kenneth","Nicky"],"index":1220,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9244576097,"difficulty":0.0755423903}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathleen's card is shown to Joseph. Harold's card is shown to Joseph. Cathleen's card is shown to Cathleen. Harold's card is shown to Harold. 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":"Cathleen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Cathleen","Harold"],"index":14535,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984880686,"difficulty":0.0015119314}
{"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 Stacey. Mary's card is shown to Mary. Stacey'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 Stacey picked a red card. It is publicly announced that Mary does not know whether Stacey 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) ] (Agenta knows whether 2)","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":"Stacey can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stacey","Mary","David"],"index":52224,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9061954021,"difficulty":0.0938045979}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to John. Rosemary's card is shown to Rosemary. Curtis's card is shown to Lillian. Curtis's card is shown to Curtis. It is publicly announced that someone picked a red card. It is publicly announced that Lillian does not know whether Lillian picked a red card. It is publicly announced that Rosemary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] 0","hypothesis":"John can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Rosemary","Lillian","Curtis"],"index":15006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982104301,"difficulty":0.0017895699}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Angelina. Preston's card is shown to Preston. Shannon's card is shown to Preston. George's card is shown to Preston. Preston's card is shown to Shannon. Shannon's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that George does not know whether 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)) ] (Agentc knows that 4)","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":"Shannon can now know that George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angelina","Preston","Shannon","George"],"index":13993,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6083693504,"difficulty":0.3916306496}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myra's card is shown to Myra. Myra'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 Patricia knows whether Patricia 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 (Agenta knows that (~(1|2)))","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":"Patricia can now know that Myra can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Myra","Patricia"],"index":2715,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985237718,"difficulty":0.0014762282}
{"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 Mary. Mary's card is shown to Seth. Michele's card is shown to Michele. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card. It is publicly announced that Mary does not know whether Michele 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) ] Agenta knows that (Agentb knows whether 2)","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":"Mary can now know that Seth can know whether Seth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Seth","Michele"],"index":21480,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.944280684,"difficulty":0.055719316}
{"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. Ralph's card is shown to Mary. Ralph's card is shown to Ralph. Marilyn's card is shown to Ralph. Dana's card is shown to Marilyn. Ralph'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 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dana can now know whether Ralph can know that Ralph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Ralph","Marilyn","Dana"],"index":47302,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9370186329,"difficulty":0.0629813671}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Juan. Patricia's card is shown to Juan. Robert's card is shown to Juan. Juan's card is shown to Patricia. Robert'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:1,2,3 Agentb:1 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:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Juan can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juan","Patricia","Robert"],"index":37621,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984531403,"difficulty":0.0015468597}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Noemi's card is shown to Terrance. Noemi's card is shown to Joanne. Terrance's card is shown to Noemi. Noemi's card is shown to Noemi. It is publicly announced that someone picked a red card. It is publicly announced that Noemi 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:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (1&2&3) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Joanne can now know that Noemi can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Terrance","Joanne","Noemi"],"index":59226,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9877080917,"difficulty":0.0122919083}
{"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 Cherish. Alex's card is shown to Alex. 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:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Cherish can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cherish","Alex","Virginia"],"index":26110,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919703007,"difficulty":0.0080296993}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Laura. Nicholas's card is shown to Jason. Scott's card is shown to Nicholas. Nicholas'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:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know that Scott can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Jason","Nicholas","Scott"],"index":28150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998374939,"difficulty":0.001625061}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Marvin. Kim's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Marvin knows whether someone picked a red card. It is publicly announced that Marvin does not know whether or not everyone picked a red card. It is publicly announced that Marvin 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 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":"Kim can now know that Kim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marvin","Kim"],"index":38470,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8964804411,"difficulty":0.1035195589}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Van's card is shown to Kimberly. Ruth's card is shown to Kimberly. Van's card is shown to Van. Van's card is shown to Roland. 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 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:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roland can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kimberly","Van","Roland","Ruth"],"index":49049,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997264743,"difficulty":0.0002735257}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwayne's card is shown to Arturo. Arturo's card is shown to Linda. Linda's card is shown to Linda. Dwayne's card is shown to Linda. Maria's card is shown to Dwayne. Arturo's card is shown to Dwayne. Linda's card is shown to Dwayne. Dwayne's card is shown to Dwayne. 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:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know that Linda can know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Arturo","Linda","Dwayne"],"index":47166,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8787176609,"difficulty":0.1212823391}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to Rhonda. Cynthia's card is shown to Rhonda. Rhonda's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Rhonda picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Cynthia can now know that Rhonda can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rhonda","Cynthia"],"index":44754,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985075593,"difficulty":0.0014924407}
{"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 Albert. Thelma's card is shown to Donald. Albert's card is shown to Thelma. Albert's card is shown to Richard. Donald's card is shown to Richard. Thelma's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether Donald picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Donald can now know whether Thelma can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Donald","Thelma","Richard"],"index":19774,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997772574,"difficulty":0.0002227426}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Dale. Kay's card is shown to Dale. Dale's card is shown to Kay. Dale's card is shown to Leonard. 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) ] (Agenta knows that (~(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":"Dale can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dale","Kay","Marion","Leonard"],"index":65146,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998357594,"difficulty":0.001642406}
{"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 Eric. Madelyn's card is shown to Eric. Faustino's card is shown to Faustino. 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) ] (Agentb knows whether 1)","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":"Madelyn can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Madelyn","Letitia","Faustino"],"index":1903,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7372769117,"difficulty":0.2627230883}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Ralph. Cynthia's card is shown to Sammy. Ralph's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Ralph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Sammy can now know whether Sammy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Sammy","Cynthia"],"index":2883,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6956377029,"difficulty":1.6956377029}
{"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 Wilma. Catherine's card is shown to Wilma. Raymond's card is shown to Raymond. Raymond's card is shown to Lynn. 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 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:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymond can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wilma","Raymond","Lynn","Catherine"],"index":45603,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932994843,"difficulty":0.0067005157}
{"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 Teresa. Patricia's card is shown to Patricia. Stephen's card is shown to Patricia. Ruby's card is shown to Stephen. 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. It is publicly announced that Stephen does not know whether Teresa picked a red card. It is publicly announced that Teresa does not know whether Ruby 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) ] (Agentb knows that 2)","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":"Patricia can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Teresa","Patricia","Stephen","Ruby"],"index":12580,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5783175826,"difficulty":0.4216824174}
{"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 Alberta. Alberta's card is shown to Linda. Edwin's card is shown to Linda. Chad's card is shown to Edwin. Linda'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:2 Agentb:1,4 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:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alberta can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alberta","Chad","Linda","Edwin"],"index":10621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997227788,"difficulty":0.0002772212}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Chris. Clara's card is shown to Chris. Gregg's card is shown to Gregg. Clara's card is shown to Clara. 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:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clara can now know whether Gregg can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chris","Gregg","Clara"],"index":51180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997125268,"difficulty":0.0002874732}
{"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 Abigail. Abigail's card is shown to Abigail. Abigail's card is shown to Francis. It is publicly announced that someone picked a red card. It is publicly announced that Francis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Christopher can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adele","Christopher","Abigail","Francis"],"index":35623,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982713461,"difficulty":0.0017286539}
{"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 Daniel. Rosa'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:3 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know whether Raymond picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacob","Daniel","Rosa","Raymond"],"index":7963,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9500477314,"difficulty":0.0499522686}
{"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 Ann. Ann's card is shown to Nicole. 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 Robert 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) ] (Agenta 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":"Ann can now know that Ann picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ann","Nicole","Robert"],"index":9477,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944936037,"difficulty":0.0055063963}
{"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 Evelyn. Johnie's card is shown to Evelyn. German's card is shown to Evelyn. Johnie's card is shown to Johnie. German's card is shown to Johnie. Evelyn's card is shown to German. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Johnie does not know whether Robert 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 2)","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":"Robert can now know whether Johnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Johnie","German","Robert"],"index":57253,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7312379479,"difficulty":0.2687620521}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Maritza. Maritza's card is shown to Elida. Elida's card is shown to Elida. Chris's card is shown to Elida. Maritza's card is shown to Chris. Elida's card is shown to Chris. Chris's card is shown to Chris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elida can now know whether Chris can know that Chris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maritza","Elida","Chris"],"index":26268,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9200591445,"difficulty":0.0799408555}
{"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 Robert. Robert's card is shown to Katherine. Katherine's card is shown to Katherine. Gary's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lloyd can now know whether Robert can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Katherine","Lloyd","Gary"],"index":46373,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9841252565,"difficulty":0.0158747435}
{"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 Enriqueta. Aaron's card is shown to James. Enriqueta'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:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Enriqueta can now know whether James can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Enriqueta","James","Aaron"],"index":43671,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997699857,"difficulty":0.0002300143}
{"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 Ernestina. Ernestina's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether or not everyone picked a red card. It is publicly announced that Cynthia does not know whether Cynthia 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) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ernestina can now know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ernestina","Cynthia"],"index":30258,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9134255648,"difficulty":0.0865744352}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Norma. Dora's card is shown to Norma. Greg's card is shown to George. Norma's card is shown to Dora. Dora's card is shown to Dora. Dora's card is shown to Greg. Greg's card is shown to Greg. 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 whether (Agentd knows whether 2)","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":"Norma can now know whether Greg can know whether George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norma","George","Dora","Greg"],"index":21282,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997969687,"difficulty":0.002030313}
{"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. Larry's card is shown to Tyler. Judy'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:1 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Judy can now know whether Martin can know that Larry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Judy","Martin","Tyler","Larry"],"index":14217,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9022735953,"difficulty":1.9022735953}
{"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 Willie. Robert's card is shown to Rebecca. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether Willie picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Rebecca picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Willie can now know whether Rebecca can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Willie","Rebecca","Robert"],"index":55707,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9557442069,"difficulty":0.0442557931}
{"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 Willie. Lee's card is shown to Crystal. Willie's card is shown to Lee. Crystal's card is shown to Lee. 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 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) ] Agentc knows that (Agentb knows whether 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":"Lee can now know that Crystal can know whether Lee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Willie","Crystal","Lee"],"index":42262,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5413293242,"difficulty":1.5413293242}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. Curtis's card is shown to Sarah. Hazel's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Hazel does not know whether Sarah picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Hazel can now know whether Curtis can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Curtis","Hazel","Sarah"],"index":11104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. James's card is shown to John. John's card is shown to James. James'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:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arthur","Andrea","John","James"],"index":48891,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982535243,"difficulty":0.0017464757}
{"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. Robert's card is shown to Frances. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Frances picked a red card. It is publicly announced that Robert does not know whether Frances 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 that (Agenta knows whether 1)","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":"Frances can now know that Robert can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Frances"],"index":62776,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9946405888,"difficulty":0.0053594112}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candy's card is shown to Margaret. Erik's card is shown to James. Erik's card is shown to Erik. Margaret's card is shown to Candy. James's card is shown to Candy. It is publicly announced that someone picked a red card. It is publicly announced that Erik 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 that (Agentc knows that 2)","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":"Margaret can now know that Erik can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","James","Erik","Candy"],"index":12257,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6138776541,"difficulty":0.3861223459}
{"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 Gwendolyn. Steven's card is shown to Steven. Diann's card is shown to Steven. Gwendolyn's card is shown to Kareem. Kareem's card is shown to Kareem. Gwendolyn's card is shown to Diann. 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) ] (Agentd 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 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Diann can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gwendolyn","Steven","Kareem","Diann"],"index":23850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
{"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 Hettie. Timothy's card is shown to Harry. Hettie's card is shown to Betty. Harry's card is shown to Betty. Timothy's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Hettie does not know whether Betty picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Timothy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Hettie","Harry","Timothy","Betty"],"index":17086,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kirk's card is shown to Roselyn. Roselyn's card is shown to Kirk. It is publicly announced that someone picked a red card. It is publicly announced that Kirk 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)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Roselyn can now know that Kirk can know whether Kirk picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Roselyn","Kirk"],"index":60816,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9615015984,"difficulty":1.9615015984}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ivy's card is shown to Erica. Erica's card is shown to Mary. Mary's card is shown to Mary. Ivy's card is shown to Mary. Erica's card is shown to Ivy. It is publicly announced that someone picked a red card. It is publicly announced that Ivy 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)) ] Agentb knows that (Agentc knows whether 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":"Mary can now know that Ivy can know whether Ivy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Erica","Mary","Ivy"],"index":26720,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.861341536,"difficulty":1.861341536}
{"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. Richard's card is shown to Maria. Shirley's card is shown to Maria. Carolyn's card is shown to Maria. Maria's card is shown to Richard. Shirley's card is shown to Shirley. Maria's card is shown to Carolyn. 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:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know that Carolyn can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Richard","Shirley","Carolyn"],"index":31720,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984764457,"difficulty":0.0015235543}
{"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 Shauna. Kathleen's card is shown to Shauna. Kathleen's card is shown to Mary. Shauna's card is shown to Kathleen. 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) ] Agentb knows that (Agenta knows that 1)","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":"Mary can now know that Shauna can know that Shauna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shauna","Mary","Kathleen"],"index":34460,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919638634,"difficulty":0.0080361366}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Shirley. Shirley's card is shown to Ofelia. It is publicly announced that someone picked a red card. It is publicly announced that Shirley does not know whether Ofelia picked a red card. It is publicly announced that Shirley 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))) ] (Agentb 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 (~(1|2))) ] 0","hypothesis":"Ofelia can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shirley","Ofelia"],"index":35808,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997163415,"difficulty":0.0002836585}
{"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 Jerry. Lorraine's card is shown to Inez. Inez's card is shown to Inez. 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 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lorraine can now know whether Jerry can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerry","Lorraine","Christopher","Inez"],"index":63966,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9263662696,"difficulty":0.0736337304}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eilene's card is shown to Tamara. Elizabeth's card is shown to Eilene. Eilene's card is shown to Mae. 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) ] (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":"Eilene can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Tamara","Eilene","Mae"],"index":16130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997668862,"difficulty":0.0002331138}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pearl's card is shown to Pearl. Nettie's card is shown to Pearl. Pearl's card is shown to Nettie. Nettie's card is shown to Nettie. Gary's card is shown to Nettie. Pearl's card is shown to Gary. Gary's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nettie can now know that Pearl can know whether Nettie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pearl","Nettie","Gary"],"index":27860,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6012396812,"difficulty":1.6012396812}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Salvador's card is shown to Jill. Salvador's card is shown to Salvador. 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 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":"Salvador can now know that Jill can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jill","Salvador","Jo"],"index":42258,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983949065,"difficulty":0.0016050935}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keisha's card is shown to Keisha. It is publicly announced that someone picked a red card. It is publicly announced that Gary knows whether Gary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Gary can now know whether Keisha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gary","Keisha"],"index":59360,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7427507043,"difficulty":1.7427507043}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Eugene's card is shown to Michael. Cheryl's card is shown to Cheryl. It is publicly announced that someone picked a red card. It is publicly announced that Eugene knows whether or not nobody picked a red card. It is publicly announced that Eugene does not know whether Cheryl 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 whether (~(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":"Cheryl can now know whether Eugene can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","Michael","Cheryl"],"index":37832,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997034669,"difficulty":0.0002965331}
{"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. Tara's card is shown to Christopher. Tara's card is shown to Tara. Christopher's card is shown to Ray. 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 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tara can now know that Tara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Tara","Ray"],"index":63405,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951559305,"difficulty":0.0048440695}
{"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 Viola. Viola's card is shown to Viola. Carrie's card is shown to Viola. Steven's card is shown to Carrie. Victor's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that Viola does not know whether Viola picked a red card. It is publicly announced that Carrie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Viola can now know that Steven can know whether Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Viola","Carrie","Victor"],"index":658,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5146448016,"difficulty":1.5146448016}
{"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 Martha. Chris's card is shown to Martha. Alexandra's card is shown to Evelyn. Martha's card is shown to Chris. Chris's card is shown to Chris. Chris's card is shown to Alexandra. Alexandra's card is shown to Alexandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1,3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1,3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alexandra can now know that Evelyn can know whether Chris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Evelyn","Chris","Alexandra"],"index":37816,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5272200704,"difficulty":1.5272200704}
{"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 Norman. Loretta's card is shown to Norman. Norman's card is shown to Edward. Edward's card is shown to Loretta. Loretta's card is shown to Loretta. It is publicly announced that someone picked a red card. It is publicly announced that Loretta picked a red card. It is publicly announced that Norman does not know whether or not everyone picked a red card. It is publicly announced that Norman knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Edward can now know that Loretta can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norman","Edward","Loretta"],"index":37334,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9843969941,"difficulty":0.0156030059}
{"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 Rodney. Helen's card is shown to Helen. Rodney'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:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rodney can now know whether Helen can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rodney","Helen","Walter"],"index":21126,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9233813286,"difficulty":0.0766186714}
{"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 Edna. Neil's card is shown to Neil. Edna'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.","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) ] (Agentb knows whether 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":"Neil can now know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edna","Neil","James","Carol"],"index":49140,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9934798479,"difficulty":0.0065201521}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonio's card is shown to Nathan. Robert's card is shown to William. Antonio's card is shown to Robert. Robert'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:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nathan","Antonio","William","Robert"],"index":56208,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980390668,"difficulty":0.0019609332}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bettie's card is shown to Johnnie. Matt's card is shown to Johnnie. Bettie's card is shown to Matt. 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 (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bettie can now know whether Johnnie can know whether Matt picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnnie","Bettie","Matt"],"index":42788,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987776875,"difficulty":0.0012223125}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalia's card is shown to Clara. Rosalia's card is shown to Rosalia. It is publicly announced that someone picked a red card. It is publicly announced that Clara 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 (Agentb 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|2))) ] 0","hypothesis":"Clara can now know whether Rosalia can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Clara","Rosalia"],"index":481,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997730851,"difficulty":0.0002269149}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paulette's card is shown to Angela. Angela's card is shown to Paulette. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Paulette can now know whether Angela can know whether Paulette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Angela","Paulette"],"index":49460,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977315068,"difficulty":0.0022684932}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Scott. Shari's card is shown to Scott. Scott's card is shown to Willa. Willa's card is shown to Willa. Shari's card is shown to Shari. 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) ] Agenta knows that (Agentb knows whether (1|2|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":"Scott can now know that Willa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Willa","Shari"],"index":53653,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
{"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 James. Patrick's card is shown to Patrick. James's card is shown to Myrtle. Patrick's card is shown to Myrtle. Pearl's card is shown to Myrtle. 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:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Patrick","Pearl","Myrtle"],"index":52786,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985342026,"difficulty":0.0014657974}
{"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 Lynn. Maria's card is shown to Lynn. Maria's card is shown to Philip. Alexis's card is shown to Alexis. Maria's card is shown to Alexis. Philip's card is shown to Maria. Alexis's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:3,4 Agentd: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:2,4 Agentb:4 Agentc:3,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Philip can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lynn","Philip","Alexis","Maria"],"index":4652,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997754693,"difficulty":0.0002245307}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elsie's card is shown to John. John's card is shown to Anna. Elsie's card is shown to Anna. Elsie's card is shown to Elsie. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Anna picked a red card. It is publicly announced that Elsie 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:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Anna can now know that Elsie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Anna","Elsie"],"index":27805,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
{"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 Bryon. John's card is shown to Angela. Angela'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 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 whether (Agentc knows whether 1)","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":"Angela can now know whether John can know whether Bryon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bryon","Angela","John"],"index":4850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979276657,"difficulty":0.0020723343}
{"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 Maria. Maria's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Maria can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Maria","Mary"],"index":34992,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997232556,"difficulty":0.0002767444}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Elenora. Elenora's card is shown to Virginia. Wilburn's card is shown to Wilburn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 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 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Virginia can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elenora","Virginia","Wilburn"],"index":21086,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983941913,"difficulty":0.0016058087}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffery's card is shown to Jeffery. Jeffery's card is shown to Tamara. Tamara's card is shown to Tamara. 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 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Tamara can now know that Jeffery can know whether Jeffery picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeffery","Tamara"],"index":30101,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9719654322,"difficulty":0.0280345678}
{"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. Albert's card is shown to Jeffrey. Jeffrey's card is shown to Albert. Jeffrey's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Karen picked a red card. It is publicly announced that Albert does not know whether Albert 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) ] (Agentb knows whether 2)","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":"Albert can now know whether Albert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffrey","Albert","Karen"],"index":37425,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9246504307,"difficulty":1.9246504307}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luther's card is shown to Clarence. Luther's card is shown to Luther. It is publicly announced that someone picked a red card. It is publicly announced that Luther does not know whether Clarence 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|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":"Luther can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Clarence","Luther"],"index":43480,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
{"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 Vanessa. Vanessa's card is shown to Billy. Billy's card is shown to Billy. It is publicly announced that someone picked a red card. It is publicly announced that Vanessa knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Vanessa can now know whether Vanessa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vanessa","Billy"],"index":62618,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9863670468,"difficulty":0.0136329532}
{"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 Mary. Mary's card is shown to Mary. John's card is shown to Mary. Mary's card is shown to John. John's card is shown to John. Glen's card is shown to John. Glen's card is shown to Glen. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Charles can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Mary","John","Glen"],"index":17405,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997691512,"difficulty":0.0002308488}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Sara. Sara's card is shown to Victoria. Victoria's card is shown to Victoria. It is publicly announced that someone picked a red card. It is publicly announced that Sara knows whether Earl 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) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Earl can now know whether Sara can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Earl","Sara","Victoria"],"index":67444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997031093,"difficulty":0.0002968907}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. Flora's card is shown to Betty. Elizabeth's card is shown to Betty. Betty's card is shown to Flora. Flora's card is shown to Flora. Elizabeth's card is shown to Flora. Flora's card is shown to Elizabeth. Elizabeth'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:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Flora","Elizabeth"],"index":36026,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9622592926,"difficulty":0.0377407074}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ella's card is shown to Ella. Deborah's card is shown to Deborah. Ella's card is shown to Jacqueline. It is publicly announced that someone picked a red card. It is publicly announced that Jacqueline does not know whether Jacqueline 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) ] (Agentc 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":"Jacqueline can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ella","Deborah","Jacqueline"],"index":47848,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
{"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. Jim's card is shown to Jonathan. Katrina's card is shown to Jonathan. Julia's card is shown to Jim. Julia's card is shown to Katrina. It is publicly announced that someone picked a red card. It is publicly announced that Katrina does not know whether Katrina picked a red card. It is publicly announced that Jim 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)) ] (Agentb knows that 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":"Jonathan can now know that Jim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julia","Jonathan","Jim","Katrina"],"index":8442,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9920619726,"difficulty":0.0079380274}
{"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 Roger. Roger's card is shown to Robin. Robin's card is shown to Shawn. Shawn's card is shown to Shawn. Roger's card is shown to Louis. Louis's card is shown to Louis. It is publicly announced that someone picked a red card. It is publicly announced that Roger does not know whether or not everyone picked a red card. It is publicly announced that Roger picked a red card. It is publicly announced that Roger 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)) ] Agenta knows that (Agentb knows whether 4)","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":"Roger can now know that Robin can know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Robin","Shawn","Louis"],"index":39305,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9561376572,"difficulty":1.9561376572}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnathon's card is shown to Carolyn. Johnathon's card is shown to Linda. 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:2 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Johnathon can now know whether Carolyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carolyn","Johnathon","Linda"],"index":13542,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9220173359,"difficulty":0.0779826641}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryn's card is shown to Kathryn. Kathryn's card is shown to Sharon. Rocky's card is shown to Sharon. Rocky's card is shown to Rocky. 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 whether 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":"Rocky can now know whether Sharon can know whether Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathryn","Sharon","Rocky"],"index":57166,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9892019033,"difficulty":1.9892019033}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raven's card is shown to Raven. Joseph's card is shown to Joseph. Willie's card is shown to Joseph. Raven's card is shown to Willie. Joseph's card is shown to Willie. Willie's card is shown to Willie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Willie can now know that Raven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raven","Joseph","Willie"],"index":28851,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979060888,"difficulty":0.0020939112}
{"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. Richard's card is shown to Susan. 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 or not everyone picked a red card. It is publicly announced that Richard knows whether Richard 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:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Susan can now know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Susan","Richard"],"index":15383,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9916981459,"difficulty":0.0083018541}
{"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. Harold's card is shown to Karen. Carol's card is shown to Karen. Karen's card is shown to Jamika. Jamika's card is shown to Jamika. Carol's card is shown to Jamika. Karen'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:1,2,4 Agentb:1,3,4 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:1,2,4 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that Harold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Harold","Jamika","Carol"],"index":18510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978790283,"difficulty":0.0021209717}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Betty. Darren's card is shown to Betty. Betty's card is shown to Alberta. Norman's card is shown to Alberta. Norman's card is shown to Norman. Alberta's card is shown to Darren. It is publicly announced that someone picked a red card. It is publicly announced that Darren picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Darren can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Alberta","Norman","Darren"],"index":50567,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985302687,"difficulty":0.0014697313}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terrance's card is shown to Eric. Terrance's card is shown to Terrance. Terrance's card is shown to Cynthia. Cynthia's card is shown to Cynthia. Cynthia'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:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Terrance","Cynthia","Alex"],"index":1017,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8592564464,"difficulty":0.1407435536}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roderick's card is shown to Everett. Everett's card is shown to Roderick. It is publicly announced that someone picked a red card. It is publicly announced that Roderick does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether 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":"Roderick can now know whether Roderick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Everett","Roderick"],"index":52961,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9954144955,"difficulty":1.9954144955}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jasper's card is shown to James. James's card is shown to Jasper. 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. It is publicly announced that James does not know whether James picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jasper can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Jasper"],"index":30209,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985992312,"difficulty":0.0014007688}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geraldine's card is shown to Mary. Mary's card is shown to Geraldine. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Mary can now know whether Geraldine can know that Geraldine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Geraldine"],"index":26681,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6342986226,"difficulty":0.3657013774}
{"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 Cheryl. Cheryl's card is shown to Judith. Judith's card is shown to Polly. Ronald'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:1 Agentc:2 Agentd:4 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:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cheryl can now know whether Polly can know whether Ronald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Judith","Polly","Ronald"],"index":61691,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988372922,"difficulty":0.0011627078}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Earl's card is shown to Jesse. Walter's card is shown to Earl. Walter's card is shown to Walter. 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) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Earl can now know that Jesse can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesse","Earl","Walter"],"index":13699,"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 Anne. Anne's card is shown to David. David's card is shown to David. David's card is shown to Ronny. Ronny's card is shown to Ronny. It is publicly announced that someone picked a red card. It is publicly announced that Ronny does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ronny can now know that Anne can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anne","David","Ronny"],"index":21891,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9910491705,"difficulty":0.0089508295}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnette's card is shown to Jennifer. Elsie's card is shown to Jennifer. Katrina's card is shown to Arnette. Arnette's card is shown to Arnette. Arnette's card is shown to Elsie. 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 Agentc: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:3,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Katrina can know whether Arnette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Katrina","Arnette","Elsie"],"index":21786,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8307029605,"difficulty":0.1692970395}
{"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. Jean's card is shown to Kevin. Juan's card is shown to Raymond. Kevin's card is shown to Jean. Raymond's card is shown to Juan. Jean's card is shown to Juan. 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) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know whether Raymond can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Raymond","Jean","Juan"],"index":16555,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995923638,"difficulty":0.0004076362}
{"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 Rita. Catherine's card is shown to Rita. Rita's card is shown to Donna. Catherine's card is shown to Catherine. 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) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Catherine can now know whether Rita can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rita","Donna","Catherine"],"index":20355,"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). Jack's card is shown to Caleb. James's card is shown to Caleb. James's card is shown to Eric. Jack's card is shown to Jack. Eric'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 Jack knows whether someone picked a red card. It is publicly announced that Caleb picked a red card. It is publicly announced that Eric does not know whether Jack 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 whether (Agentd knows that (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":"Eric can now know whether James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Caleb","Eric","Jack","James"],"index":27593,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999779284,"difficulty":0.000220716}
{"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 Emily. Connie's card is shown to Emily. Emily's card is shown to Stanley. Emily's card is shown to Connie. 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 whether 1)","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":"Stanley can now know whether Emily picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emily","Stanley","Connie"],"index":7065,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9623007178,"difficulty":0.0376992822}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Billy. Billy's card is shown to Laura. Michael's card is shown to Laura. Laura's card is shown to Michael. Karl's card is shown to Michael. Laura's card is shown to Karl. 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 Billy knows whether Billy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Laura can now know whether Billy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","Laura","Michael","Karl"],"index":16556,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6232616305,"difficulty":0.3767383695}
{"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 Patricia. Patricia's card is shown to Patricia. 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|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Patricia can now know that Michael can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Patricia"],"index":45580,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Deborah. Deborah's card is shown to Patricia. Chad's card is shown to Patricia. Chad's card is shown to Kerry. Kerry's card is shown to Chad. Chad's card is shown to Chad. 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) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deborah can now know whether Patricia can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Patricia","Kerry","Chad"],"index":34531,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Franklyn's card is shown to Franklyn. Anglea's card is shown to Franklyn. Anglea's card is shown to Anglea. It is publicly announced that someone picked a red card. It is publicly announced that Anglea does not know whether Franklyn picked a red card. It is publicly announced that Anglea 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Anglea can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Franklyn","Anglea"],"index":62225,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977846742,"difficulty":0.0022153258}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zachary's card is shown to Ronald. Eric's card is shown to Ronald. Zachary'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: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:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ronald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Zachary","Eric"],"index":52536,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983316064,"difficulty":0.0016683936}
{"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 John. Antonette's card is shown to John. William's card is shown to John. William's card is shown to Dwight. John's card is shown to Antonette. Dwight's card is shown to Antonette. Antonette's card is shown to Antonette. John's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Dwight does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1,2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1,2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know whether Antonette can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Dwight","Antonette","William"],"index":45445,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9940828681,"difficulty":1.9940828681}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Elizabeth. Elizabeth's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Gary 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 (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":"Elizabeth can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Elizabeth","Gary"],"index":7573,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985679388,"difficulty":0.0014320612}
{"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 Erin. Erin's card is shown to Kathy. It is publicly announced that someone picked a red card. It is publicly announced that Kathy does not know whether Candace picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Erin can now know that Erin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erin","Kathy","Candace"],"index":52784,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9743359685,"difficulty":0.0256640315}
{"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 Elizabeth. Elizabeth's card is shown to Charles. Charles's card is shown to Sharon. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Sharon 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) ] (Agenta knows whether (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":"Michelle can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michelle","Elizabeth","Charles","Sharon"],"index":58034,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9400036931,"difficulty":0.0599963069}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnold's card is shown to Arnold. Arnold's card is shown to Brian. Helen's card is shown to Brian. Arnold's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether Helen picked a red card. It is publicly announced that Brian knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Brian can now know that Arnold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arnold","Brian","Helen"],"index":55180,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9878758192,"difficulty":0.0121241808}
{"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 Cindy. Joan's card is shown to Michael. Cindy's card is shown to Joan. Joan's card is shown to Joan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 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:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cindy","Michael","Joan"],"index":64606,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925869107,"difficulty":0.0074130893}
{"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. Amber's card is shown to Markus. Markus's card is shown to Markus. 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:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Sandra can now know that Amber can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amber","Sandra","Markus"],"index":63809,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930039048,"difficulty":0.0069960952}
{"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. Jane's card is shown to Matthew. Eleanor's card is shown to Eleanor. Matthew'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:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jane can now know that Rose can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Matthew","Eleanor","Jane"],"index":9235,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983094931,"difficulty":0.0016905069}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Ronald. Charles's card is shown to Ronald. Laura's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Charles picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ronald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Charles","Laura"],"index":27669,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998470366,"difficulty":0.001529634}
{"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 Kathy. Patricia's card is shown to Shelia. Kathy's card is shown to Patricia. Shelia'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:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlie can now know that Kathy can know whether Kathy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlie","Kathy","Shelia","Patricia"],"index":29963,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.693003118,"difficulty":1.693003118}
{"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 Diane. William's card is shown to Diane. Shirley's card is shown to Shirley. William's card is shown to Shirley. Dorothy's card is shown to Shirley. Shirley's card is shown to William. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Shirley knows whether Dorothy picked a red card. It is publicly announced that Dorothy does not know whether Diane picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Dorothy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diane","Shirley","William","Dorothy"],"index":774,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985419512,"difficulty":0.0014580488}
{"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 Howard. Jason's card is shown to Howard. Jason's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Howard can now know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Howard","Jason","Matthew"],"index":61076,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.863888979,"difficulty":0.136111021}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harry's card is shown to Harry. Roy's card is shown to Michael. Amber's card is shown to Amber. Michael'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:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amber can now know whether Roy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harry","Michael","Amber","Roy"],"index":38665,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9943776727,"difficulty":0.0056223273}
{"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. Charles's card is shown to Alvin. Rebecca's card is shown to Alvin. Rebecca'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:1 Agentb:1,3 Agentc:3 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:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rebecca can now know whether Charles can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Alvin","Rebecca"],"index":21751,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997005463,"difficulty":0.0002994537}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michele's card is shown to Patricia. Ralph's card is shown to Ralph. Patricia's card is shown to Jeff. Patricia's card is shown to Michele. Ralph's card is shown to Michele. 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) ] Agentd 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":"Michele can now know that Ralph can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Ralph","Jeff","Michele"],"index":64976,"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). Jill's card is shown to Jill. Jill's card is shown to Matthew. 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:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Jill can now know that Matthew can know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jill","Matthew"],"index":55331,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948688745,"difficulty":0.0051311255}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobbie's card is shown to Bobbie. Fawn's card is shown to Bobbie. Fawn's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb: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:1,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bobbie can now know whether Brian can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bobbie","Brian","Fawn"],"index":47829,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994033575,"difficulty":0.0005966425}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Meagan's card is shown to Meagan. Nathaniel's card is shown to Meagan. Lawrence's card is shown to Meagan. Lawrence's card is shown to Nathaniel. Lawrence's card is shown to Lawrence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Meagan can now know whether Nathaniel can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Meagan","Nathaniel","Lawrence"],"index":62116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99925071,"difficulty":0.00074929}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittni's card is shown to James. Thomas's card is shown to James. Ashleigh's card is shown to Ashleigh. Thomas's card is shown to Ashleigh. James's card is shown to Brittni. Ashleigh'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:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Brittni can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Ashleigh","Brittni","Thomas"],"index":12170,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992181063,"difficulty":0.0007818937}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shawanda's card is shown to Al. Sophie's card is shown to Sophie. Shawanda's card is shown to Sophie. Shawanda's card is shown to Shawanda. It is publicly announced that someone picked a red card. It is publicly announced that Shawanda does not know whether Sophie 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 whether (Agentc knows that 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":"Al can now know whether Shawanda can know that Shawanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Al","Sophie","Shawanda"],"index":13173,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8449754715,"difficulty":0.1550245285}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindie's card is shown to Ashley. Robin's card is shown to Robin. Ashley's card is shown to Cindie. 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 whether (Agenta knows that 1)","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":"Cynthia can now know whether Ashley can know that Ashley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ashley","Robin","Cynthia","Cindie"],"index":2083,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9542936683,"difficulty":0.0457063317}
{"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 Debbie. Harold's card is shown to Micheal. Debbie's card is shown to Micheal. Micheal's card is shown to Micheal. It is publicly announced that someone picked a red card. It is publicly announced that Harold does not know whether Harold picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Debbie can now know that Debbie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harold","Debbie","Thomas","Micheal"],"index":10553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9913411736,"difficulty":0.0086588264}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janie's card is shown to Janie. Jaime's card is shown to Janie. Janie's card is shown to Damon. Susan's card is shown to Damon. Jaime's card is shown to Damon. Susan's card is shown to Susan. Jaime's card is shown to Susan. Janie's card is shown to Jaime. Jaime's card is shown to Jaime. It is publicly announced that someone picked a red card. It is publicly announced that Damon 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))) ] (Agenta knows whether 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":"Janie can now know whether Jaime picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janie","Damon","Susan","Jaime"],"index":25371,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7005489469,"difficulty":0.2994510531}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to Stephen. Frank's card is shown to June. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"June can now know that Stephen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephen","June","Frank"],"index":60565,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988155365,"difficulty":0.0011844635}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steve's card is shown to Marvin. Lynne's card is shown to Marvin. Marvin's card is shown to Richard. Steve's card is shown to Richard. Richard's card is shown to Steve. Steve's card is shown to Steve. Lynne's card is shown to Steve. Marvin's card is shown to Lynne. 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 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marvin can now know that Richard can know that Steve picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","Richard","Steve","Lynne"],"index":37809,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978197813,"difficulty":0.0021802187}
{"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 Michael. Matthew's card is shown to Margie. Grace's card is shown to Grace. Margie's card is shown to Matthew. Grace's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Grace does not know whether Margie picked a red card. It is publicly announced that Michael knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Matthew can now know that Michael can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Margie","Grace","Matthew"],"index":63915,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994516969,"difficulty":0.0005483031}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eunice's card is shown to Kathleen. Danielle's card is shown to Danielle. Eunice's card is shown to Danielle. Eunice's card is shown to Eunice. It is publicly announced that someone picked a red card. It is publicly announced that Eunice does not know whether Danielle 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)","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":"Kathleen can now know that Eunice can know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathleen","Danielle","Eunice"],"index":50347,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975630045,"difficulty":0.0024369955}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Jayna. Kathryn's card is shown to Lisa. Lisa's card is shown to Douglas. Kathryn's card is shown to Douglas. Jayna's card is shown to Kathryn. Lisa's card is shown to Kathryn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know whether Jayna can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jayna","Lisa","Douglas","Kathryn"],"index":46413,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994009733,"difficulty":0.0005990267}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Billy. Alfred's card is shown to Billy. Marion's card is shown to Eddie. Billy's card is shown to Alfred. Alfred's card is shown to Alfred. 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 Agentc:1,4 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:3,4 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Billy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","Eddie","Marion","Alfred"],"index":46396,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993754029,"difficulty":0.0006245971}
{"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 Thomas. Patricia's card is shown to Patricia. Jeremy's card is shown to Daniel. Jeremy's card is shown to Jeremy. It is publicly announced that someone picked a red card. It is publicly announced that Jeremy does not know whether Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Patricia can now know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Patricia","Daniel","Jeremy"],"index":19225,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9842018485,"difficulty":0.0157981515}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lonnie's card is shown to Jo. Jo's card is shown to Lonnie. 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)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Jo can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jo","Lonnie"],"index":12819,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993461967,"difficulty":0.0006538033}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonas's card is shown to Deborah. Zachery's card is shown to Deborah. Deborah's card is shown to Mary. Jonas's card is shown to Mary. Mary's card is shown to Jonas. Jonas's card is shown to Jonas. Zachery's card is shown to Jonas. Deborah's card is shown to Zachery. 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 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Zachery can now know that Mary can know whether Jonas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Mary","Jonas","Zachery"],"index":54860,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5642182231,"difficulty":0.4357817769}
{"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 Marian. Kristy's card is shown to Josephine. Kristy's card is shown to Kristy. It is publicly announced that someone picked a red card. It is publicly announced that Kristy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kristy can now know whether Josephine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marian","Josephine","Kristy"],"index":59017,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992873073,"difficulty":0.0007126927}
{"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. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Jonathan can now know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Anthony","Jonathan"],"index":59560,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6108977199,"difficulty":1.6108977199}
{"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. Harvey's card is shown to Robert. Harvey's card is shown to Harvey. It is publicly announced that someone picked a red card. It is publicly announced that Harvey picked a red card. It is publicly announced that Harvey 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)) ] (Agentb knows whether (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":"Harvey can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Harvey"],"index":26838,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6589302421,"difficulty":0.3410697579}
{"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 Jeanne. Adam's card is shown to Donald. Christina's card is shown to Adam. Adam's card is shown to Christina. It is publicly announced that someone picked a red card. It is publicly announced that Adam does not know whether or not everyone picked a red card. It is publicly announced that Jeanne does not know whether Jeanne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Donald can now know whether Christina can know whether Jeanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeanne","Donald","Adam","Christina"],"index":18874,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979193807,"difficulty":0.0020806193}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristine's card is shown to Roy. Cristine's card is shown to Jared. Cristine's card is shown to Cristine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know that Roy can know whether Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roy","Jared","Ruth","Cristine"],"index":39652,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993827641,"difficulty":0.006172359}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holly's card is shown to James. Kathryn's card is shown to James. Holly's card is shown to Charles. Kathryn's card is shown to Charles. Charles's card is shown to Kathryn. Kathryn's card is shown to Kathryn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 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:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Holly can know that Holly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Charles","Holly","Kathryn"],"index":46017,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8750053644,"difficulty":0.1249946356}
{"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. Daniel's card is shown to Dorothy. Dorothy's card is shown to Daniel. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy picked a black card. It is publicly announced that Daniel knows whether or not nobody picked a red card. It is publicly announced that Daniel knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Daniel can now know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dorothy","Daniel"],"index":46841,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8283134699,"difficulty":0.1716865301}
{"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 Jeffrey. Frank's card is shown to Frank. Margaret's card is shown to Rodney. Jeffrey's card is shown to Margaret. 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:4 Agentd:1 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:4 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know whether Margaret can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Frank","Rodney","Margaret"],"index":59046,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7706487775,"difficulty":0.2293512225}
{"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 Angelina. Angelina's card is shown to James. James's card is shown to James. Joseph's card is shown to James. Angelina's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angelina","James","Joseph"],"index":54582,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966307282,"difficulty":0.0033692718}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Corina's card is shown to Corina. Corina's card is shown to Judith. Brandon's card is shown to Judith. Judith's card is shown to Brandon. 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 whether (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":"Judith can now know that Corina can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Corina","Judith","Brandon"],"index":40240,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9916732907,"difficulty":0.0083267093}
{"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 Walter. Walter'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 Robert does not know whether Robert 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) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Walter can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Walter","Robert"],"index":56474,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990459085,"difficulty":0.0009540915}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Richard's card is shown to Georgianna. Anthony's card is shown to Nancy. Richard's card is shown to Nancy. Nancy'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:1 Agentb:4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Anthony can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Georgianna","Nancy","Richard"],"index":60080,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5027320981,"difficulty":1.5027320981}
{"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. Marco's card is shown to Mark. Raymond's card is shown to Mark. Marco's card is shown to Marco. 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 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":"Marco can now know whether Mark can know that Raymond picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Marco","Raymond"],"index":57729,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8751494884,"difficulty":1.8751494884}
{"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 Linda. Dayle's card is shown to Linda. Douglas's card is shown to Linda. Dayle's card is shown to Dayle. Douglas's card is shown to Douglas. 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 whether (1|2|3))","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":"Douglas can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Linda","Dayle","Douglas"],"index":45120,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994180202,"difficulty":0.0005819798}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Logan's card is shown to Leo. Holly's card is shown to Logan. Leo's card is shown to Holly. Logan's card is shown to Holly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Holly can now know whether Logan can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leo","Logan","Holly"],"index":28028,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994015694,"difficulty":0.0005984306}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bradly's card is shown to Bradly. Kelly's card is shown to Tracy. Kelly's card is shown to Deanna. It is publicly announced that someone picked a red card. It is publicly announced that Tracy does not know whether Bradly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Kelly can now know that Tracy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Bradly","Tracy","Deanna"],"index":37543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9892942905,"difficulty":0.0107057095}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Edward. Edward's card is shown to Tommy. It is publicly announced that someone picked a red card. It is publicly announced that Edward knows whether someone picked a red card. It is publicly announced that Tommy knows whether Tommy 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) ] (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 (1|2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Edward can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edward","Tommy"],"index":61746,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.95588696,"difficulty":1.95588696}
{"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 Sharon. Larry's card is shown to Sharon. Sharon's card is shown to Larry. 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 whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Sharon can now know whether Larry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sharon","Larry"],"index":64162,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9045239687,"difficulty":1.9045239687}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rudolph's card is shown to Ronald. Rudolph's card is shown to Bryan. Rudolph's card is shown to Rudolph. It is publicly announced that someone picked a red card. It is publicly announced that Bryan does not know whether Ronald picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Bryan picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Ronald can now know that Bryan can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Bryan","Rudolph"],"index":64018,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988019466,"difficulty":0.0011980534}
{"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. Antoinette's card is shown to Dennis. Frank's card is shown to Dennis. Dennis's card is shown to Antoinette. Dennis's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Frank can now know whether Antoinette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Antoinette","Frank"],"index":4058,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5173355341,"difficulty":0.4826644659}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Owen's card is shown to Marissa. John's card is shown to Owen. Marissa's card is shown to John. Owen'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 Owen 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)","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":"John can now know that Marissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marissa","Owen","John"],"index":22224,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997535944,"difficulty":0.002464056}
{"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 Gladys. Kenneth'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:3 Agentb:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 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":"Kenneth can now know whether Gladys can know whether Ray picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Gladys","Charles","Ray"],"index":44496,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990112782,"difficulty":0.0009887218}
{"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 Sandra. Audrey's card is shown to Audrey. Vernon's card is shown to Vernon. 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) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vernon can now know that Audrey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Audrey","Vernon"],"index":18996,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978052974,"difficulty":0.0021947026}
{"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 Samuel. Ted's card is shown to Ted. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Samuel 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)) ] (Agenta knows that 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":"Samuel can now know that Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Samuel","Ted","Jerry","Mark"],"index":29116,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7118496299,"difficulty":1.7118496299}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Adam. Adam's card is shown to Nelson. Nelson's card is shown to Nelson. 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 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":"Adam can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Adam","Nelson"],"index":51735,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9905754328,"difficulty":0.0094245672}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fidel's card is shown to Fidel. Jose's card is shown to Jose. Barbara's card is shown to Jose. Jose's card is shown to Barbara. Jose's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that Fidel does not know whether Jose picked a red card. It is publicly announced that Jose 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 that (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":"Annie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Fidel","Jose","Barbara","Annie"],"index":64382,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994646907,"difficulty":0.0005353093}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Anthony's card is shown to Lester. Mike's card is shown to Lester. Anthony's card is shown to Donnie. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether Mike picked a red card. It is publicly announced that Donnie knows whether or not everyone picked a red card. It is publicly announced that Anthony does not know whether Lester 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 whether (Agenta knows whether 3)","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":"Lester can now know whether Anthony can know whether Donnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Lester","Donnie","Mike"],"index":29648,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997961998,"difficulty":0.002038002}
{"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 John. Jillian's card is shown to Jillian. Jillian's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc: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:2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jillian can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Jillian","Jeffrey"],"index":2960,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9918704033,"difficulty":0.0081295967}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Bruce. Thomas's card is shown to Thomas. 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:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Thomas can now know whether Bruce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bruce","Thomas"],"index":3920,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.880617857,"difficulty":0.119382143}
{"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 Eddie. Gloria's card is shown to Eddie. Gloria's card is shown to Helen. Eddie's card is shown to Carol. Helen's card is shown to Gloria. Carol'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:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Eddie can know that Eddie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eddie","Helen","Carol","Gloria"],"index":7540,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982335567,"difficulty":0.0017664433}
{"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 Jessica. Deborah's card is shown to Jessica. Freddie's card is shown to Jessica. Jessica's card is shown to Deborah. William's card is shown to William. Jessica's card is shown to Freddie. William's card is shown to Freddie. 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:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deborah can now know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Deborah","William","Freddie"],"index":25303,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9405893087,"difficulty":0.0594106913}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Walter. James's card is shown to Walter. Walter'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 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 that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Walter can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Walter","James"],"index":48611,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949126244,"difficulty":0.0050873756}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Retta. Eugene's card is shown to Eugene. Doris's card is shown to Eugene. Eugene's card is shown to Doris. Doris's card is shown to Doris. It is publicly announced that someone picked a red card. It is publicly announced that Doris picked a red card. It is publicly announced that Doris does not know whether Retta picked a red card. It is publicly announced that Doris 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) ] (Agentc 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":"Doris can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Retta","Eugene","Doris"],"index":45282,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986996651,"difficulty":0.0013003349}
{"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. Mamie's card is shown to James. James's card is shown to Mamie. James'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:1,2 Agentb:1 Agentc:1 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:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Mamie","Michael","John"],"index":15235,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982364178,"difficulty":0.0017635822}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwayne's card is shown to Dwayne. Dwayne's card is shown to Bridget. Matt's card is shown to Matt. 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:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bridget can now know that Matt picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dwayne","Judy","Bridget","Matt"],"index":60427,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966484904,"difficulty":0.0033515096}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Inez's card is shown to Lakisha. Michael's card is shown to Inez. Inez'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 Lakisha 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)) ] Agentc knows that (Agentb knows whether 2)","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":"Michael can now know that Inez can know whether Inez picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lakisha","Inez","Michael"],"index":22405,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.777705133,"difficulty":1.777705133}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rutha's card is shown to Rutha. Judith's card is shown to Rutha. Judith's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that Judith knows whether or not nobody picked a red card. It is publicly announced that Judith does not know whether Rutha picked a red card. It is publicly announced that Rutha picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Judith can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rutha","Judith"],"index":24708,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984478951,"difficulty":0.0015521049}
{"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. Charles's card is shown to Charles. Charles's card is shown to Willie. Willie's card is shown to Willie. 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:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Willie can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Charles","Willie"],"index":44360,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.818497479,"difficulty":0.181502521}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to William. Maureen's card is shown to Steven. William's card is shown to Andrew. William's card is shown to Maureen. 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 whether (1&2&3&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":"Steven can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Steven","Andrew","Maureen"],"index":30503,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968485236,"difficulty":0.0031514764}
{"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 Zaida. Zaida's card is shown to Zaida. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Hunter can now know that Zaida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hunter","Carolyn","Chad","Zaida"],"index":4676,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9890322089,"difficulty":0.0109677911}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Mattie. Mattie's card is shown to Michele. Virginia's card is shown to Michele. William's card is shown to William. Virginia'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:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mattie can now know whether Michele can know whether Mattie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mattie","Michele","William","Virginia"],"index":65359,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985331297,"difficulty":0.0014668703}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Donald's card is shown to Cecil. 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:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Cecil can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Donald","Cecil"],"index":35085,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993802309,"difficulty":0.0006197691}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myron's card is shown to Donald. Myron's card is shown to Myron. Samuel's card is shown to Myron. Freddy's card is shown to Myron. Myron's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether Samuel picked a red card. It is publicly announced that Myron picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Myron can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Myron","Samuel","Freddy"],"index":53869,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985547662,"difficulty":0.0014452338}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Brian. John's card is shown to Brian. Brian's card is shown to Daniel. Daniel's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether Brian 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) ] Agentb knows that (Agenta knows that 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":"Daniel can now know that Brian can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Daniel","John"],"index":18673,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960120916,"difficulty":0.0039879084}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Ronald. Ronald's card is shown to Craig. 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:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Mattie can now know whether Mattie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Mattie","Craig"],"index":29132,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9156314731,"difficulty":0.0843685269}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Kristi. Kristi's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Kristi 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 whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Maria can now know whether Kristi can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kristi","Maria"],"index":64513,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9938752055,"difficulty":0.0061247945}
{"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. Margaret's card is shown to James. James's card is shown to Marion. Charles's card is shown to Marion. Margaret's card is shown to Marion. Charles's card is shown to Charles. Margaret's card is shown to Charles. James'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 Marion 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 whether (~(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":"Margaret can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Marion","Charles","Margaret"],"index":26158,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993342757,"difficulty":0.0006657243}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harriet's card is shown to Harriet. Dennis's card is shown to Clyde. Clyde's card is shown to Darlene. Dennis's card is shown to Darlene. Darlene's card is shown to Darlene. It is publicly announced that someone picked a red card. It is publicly announced that Harriet picked a red card. It is publicly announced that Dennis 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) ] [ ! 1 ] [ ! 3 ] (Agentc knows that (~(1|2|3|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) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Dennis can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harriet","Clyde","Dennis","Darlene"],"index":41239,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990469813,"difficulty":0.0009530187}
{"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 Rebecca. Reggie's card is shown to Reggie. Jose's card is shown to Reggie. Reggie's card is shown to Brittany. Brittany's card is shown to Jose. Jose's card is shown to Jose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jose can now know that Reggie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebecca","Reggie","Brittany","Jose"],"index":59888,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973348975,"difficulty":0.0026651025}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wallace's card is shown to Norma. Kevin's card is shown to Norma. Kevin's card is shown to Wallace. Norma's card is shown to Kevin. 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) ] Agenta knows that (Agentb 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":"Norma can now know that Wallace can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Norma","Wallace","Kevin"],"index":22665,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993484616,"difficulty":0.0006515384}
{"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. Nannie's card is shown to Nannie. Shelby's card is shown to Nannie. Dorothy's card is shown to Shelby. 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) ] Agentb knows whether (Agenta 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":"Nannie can now know whether Dorothy can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Nannie","Shelby"],"index":6175,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992744327,"difficulty":0.0007255673}
{"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 Rex. Aaron's card is shown to Aaron. Rex's card is shown to Peggy. Elizabeth's card is shown to Peggy. It is publicly announced that someone picked a red card. It is publicly announced that Aaron does not know whether Elizabeth picked a red card. It is publicly announced that Aaron knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Aaron can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rex","Aaron","Peggy","Elizabeth"],"index":10640,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9934660792,"difficulty":0.0065339208}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tricia's card is shown to Tricia. Eric's card is shown to Tricia. Tricia's card is shown to Helen. Tricia'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 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 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eric can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tricia","Helen","Eric"],"index":42205,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8720653653,"difficulty":0.1279346347}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. Jack's card is shown to Betty. Betty's card is shown to Jack. 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 whether (Agenta knows whether (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":"Jack can now know whether Betty can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Betty","Jack"],"index":48828,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994385839,"difficulty":0.0005614161}
{"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. Catherine'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 Deborah 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Catherine can now know whether Deborah can know that Deborah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Deborah"],"index":1557,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8723253012,"difficulty":0.1276746988}
{"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 Andrea. Dana's card is shown to Andrea. Dana's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Eleanor picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Eleanor can now know whether Eleanor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andrea","Eleanor","Dana"],"index":14251,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7666087151,"difficulty":0.2333912849}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Julie. Rosa's card is shown to Philip. Rosa's card is shown to Rosa. Michael's card is shown to Rosa. Philip'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 Michael does not know whether Rosa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Julie can now know that Rosa can know that Philip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Philip","Rosa","Michael"],"index":54068,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975939393,"difficulty":0.0024060607}
{"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 Elsie. Maurice's card is shown to Maurice. Twila's card is shown to Maurice. It is publicly announced that someone picked a red card. It is publicly announced that Elsie 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|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":"Maurice can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elsie","Maurice","Russ","Twila"],"index":45914,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994458556,"difficulty":0.0005541444}
{"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 Anita. Mildred's card is shown to Sharon. Anita's card is shown to Robert. Sharon's card is shown to Robert. Sharon's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc 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:4 Agentb:4 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Sharon can now know whether Anita can know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anita","Sharon","Robert","Mildred"],"index":14014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8750885725,"difficulty":0.1249114275}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Cyndy. Cyndy's card is shown to Julie. Cyndy's card is shown to Luis. 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) ] Agentb knows that (Agenta knows whether 3)","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":"John can now know that Cyndy can know whether Julie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cyndy","John","Julie","Luis"],"index":50653,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9529048204,"difficulty":1.9529048204}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Donna's card is shown to Donna. Jonathon's card is shown to Jonathon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donna can now know whether Valerie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Valerie","Donna","Jonathon"],"index":59249,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9236021042,"difficulty":0.0763978958}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Steve. Tabitha's card is shown to Lucy. Dorothy's card is shown to Lucy. Tabitha's card is shown to Tabitha. Dorothy's card is shown to Tabitha. Lucy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Tabitha does not know whether Lucy picked a red card. It is publicly announced that Tabitha does not know whether Lucy 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: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 whether (Agentd knows that 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":"Lucy can now know whether Dorothy can know that Lucy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steve","Lucy","Tabitha","Dorothy"],"index":49360,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9082512856,"difficulty":0.0917487144}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqueline's card is shown to Jacqueline. Jacqueline's card is shown to Dennis. Alan's card is shown to Dennis. Duncan's card is shown to Duncan. Dennis's card is shown to Alan. 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) ] (Agentb knows whether (1&2&3&4))","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":"Dennis can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacqueline","Dennis","Duncan","Alan"],"index":28009,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957398176,"difficulty":0.0042601824}
{"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 Randy. Randy's card is shown to Victor. Richard's card is shown to Victor. Randy's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1,3 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 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Victor can now know that Richard can know that Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Randy","Victor","Richard"],"index":30821,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9904452562,"difficulty":0.0095547438}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to Ricardo. Erin's card is shown to Erin. Erin'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:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Erin can now know whether Richard can know that Ricardo picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Ricardo","Erin","James"],"index":36217,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9412826896,"difficulty":0.0587173104}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michele's card is shown to Mark. Mark's card is shown to Mary. Michele's card is shown to Mary. Mary's card is shown to Michele. Michele's card is shown to Michele. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not nobody 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 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 (~(1|2|3))) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Mary","Michele"],"index":46073,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5992802978,"difficulty":0.4007197022}
{"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 Del. James's card is shown to Sallie. Karen's card is shown to Karen. Sallie's card is shown to James. Karen's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Sallie picked a red card. It is publicly announced that Del knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Karen can now know that James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Del","Sallie","Karen","James"],"index":52640,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8746550083,"difficulty":0.1253449917}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Levi's card is shown to Levi. Penny's card is shown to Penny. 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 Levi does not know whether Penny picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Levi can now know whether Penny can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Levi","Penny"],"index":58716,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994395375,"difficulty":0.0005604625}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tara's card is shown to Tara. Tara's card is shown to Juan. Juan's card is shown to Juan. 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:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Tara can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tara","Juan"],"index":59126,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989748001,"difficulty":0.0010251999}
{"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 Agnes. Agnes's card is shown to Agnes. Paul's card is shown to Agnes. Joseph's card is shown to Agnes. Paul's card is shown to Paul. Joseph's card is shown to Paul. Agnes's card is shown to Joseph. 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:1,2,3,4 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Steven can now know that Agnes can know that Agnes picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Agnes","Paul","Joseph"],"index":64358,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9931898713,"difficulty":0.0068101287}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Melvin. Laurene's card is shown to Melvin. Laurene's card is shown to Miguel. Melvin's card is shown to Laurene. Melvin's card is shown to Dexter. It is publicly announced that someone picked a red card. It is publicly announced that Dexter does not know whether Miguel picked a red card. It is publicly announced that Dexter does not know whether Dexter picked a red card. It is publicly announced that Miguel does not know whether Dexter 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) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","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":"Melvin can now know that Dexter can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melvin","Miguel","Laurene","Dexter"],"index":35943,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994039536,"difficulty":0.0005960464}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffani's card is shown to Tiffani. Tiffani's card is shown to Milton. Milton's card is shown to Milton. It is publicly announced that someone picked a red card. It is publicly announced that Milton knows whether Milton 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 whether (Agentb knows that (1&2))","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":"Tiffani can now know whether Milton can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tiffani","Milton"],"index":38064,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9781832695,"difficulty":1.9781832695}
{"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 Richard. Robert's card is shown to Richard. Jessica's card is shown to Jessica. Robert's card is shown to Jessica. Robert's card is shown to Robert. Nakita's card is shown to Robert. Nakita's card is shown to Nakita. 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 everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jessica can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Jessica","Robert","Nakita"],"index":30964,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9905418754,"difficulty":0.0094581246}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Floyd's card is shown to Floyd. Jeffrey's card is shown to Floyd. Floyd's card is shown to Jeffrey. Ha's card is shown to Arnold. Jeffrey's card is shown to Arnold. Arnold's card is shown to Arnold. 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 (Agentc 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":"Ha can now know that Jeffrey can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ha","Floyd","Jeffrey","Arnold"],"index":44353,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993846416,"difficulty":0.0006153584}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Austin's card is shown to Sharon. Austin's card is shown to Steven. Steven's card is shown to Steven. Mary's card is shown to Steven. Sharon'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 Steven 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 whether (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":"Steven can now know whether Sharon can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Austin","Sharon","Steven","Mary"],"index":35711,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994391799,"difficulty":0.0005608201}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eula's card is shown to Craig. Craig's card is shown to Eula. Matthew's card is shown to Eula. 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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Matthew can now know whether Craig can know whether Craig picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Craig","Matthew","Eula"],"index":15804,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9856993556,"difficulty":0.0143006444}
{"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 Jason. Jason's card is shown to Edward. Leo's card is shown to Leo. It is publicly announced that someone 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:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jason can now know that Lori can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jason","Lori","Edward","Leo"],"index":31216,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990104437,"difficulty":0.0009895563}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carrie's card is shown to Carrie. Robert's card is shown to Robert. Patti's card is shown to Robert. Patti's card is shown to Patti. Carrie's card is shown to Sandy. 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)) ] (Agentb 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":"Robert can now know whether Carrie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carrie","Robert","Patti","Sandy"],"index":24335,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.979539156,"difficulty":1.979539156}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Claudia's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Roger's card is shown to Carolyn. Claudia's card is shown to Roger. Carolyn's card is shown to Roger. Roger's card is shown to Roger. 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) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Claudia can now know that Carolyn can know that Roger picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Claudia","Carolyn","Roger"],"index":45507,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973466396,"difficulty":0.0026533604}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shane's card is shown to Shane. Ann's card is shown to Daniel. Luis's card is shown to Ann. Shane's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Shane knows whether Shane picked a red card. It is publicly announced that Shane does not know whether or not everyone picked a red card. It is publicly announced that Daniel does not know whether Daniel picked a red card. It is publicly announced that Ann does not know whether Daniel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Daniel can now know that Luis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shane","Daniel","Ann","Luis"],"index":65813,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9312731624,"difficulty":0.0687268376}
{"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 Catherine. Catherine's card is shown to Antone. Antone's card is shown to Antone. 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 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":"Catherine can now know whether Zachary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Catherine","Cynthia","Antone","Zachary"],"index":54638,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981377125,"difficulty":0.0018622875}
{"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. Kimberly's card is shown to Mary. Gary'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:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 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":["Gary","Mary","Norma","Kimberly"],"index":41641,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994020462,"difficulty":0.0005979538}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monique's card is shown to Monique. Monroe's card is shown to Monroe. Joshua's card is shown to Monroe. Joshua's card is shown to Joshua. Monique's card is shown to Cory. 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)) ] (Agentc knows whether (~(1|2|3|4)))","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":"Joshua can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Monique","Monroe","Joshua","Cory"],"index":66463,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993724227,"difficulty":0.0006275773}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Albert. Albert's card is shown to Sharon. Thea's card is shown to Sharon. Duane's card is shown to Duane. Thea's card is shown to Duane. 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:3,4 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:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sharon can now know that Duane can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Albert","Sharon","Duane","Thea"],"index":32945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988617897,"difficulty":0.0011382103}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Katherine. Deanna's card is shown to Katherine. Katherine's card is shown to Lisa. Katherine's card is shown to Deanna. Lisa's card is shown to Deanna. 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:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deanna can now know that Lisa can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Katherine","Lisa","Deanna"],"index":20427,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981049299,"difficulty":0.0018950701}
{"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 Ida. Ida's card is shown to Charles. Richard's card is shown to Charles. Ida's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that Charles can know that Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ida","Charles","Richard"],"index":20551,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971504807,"difficulty":0.0028495193}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Brooke. Sue's card is shown to Sue. Brooke'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:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brooke can now know that Sue can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brooke","Sue","Ashley"],"index":41671,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990216494,"difficulty":0.0009783506}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Amy's card is shown to Pedro. 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 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Pedro can now know that Amy can know that Pedro picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Amy","Pedro"],"index":54464,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996943295,"difficulty":0.003056705}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Ola. Ola's card is shown to Sara. It is publicly announced that someone picked a red card. It is publicly announced that Ola picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Ola can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ola","Sara"],"index":65677,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994683862,"difficulty":0.0005316138}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernestine's card is shown to Ernestine. Angeline's card is shown to Angeline. 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 whether (Agentb 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":"Ernestine can now know whether Angeline can know that Angeline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ernestine","Angeline"],"index":23789,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8530878425,"difficulty":1.8530878425}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mallory's card is shown to Mallory. Justin's card is shown to Mallory. Joanne's card is shown to Mallory. Justin's card is shown to Justin. Justin's card is shown to Joanne. Mallory's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Mallory picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Mallory can now know whether Joanne can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mallory","Justin","Joanne","Fred"],"index":47714,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999132812,"difficulty":0.000867188}
{"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. John's card is shown to Nathan. Nathan's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Mark knows whether or not everyone picked a red card. It is publicly announced that Nathan 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)) ] (Agentb knows that (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":"Nathan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Nathan","John"],"index":2281,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994662404,"difficulty":0.0005337596}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beau's card is shown to Mildred. Sean's card is shown to Alice. Alice's card is shown to Alice. Sean's card is shown to Beau. Mildred's card is shown to Beau. Beau's card is shown to Beau. It is publicly announced that someone picked a red card. It is publicly announced that Mildred knows whether Alice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Alice can now know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sean","Mildred","Alice","Beau"],"index":63673,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9527548552,"difficulty":1.9527548552}
{"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. Jason's card is shown to William. Steven's card is shown to Jason. Leland'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:1,4 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Steven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Steven","Leland","Jason"],"index":14324,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996981442,"difficulty":0.003018558}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Michael. Mikel's card is shown to Ruth. Ruth's card is shown to Mikel. It is publicly announced that someone picked a red card. It is publicly announced that Mikel does not know whether Mikel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mikel can now know that Ruth can know that Mikel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Ruth","Mikel","Jack"],"index":39112,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9915286303,"difficulty":0.0084713697}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Floyd's card is shown to Floyd. Peter's card is shown to Floyd. James's card is shown to Floyd. Floyd's card is shown to Richard. Richard's card is shown to James. James'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:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Floyd can now know that Peter can know that Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Floyd","Richard","Peter","James"],"index":67008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982308745,"difficulty":0.0017691255}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beau's card is shown to Marilyn. John's card is shown to Beau. Beau's card is shown to Beau. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Marilyn can know that Marilyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Marilyn","Beau"],"index":7489,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972658157,"difficulty":0.0027341843}
{"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. Charles's card is shown to Eva. It is publicly announced that someone picked a red card. It is publicly announced that Eva knows whether someone picked a red card. It is publicly announced that Eva does not know whether Eva 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) ] Agentb knows that (Agenta knows that 1)","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":"Eva can now know that Charles can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Eva","Leslie"],"index":38621,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9550372362,"difficulty":0.0449627638}
{"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 Shirley. Rose's card is shown to Justin. Silvia's card is shown to Justin. Shirley's card is shown to Rose. Justin'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:3 Agentb:3,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know that Rose can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirley","Justin","Rose","Silvia"],"index":40971,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990327358,"difficulty":0.0009672642}
{"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 Michael. Michael's card is shown to Michael. David's card is shown to Michael. Matthew's card is shown to David. Martha's card is shown to David. Martha's card is shown to Martha. It is publicly announced that someone picked a red card. It is publicly announced that Martha 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 ] Agenta knows whether (Agentc knows whether 4)","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":"Matthew can now know whether David can know whether Martha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Michael","David","Martha"],"index":39134,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989314675,"difficulty":0.0010685325}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Soila's card is shown to Ronnie. Soila's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ronnie can now know that Ronnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronnie","Joseph","Soila"],"index":13144,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9914242625,"difficulty":0.0085757375}
{"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 George. Paul's card is shown to George. George's card is shown to Kristina. Paul's card is shown to Kristina. Kristina'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 George 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 3)","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":"George can now know whether Paul can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Kristina","Paul"],"index":21020,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977059364,"difficulty":0.0022940636}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Julia. Marie's card is shown to Julia. Julia's card is shown to Marie. Thelma's card is shown to Marie. Kenneth's card is shown to Marie. 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 Thelma does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thelma can now know that Thelma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julia","Thelma","Kenneth","Marie"],"index":41884,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7828445435,"difficulty":1.7828445435}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susanna's card is shown to Mary. Virgina's card is shown to Virgina. Lisa's card is shown to Virgina. Virgina's card is shown to Lisa. Susanna's card is shown to Susanna. 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:2 Agentd:4 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:4 Agentb:2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susanna 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","Virgina","Lisa","Susanna"],"index":63550,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991606474,"difficulty":0.0008393526}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilma's card is shown to Wilma. Natalia's card is shown to Natalia. Donald's card is shown to Natalia. Lloyd's card is shown to Lloyd. 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:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilma can now know whether Wilma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wilma","Natalia","Lloyd","Donald"],"index":9385,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5755204558,"difficulty":0.4244795442}
{"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 Antonio. Antonio's card is shown to Larry. Larry's card is shown to Jessica. Larry's card is shown to Joe. It is publicly announced that someone picked a red card. It is publicly announced that Jessica knows whether or not everyone picked a red card. It is publicly announced that Joe does not know whether Jessica picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Larry can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Antonio","Larry","Jessica","Joe"],"index":25460,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994714856,"difficulty":0.0005285144}
{"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 Terrie. Terrie's card is shown to David. 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 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"David can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terrie","David","Robert"],"index":3348,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9269023538,"difficulty":1.9269023538}
{"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 Joyce. Anthony's card is shown to Joyce. Carol's card is shown to Anthony. Joyce's card is shown to Anthony. Anthony'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:1,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Jose","Joyce","Anthony"],"index":40717,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966611862,"difficulty":0.0033388138}
{"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 Barbara. Leo's card is shown to Leo. Amy's card is shown to Leo. Barbara's card is shown to Amy. Leo's card is shown to Amy. Amy's card is shown to Amy. 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. It is publicly announced that Amy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Barbara can now know whether Amy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Leo","Amy"],"index":36033,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994366765,"difficulty":0.0005633235}
{"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. Betty's card is shown to Clarence. Clarence's card is shown to Jeffrey. Betty's card is shown to Jeffrey. Jeffrey's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Betty 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:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jeffrey can now know that Clarence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clarence","Betty","Jeffrey","Willie"],"index":48808,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9428229928,"difficulty":1.9428229928}
{"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 Lewis. Lewis's card is shown to Jane. Patricia's card is shown to Jane. Patricia's card is shown to Patricia. Jane'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 James does not know whether Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jane can now know whether James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lewis","Jane","Patricia","James"],"index":16396,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992208481,"difficulty":0.0007791519}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Winnie's card is shown to Winnie. Francisco's card is shown to Francisco. Andrea's card is shown to Francisco. Winnie's card is shown to Andrea. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Andrea can now know whether Francisco can know whether Winnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Winnie","Francisco","Andrea"],"index":11329,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9989032745,"difficulty":1.9989032745}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Don's card is shown to Ashley. Kathy's card is shown to Ashley. Don's card is shown to Don. Kathy's card is shown to Don. Kathy's card is shown to Linda. Don's card is shown to Kathy. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Don 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) ] Agentb knows that (Agentc knows that 3)","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":"Don can now know that Linda can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ashley","Don","Linda","Kathy"],"index":10229,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9906518459,"difficulty":0.0093481541}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Coleen's card is shown to Coleen. Jesse's card is shown to Coleen. Coleen's card is shown to Jesse. 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 Jesse picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Jesse can now know whether Coleen can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Coleen","Jesse"],"index":8891,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9963130355,"difficulty":0.0036869645}
{"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 Joseph. Abram's card is shown to Joseph. Joseph's card is shown to Abram. 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) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Abram can now know that Joseph can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Abram"],"index":51828,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993596673,"difficulty":0.0006403327}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeanna's card is shown to Jeanna. Ellen's card is shown to Dollie. Steven's card is shown to Ellen. It is publicly announced that someone picked a red card. It is publicly announced that Ellen does not know whether Ellen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ellen can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeanna","Dollie","Ellen","Steven"],"index":41227,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990385771,"difficulty":0.0009614229}
{"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 Matthew. Jose's card is shown to Helen. Jose's card is shown to Ginger. It is publicly announced that someone picked a red card. It is publicly announced that Jose picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Helen can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Jose","Helen","Ginger"],"index":33266,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9883745909,"difficulty":0.0116254091}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Loyd. Loyd'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 Patricia knows whether Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Loyd","Patricia"],"index":55517,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994508624,"difficulty":0.0005491376}
{"premise":"There are two 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 Paul. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether someone picked a red card. It is publicly announced that Charles does not know whether Paul 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) ] (Agenta knows whether 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":"Charles can now know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Paul"],"index":64660,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8412932158,"difficulty":1.8412932158}
{"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. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Andrew picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb: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:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Donald can now know that Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrew","Donald","Raymond"],"index":7033,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9913411736,"difficulty":0.0086588264}
{"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 Renee. Peter's card is shown to Peter. Christopher's card is shown to Christopher. 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:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Keith","Renee","Peter","Christopher"],"index":67652,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9877748489,"difficulty":1.9877748489}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Lucy. Evelyn's card is shown to Lucy. Dennis's card is shown to Dennis. Evelyn's card is shown to Dennis. George's card is shown to Dennis. Dennis's card is shown to Evelyn. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Dennis knows whether George picked a red card. It is publicly announced that George does not know whether Lucy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Evelyn can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lucy","Dennis","Evelyn","George"],"index":37724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994438291,"difficulty":0.0005561709}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Kristen. 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 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Annie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Annie","Roland","Kristen"],"index":3155,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9938568473,"difficulty":0.0061431527}
{"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 Steven. James's card is shown to James. It is publicly announced that someone 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:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Steven can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Steven","James"],"index":37162,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993823767,"difficulty":0.0006176233}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ian's card is shown to Ian. Pablo's card is shown to Ian. Pablo's card is shown to Pablo. Julie's card is shown to Pablo. Ian's card is shown to Sarah. Pablo's card is shown to Sarah. Ian'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 Ian knows whether Ian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ian can now know whether Pablo can know whether Ian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ian","Pablo","Sarah","Julie"],"index":60619,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987615347,"difficulty":0.0012384653}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Matthew. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Matthew 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)) ] (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":"Matthew can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Matthew","Douglas"],"index":48252,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994136095,"difficulty":0.0005863905}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqueline's card is shown to Jacqueline. Diane's card is shown to Jacqueline. Diane's card is shown to Diane. It is publicly announced that someone picked a red card. It is publicly announced that Diane does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Diane can now know whether Jacqueline can know that Jacqueline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jacqueline","Diane"],"index":13681,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6916381717,"difficulty":1.6916381717}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Jose. Zenaida's card is shown to Jose. Elaine's card is shown to Elaine. Elaine's card is shown to Zenaida. Zenaida's card is shown to Zenaida. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Jose picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Elaine can now know whether Jose can know that Elaine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jose","Elaine","Zenaida"],"index":9305,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9392780662,"difficulty":0.0607219338}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dora's card is shown to Dora. Dora's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Dora does not know whether Scott picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Scott can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dora","Scott"],"index":45201,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988490343,"difficulty":0.0011509657}
{"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 Matthew. Matthew's card is shown to Roger. Roger's card is shown to Roger. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Alan 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 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jose can now know whether Jose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Jose","Alan","Roger"],"index":56123,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5780153275,"difficulty":1.5780153275}
{"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. Laura's card is shown to Laura. Joseph's card is shown to Kristen. It is publicly announced that someone 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:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Laura can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Laura","Kristen","David"],"index":18552,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965590835,"difficulty":0.0034409165}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Phil. Cassondra's card is shown to Cassondra. Francis's card is shown to Cassondra. Ann's card is shown to Cassondra. Cassondra's card is shown to Francis. Francis's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Ann 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 4)","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":"Cassondra can now know that Ann picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Phil","Cassondra","Francis","Ann"],"index":10579,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8196542263,"difficulty":0.1803457737}
{"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 Dorothy. Leonard's card is shown to Gloria. Gloria's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether Dorothy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dorothy can now know that Leonard can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Leonard","Gloria"],"index":47721,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993991852,"difficulty":0.0006008148}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Earl's card is shown to David. David's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Michael 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 whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"David can now know whether Michael can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","David","Earl"],"index":22139,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993872643,"difficulty":0.0006127357}
{"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 Jonathan. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Catherine picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Catherine can now know whether Jonathan can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jonathan","Catherine"],"index":56295,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994615912,"difficulty":0.0005384088}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Julie. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Julie knows whether or not nobody picked a red card. It is publicly announced that Evelyn knows whether Julie 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) ] Agentb knows whether (Agenta 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 (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Evelyn can now know whether Julie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Julie","Evelyn"],"index":3561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9830806851,"difficulty":0.0169193149}
{"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 Jeffrey. Lucille's card is shown to Lucille. Ann's card is shown to Lucille. Ann's card is shown to Barbara. Jeffrey's card is shown to Ann. Lucille's card is shown to Ann. Barbara's card is shown to Ann. 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 (Agentb knows whether (1|2|3|4))","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":"Ann can now know whether Lucille can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Lucille","Barbara","Ann"],"index":56298,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993950129,"difficulty":0.0006049871}
{"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 Louis. Shanon's card is shown to Louis. Michelle's card is shown to Michelle. Louis's card is shown to Shanon. 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 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michelle can now know whether Louis can know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louis","Michelle","Shanon"],"index":7536,"s-l":"explicit-1","deberta_pred":1,"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). Iola's card is shown to Bernice. Cortez's card is shown to Bernice. Iola's card is shown to Iola. Bernice's card is shown to Cortez. Iola's card is shown to Cortez. Cortez's card is shown to Cortez. 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 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":"Cortez can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bernice","Iola","Cortez"],"index":18114,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994015694,"difficulty":0.0005984306}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Classie's card is shown to Mary. Mary's card is shown to Classie. Classie's card is shown to Patricia. 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:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Classie can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Classie","Patricia"],"index":29768,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8596377969,"difficulty":0.1403622031}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robbie's card is shown to Kevin. Jeremy's card is shown to Wendell. Robbie's card is shown to Wendell. Jeremy's card is shown to Jeremy. Jeremy's card is shown to Robbie. It is publicly announced that someone picked a red card. It is publicly announced that Kevin does not know whether Jeremy 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:4 Agentb:3,4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] Agentd knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Robbie can now know that Jeremy can know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Wendell","Jeremy","Robbie"],"index":29564,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8795459867,"difficulty":0.1204540133}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Renee. Anthony's card is shown to Robert. Rhoda's card is shown to Rhoda. Robert's card is shown to Anthony. Rhoda's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Rhoda does not know whether Robert picked a red card. It is publicly announced that Renee knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that Anthony can know that Renee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Renee","Robert","Rhoda","Anthony"],"index":63253,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9894869328,"difficulty":0.0105130672}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmelita's card is shown to Carmelita. Bradley's card is shown to Bradley. It is publicly announced that someone picked a red card. It is publicly announced that Bradley 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) ] [ ! 2 ] [ ! (1&2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Bradley can now know that Bradley picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Carmelita","Bradley"],"index":63516,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9954684973,"difficulty":0.0045315027}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Russell's card is shown to Jessica. Terry's card is shown to Jessica. Russell's card is shown to Terry. 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 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Russell","Jessica","Terry"],"index":54305,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5943257809,"difficulty":0.4056742191}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to Ralph. Jesus's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Ralph knows whether Ralph picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jesus can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ralph","Jesus"],"index":9212,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994527698,"difficulty":0.0005472302}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Sarah. Sarah's card is shown to Dora. Ronald's card is shown to Dora. Sarah's card is shown to Ronald. Dora's card is shown to Ronald. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dora can now know whether Sarah can know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Dora","Ronald"],"index":49398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9975226521,"difficulty":0.0024773479}
{"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. Curtis's card is shown to Dorothy. Curtis's card is shown to Curtis. Tim's card is shown to Curtis. Jeffery's card is shown to Tim. Curtis's card is shown to Jeffery. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know whether Tim can know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Curtis","Tim","Jeffery"],"index":44138,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8990504146,"difficulty":0.1009495854}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hannah's card is shown to Hannah. Angelo's card is shown to Angelo. It is publicly announced that someone picked a red card. It is publicly announced that Angelo does not know whether Hannah picked a red card. It is publicly announced that Hannah 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 (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Angelo can now know that Hannah can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Hannah","Angelo"],"index":21668,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976569414,"difficulty":0.0023430586}
{"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 Ida. Robert's card is shown to Robert. Ida's card is shown to Vivian. Robert's card is shown to Vivian. 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:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brenda can now know whether Ida can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ida","Robert","Brenda","Vivian"],"index":62313,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992340803,"difficulty":0.0007659197}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Valerie's card is shown to Diane. Diane's card is shown to Diane. Valerie'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 Valerie 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:1 Agentb:1,2 Agentc:1,3 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:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Valerie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Valerie","Diane","Joseph"],"index":6860,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999063313,"difficulty":0.000936687}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Marion. Marion's card is shown to James. 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) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Marion can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marion","James"],"index":7889,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956816435,"difficulty":0.0043183565}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenell's card is shown to Edgar. Kristy's card is shown to Jim. Jenell's card is shown to Kristy. 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 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:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jim can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edgar","Jim","Kristy","Jenell"],"index":22231,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989060163,"difficulty":0.0010939837}
{"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 Richard. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Kevin picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Kevin can now know that Richard can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Kevin"],"index":56107,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6359754205,"difficulty":1.6359754205}
{"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. Eric's card is shown to Louis. Stanley's card is shown to Louis. Eric's card is shown to Eric. Stanley's card is shown to Stanley. 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) ] (Agenta knows whether 1)","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":"Louis can now know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Louis","Eric","Stanley"],"index":64288,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8044627905,"difficulty":0.1955372095}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Ralph. Ralph's card is shown to Victor. Victor's card is shown to Evelyn. 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 (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":"Victor can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Victor","Evelyn"],"index":8771,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955626726,"difficulty":0.0044373274}
{"premise":"There are three 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 Leena. Leena's card is shown to Leena. Dean's card is shown to Leena. Dean's card is shown to Dean. 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:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leena can now know whether Anne can know that Dean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anne","Leena","Dean"],"index":24183,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.931119144,"difficulty":0.068880856}
{"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 Randy. Justin's card is shown to Justin. It is publicly announced that someone picked a red card. It is publicly announced that Randy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Randy can now know whether Justin can know that Randy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randy","Justin"],"index":62810,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.863463819,"difficulty":0.136536181}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Benjamin's card is shown to Benjamin. Mike's card is shown to Benjamin. Benjamin's card is shown to Sebastian. Mike's card is shown to Mike. Mike'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:1,3 Agentb:1 Agentc:3 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:1,3 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sebastian can now know whether Benjamin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Benjamin","Sebastian","Mike","Lisa"],"index":16233,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7797218561,"difficulty":0.2202781439}
{"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 Hugh. Laura's card is shown to Hugh. Joan's card is shown to Joan. Joan's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Hugh 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 1) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Hugh can now know that Laura can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Hugh","Joan","Laura"],"index":57353,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948108196,"difficulty":0.0051891804}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathleen's card is shown to Agustin. Agustin's card is shown to Agustin. Daniel's card is shown to Agustin. Agustin's card is shown to Daniel. Cathleen's card is shown to Phillip. It is publicly announced that someone picked a red card. It is publicly announced that Cathleen knows whether Phillip picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta 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 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Daniel can now know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cathleen","Agustin","Daniel","Phillip"],"index":496,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5789374709,"difficulty":1.5789374709}
{"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 David. Stacie's card is shown to David. Stacie's card is shown to Norma. Ella's card is shown to Norma. David's card is shown to Stacie. Stacie's card is shown to Stacie. Ella's card is shown to Stacie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stacie can now know that Norma can know that Ella picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Norma","Stacie","Ella"],"index":35798,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977641106,"difficulty":0.0022358894}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Jeanette's card is shown to Jeanette. James's card is shown to Jeanette. Bradley's card is shown to Bradley. It is publicly announced that someone picked a red card. It is publicly announced that Jeanette does not know whether Valerie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Valerie can now know that James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Valerie","Jeanette","James","Bradley"],"index":4455,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953971505,"difficulty":0.0046028495}
{"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 Brenda. Joan's card is shown to George. Brenda's card is shown to Joan. George's card is shown to Joan. 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. It is publicly announced that George does not know whether Brenda 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) ] (Agentb knows whether (1&2&3))","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":"George can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brenda","George","Joan"],"index":7525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935203195,"difficulty":0.0064796805}
{"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 Steve. Steve's card is shown to Patrick. Joseph's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Patrick 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) ] [ ! 3 ] (Agenta knows whether (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) ] [ ! 3 ] 0","hypothesis":"Joseph can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Steve","Patrick","Mary"],"index":62355,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6732701659,"difficulty":1.6732701659}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyung's card is shown to Aaron. Regina's card is shown to Aaron. Angela's card is shown to Angela. Angela's card is shown to Regina. 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 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kyung can now know whether Aaron can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aaron","Kyung","Angela","Regina"],"index":26000,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993891716,"difficulty":0.0006108284}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janeen's card is shown to Janeen. Janeen's card is shown to Amos. Amos's card is shown to Amos. Joyce's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Joyce knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Amos can now know that Janeen can know whether Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Janeen","Amos","John"],"index":62429,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6859180331,"difficulty":0.3140819669}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dylan's card is shown to Lisa. Barbara's card is shown to Lisa. Lisa's card is shown to Dylan. It is publicly announced that someone picked a red card. It is publicly announced that Dylan does not know whether Barbara picked a red card. It is publicly announced that Lisa does not know whether Lisa 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 3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lisa can now know that Dylan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Dylan","Barbara"],"index":39656,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994146824,"difficulty":0.0005853176}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Alan. Robert's card is shown to Robert. Mary's card is shown to Robert. Robert'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 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alan","Robert","Mary"],"index":22628,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943189025,"difficulty":0.0056810975}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reed's card is shown to Meredith. Meredith's card is shown to Reed. It is publicly announced that someone picked a red card. It is publicly announced that Reed 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 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":"Reed can now know whether Reed picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Meredith","Reed"],"index":1272,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6086460352,"difficulty":1.6086460352}
{"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 Carla. Jesse's card is shown to Jesse. 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 Jesse knows whether Carla 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 (~(1|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":"Jesse can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carla","Jesse"],"index":43514,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990144968,"difficulty":0.0009855032}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Yesenia. Donna's card is shown to Eliza. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bernice can now know that Bernice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernice","Yesenia","Donna","Eliza"],"index":56153,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966756105,"difficulty":0.0033243895}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rodney's card is shown to Rodney. Norman's card is shown to Rodney. Rodney's card is shown to Norman. Norman's card is shown to Norman. Julie's card is shown to Norman. Norman's card is shown to Julie. Julie'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:1,2 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rodney can now know whether Norman can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rodney","Norman","Julie"],"index":32556,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9820641279,"difficulty":1.9820641279}
{"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 Debra. Allen's card is shown to Beth. Beth's card is shown to Allen. 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 (Agentc knows whether (~(1|2|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":"Beth can now know whether Allen can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Debra","Beth","Allen"],"index":19672,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993543029,"difficulty":0.0006456971}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jamie's card is shown to Michelle. Jamie's card is shown to Jamie. It is publicly announced that someone picked a red card. It is publicly announced that Michelle knows whether Jamie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jamie can now know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michelle","Jamie"],"index":11499,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6071138978,"difficulty":0.3928861022}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Maria. George's card is shown to Marco. Jane's card is shown to Marco. Jane's card is shown to George. Marco's card is shown to Jane. Jane's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Jane does not know whether George picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Marco can now know whether George can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Marco","George","Jane"],"index":1562,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9750801921,"difficulty":0.0249198079}
{"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 Linda. Peggy's card is shown to Linda. Linda's card is shown to Jeffery. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeffery can now know that Linda can know that Jeffery picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Jeffery","Peggy"],"index":58191,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976544976,"difficulty":0.0023455024}
{"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 Clifford. Ian's card is shown to Clifford. Clifford's card is shown to Jason. Ian's card is shown to Ian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ian can now know whether Clifford can know whether Ian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clifford","Jason","Ian"],"index":43730,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983861446,"difficulty":0.0016138554}
{"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 Eloy. Jessie's card is shown to Eloy. Elizabeth's card is shown to Emma. Emma's card is shown to Jessie. Jessie's card is shown to Jessie. It is publicly announced that someone picked a red card. It is publicly announced that Jessie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Eloy can now know whether Elizabeth can know that Jessie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eloy","Elizabeth","Emma","Jessie"],"index":4653,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9690033793,"difficulty":0.0309966207}
{"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 Suzanne. James's card is shown to James. Suzanne's card is shown to Pat. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Suzanne can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Glenda","Suzanne","James","Pat"],"index":57755,"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). Joshua's card is shown to Isabelle. Ashlee's card is shown to Isabelle. Joshua's card is shown to Perry. Isabelle's card is shown to Ashlee. Ashlee's card is shown to Ashlee. 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 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joshua can now know whether Isabelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Isabelle","Perry","Joshua","Ashlee"],"index":60680,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5057765841,"difficulty":0.4942234159}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurice's card is shown to Amy. Maurice's card is shown to Maurice. It is publicly announced that someone picked a red card. It is publicly announced that Maurice 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 that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Amy can now know that Maurice can know that Maurice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Amy","Maurice"],"index":41726,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.511588335,"difficulty":0.488411665}
{"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 Tracy. Sonia's card is shown to Tracy. Martin's card is shown to Martin. Martin's card is shown to Sonia. It is publicly announced that someone picked a red card. It is publicly announced that Martin knows whether Martin picked a red card. It is publicly announced that Martin does not know whether or not everyone picked a red card. It is publicly announced that Tracy 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)) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb: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":"Sonia can now know that Martin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracy","Martin","Sonia"],"index":63072,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999437511,"difficulty":0.000562489}
{"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 Donald. Lois's card is shown to Sean. Donald's card is shown to Aaron. Sean's card is shown to Aaron. Donald's card is shown to Lois. Sean's card is shown to Lois. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 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:3 Agentb:4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know that Aaron can know that Sean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Sean","Aaron","Lois"],"index":67322,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978994131,"difficulty":0.0021005869}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dusti's card is shown to Alaina. Dusti's card is shown to Dusti. It is publicly announced that someone picked a red card. It is publicly announced that Dusti does not know whether Alaina 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 (Agentb knows that (~(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":"Alaina can now know whether Dusti can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alaina","Dusti"],"index":28940,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992367029,"difficulty":0.0007632971}
{"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 Nola. Timothy's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Nola does not know whether Timothy 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 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Nola can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nola","Timothy","Jeffrey"],"index":3810,"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). John's card is shown to John. Larry's card is shown to John. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether John picked a red card. It is publicly announced that John knows whether someone picked a red card. It is publicly announced that John knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Larry can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Larry"],"index":16150,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994086027,"difficulty":0.0005913973}
{"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. Corey's card is shown to Corey. Gregory's card is shown to Corey. Richard's card is shown to Gregory. Corey's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Corey picked a black card. It is publicly announced that Richard knows whether Richard 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 1)","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":"Corey can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Corey","Gregory"],"index":22458,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9137570858,"difficulty":0.0862429142}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Randall. Betty's card is shown to Tracie. Randall's card is shown to Kyle. Betty's card is shown to Kyle. Kyle's card is shown to Betty. 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) ] Agentb knows whether (Agentd 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":"Tracie can now know whether Betty can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randall","Tracie","Kyle","Betty"],"index":36304,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993954897,"difficulty":0.0006045103}
{"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. Robert's card is shown to Nancy. Nancy's card is shown to Jason. Nancy's card is shown to Robert. Robert'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:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jason can now know that Nancy can know that Nancy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Jason","Robert"],"index":31050,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944095016,"difficulty":0.0055904984}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julia's card is shown to Julia. Walter's card is shown to Julia. Walter's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether Julia 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 Walter 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Walter can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Julia","Walter"],"index":49096,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998285234,"difficulty":0.001714766}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terri's card is shown to Terri. Terri's card is shown to Maria. Terri's card is shown to Steven. Maria's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that Steven does not know whether Steven picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Steven can now know that Teresa can know whether Terri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Terri","Maria","Steven","Teresa"],"index":56523,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5283541679,"difficulty":0.4716458321}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kirsten's card is shown to Kirsten. Anna's card is shown to Kirsten. Vernon's card is shown to Anna. Anna's card is shown to Vernon. 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) ] (Agentc 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":"Vernon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kirsten","Anna","Vernon"],"index":7465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993436933,"difficulty":0.0006563067}
{"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 John. John's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Sharon 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)) ] (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) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Sharon can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","John","Linda"],"index":63238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940808415,"difficulty":0.0059191585}
{"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. Richard's card is shown to Timothy. Timothy's card is shown to Richard. Richard's card is shown to Richard. Melvin's card is shown to Richard. Timothy's card is shown to Melvin. Melvin's card is shown to Melvin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Timothy can now know that Richard can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Richard","Melvin"],"index":14160,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9720076919,"difficulty":1.9720076919}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenny's card is shown to Kenny. Kenny'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 Kenny knows whether or not nobody picked a red card. It is publicly announced that Kenny knows whether Jose picked a red card. It is publicly announced that Jose knows whether or not nobody picked a red card. It is publicly announced that Jose knows whether Jose 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 whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether 2)","n_announcements":4,"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) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jose can now know whether Jose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kenny","Jose"],"index":19191,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9777585268,"difficulty":0.0222414732}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilmer's card is shown to Wilmer. Diane's card is shown to Benjamin. Diane's card is shown to Diane. Wilmer's card is shown to Beulah. Beulah's card is shown to Beulah. 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 Agentd:1,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilmer can now know that Diane can know whether Diane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wilmer","Benjamin","Diane","Beulah"],"index":46677,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6365565062,"difficulty":0.3634434938}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lonnie's card is shown to Mavis. Debra's card is shown to Mavis. Lonnie's card is shown to Lonnie. Debra's card is shown to Lonnie. Mavis's card is shown to Allison. Allison's card is shown to Debra. Debra'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:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mavis can now know that Lonnie can know that Debra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mavis","Lonnie","Allison","Debra"],"index":24029,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981455803,"difficulty":0.0018544197}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Johnny. Nidia's card is shown to Johnny. Johnny's card is shown to Nidia. It is publicly announced that someone picked a red card. It is publicly announced that Johnny knows whether someone 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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Nidia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Johnny","Nidia"],"index":2449,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994142056,"difficulty":0.0005857944}
{"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 Steven. Harry's card is shown to Harry. Harry's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Harry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Steven can now know that Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Steven","Harry","Alice"],"index":37782,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5065028071,"difficulty":0.4934971929}
{"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 Rebecca. Charlotte's card is shown to Ebony. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether or not everyone picked a red card. It is publicly announced that Ebony does not know whether Ebony 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 2) ] Agentb knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ebony can now know that Rebecca can know whether Charlotte picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebecca","Ebony","Charlotte"],"index":48464,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7271595597,"difficulty":0.2728404403}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gustavo's card is shown to Beverly. Hazel's card is shown to Beverly. Beverly's card is shown to Jill. Gustavo's card is shown to Jill. Gustavo's card is shown to Gustavo. Gustavo's card is shown to Hazel. It is publicly announced that someone picked a red card. It is publicly announced that Gustavo 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)) ] (Agenta knows whether 4)","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":"Beverly can now know whether Hazel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverly","Jill","Gustavo","Hazel"],"index":3352,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5417573452,"difficulty":0.4582426548}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rene's card is shown to Thelma. Thelma's card is shown to Patricia. Patricia's card is shown to Patricia. Rene's card is shown to Patricia. Thelma's card is shown to Rene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know whether Rene can know whether Thelma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thelma","Patricia","Rene"],"index":26836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986506104,"difficulty":0.0013493896}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eda's card is shown to Louis. Mildred's card is shown to Louis. Mildred's card is shown to Eda. Mildred's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Mildred 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:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Louis can now know that Eda can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Louis","Eda","Mildred"],"index":59847,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989412427,"difficulty":0.0010587573}
{"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. William's card is shown to Carol. William's card is shown to Miguel. William's card is shown to Ralph. Ralph'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 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know whether Ralph can know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Miguel","Ralph","William"],"index":23758,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985544086,"difficulty":0.0014455914}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lizzie's card is shown to Jennifer. Joe's card is shown to Jennifer. Joe's card is shown to Elliot. Jennifer's card is shown to Lizzie. Elliot's card is shown to Joe. Lizzie's card is shown to Joe. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joe can now know whether Jennifer can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Elliot","Lizzie","Joe"],"index":38390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6349657774,"difficulty":0.3650342226}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margareta's card is shown to Ann. Russell's card is shown to Eunice. Margareta's card is shown to Margareta. 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) ] 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 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margareta can now know that Ann can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ann","Eunice","Margareta","Russell"],"index":25732,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9921978116,"difficulty":0.0078021884}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wallace's card is shown to Diane. Emma's card is shown to Diane. Emma's card is shown to Wallace. 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 whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Wallace can now know that Diane can know whether Emma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Wallace","Emma"],"index":54717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7598770261,"difficulty":0.2401229739}
{"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. Otis's card is shown to Otis. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card. It is publicly announced that Otis does not know whether Robert 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) ] Agenta knows that (Agentb 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) ] 0","hypothesis":"Robert can now know that Otis can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Otis"],"index":5409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999427855,"difficulty":0.000572145}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. Jennifer's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank knows whether or not nobody 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 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1&2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1&2) ] 0","hypothesis":"Frank can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Frank","Jennifer"],"index":28911,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.986738205,"difficulty":0.013261795}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peggy's card is shown to Peggy. Peggy's card is shown to Caroline. Michael's card is shown to Caroline. Caroline's card is shown to Caroline. Peggy's card is shown to Lucia. Lucia's card is shown to Lucia. 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:1,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Peggy can now know that Michael can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peggy","Michael","Caroline","Lucia"],"index":38518,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9581737518,"difficulty":1.9581737518}
{"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 Maryalice. Jesus's card is shown to Jesus. Maryalice'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 Gerald knows whether Maryalice picked a red card. It is publicly announced that Jesus does not know whether Maryalice 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) ] (Agenta knows that (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":"Maryalice can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maryalice","Jesus","Gerald"],"index":48599,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994463325,"difficulty":0.0005536675}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Venice's card is shown to Venice. Ina's card is shown to Ina. Ina'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:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Venice can now know whether Venice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Venice","Ina","Elizabeth"],"index":63719,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6167059541,"difficulty":0.3832940459}
{"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 Nellie. Elizabeth's card is shown to Kay. It is publicly announced that someone picked a red card. It is publicly announced that Nellie knows whether Elizabeth picked a red card. It is publicly announced that Nellie does not know whether Donna picked a red card. It is publicly announced that Kay picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(4) ] (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Nellie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Nellie","Elizabeth","Kay"],"index":31020,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999478519,"difficulty":0.000521481}
{"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 Franklin. Jonathan's card is shown to Franklin. Jeremy's card is shown to Franklin. Jonathan's card is shown to Ruth. Jonathan's card is shown to Jeremy. Jeremy's card is shown to Jeremy. 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 whether (Agenta knows that 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":"Jonathan can now know whether Franklin can know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Franklin","Ruth","Jonathan","Jeremy"],"index":10645,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9264723659,"difficulty":0.0735276341}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwardo's card is shown to Edwardo. Virginia's card is shown to Edwardo. Edwardo's card is shown to Tom. Virginia's card is shown to Virginia. 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:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Virginia can now know that Tom can know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edwardo","Tom","Virginia"],"index":8405,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5791749358,"difficulty":1.5791749358}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. Linda's card is shown to Frank. Frank's card is shown to Linda. Linda's card is shown to Linda. Frank's card is shown to Michelle. Mabel's card is shown to Michelle. Michelle's card is shown to Mabel. Mabel's card is shown to Mabel. 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 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know whether Frank can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frank","Linda","Michelle","Mabel"],"index":49658,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9178465605,"difficulty":1.9178465605}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mariano's card is shown to Geneva. Nancy's card is shown to Nancy. Geneva's card is shown to Mariano. Nancy's card is shown to Mariano. 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 (Agentc knows that (~(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":"Nancy can now know whether Mariano can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geneva","Nancy","Mariano"],"index":21889,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991939664,"difficulty":0.0008060336}
{"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 Elbert. Louie's card is shown to Elbert. Elbert's card is shown to Paul. Paul's card is shown to Sandra. Louie's card is shown to Sandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louie can now know that Elbert can know that Louie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elbert","Paul","Louie","Sandra"],"index":6485,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980431795,"difficulty":0.0019568205}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Byron's card is shown to Kenneth. Byron's card is shown to Joshua. Joshua's card is shown to Byron. 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 whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Joshua can now know whether Kenneth can know whether Byron picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Joshua","Byron"],"index":59211,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980322719,"difficulty":0.0019677281}
{"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 Linda. David's card is shown to Michael. Linda's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether David 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) ] (Agentc knows whether 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) ] 0","hypothesis":"Michael can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Linda","Michael"],"index":64471,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7558176517,"difficulty":0.2441823483}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Kathleen'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 Jason picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Kathleen knows 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) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jason can now know whether Kathleen can know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathleen","Jason"],"index":61519,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9342642426,"difficulty":0.0657357574}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beulah's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Debra picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Debra can now know that Beulah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debra","Beulah"],"index":67453,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9702712297,"difficulty":1.9702712297}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathy's card is shown to Kathy. Kathy's card is shown to Thomas. 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) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Kathy can now know that Thomas can know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kathy","Thomas"],"index":4691,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954196215,"difficulty":0.0045803785}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Troy's card is shown to Jacqulyn. Frank's card is shown to Troy. 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 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jacqulyn can now know that Frank can know whether Jacqulyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frank","Jacqulyn","Troy"],"index":61826,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7716271281,"difficulty":0.2283728719}
{"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 Benjamin. 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:1 Agentb: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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Benjamin can now know whether Ivory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Benjamin","Michael","Ivory"],"index":58885,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954853654,"difficulty":0.0045146346}
{"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 Lorraine. It is publicly announced that someone picked a red card. It is publicly announced that Lorraine knows whether someone picked a red card. It is publicly announced that Lorraine does not know whether Lorraine picked a red card. It is publicly announced that Lorraine does not know whether Lorraine picked a red card. It is publicly announced that Lorraine does not know whether Lorraine 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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta 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 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lorraine can now know whether Anthony can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anthony","Lorraine"],"index":27684,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8356627226,"difficulty":1.8356627226}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Annie. Edna's card is shown to Annie. Charles's card is shown to Charles. Danielle's card is shown to Edna. Charles's card is shown to Danielle. It is publicly announced that someone picked a red card. It is publicly announced that Edna does not know whether or not everyone picked a red card. It is publicly announced that Charles knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Annie can now know whether Annie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Annie","Charles","Edna","Danielle"],"index":15224,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7667175531,"difficulty":0.2332824469}
{"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 Matthew. Keith's card is shown to Matthew. Bruce's card is shown to Bruce. Bruce'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 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Keith can now know whether Bruce can know that Bruce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Bruce","Keith"],"index":20659,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8342635632,"difficulty":0.1657364368}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derrick's card is shown to Derrick. Vera's card is shown to Maria. Derrick's card is shown to Vera. Vera's card is shown to Vera. 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) ] (Agentb knows that 3)","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":"Maria can now know that Vera picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Derrick","Maria","Vera"],"index":15316,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956234097,"difficulty":0.0043765903}
{"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 Pamela. Pamela's card is shown to Pamela. 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:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julie","Lee","Pamela"],"index":47139,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994182587,"difficulty":0.0005817413}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ana's card is shown to Ana. Ana's card is shown to Anthony. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether Anthony 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 (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":"Ana can now know that Anthony can know that Ana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ana","Anthony"],"index":59186,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9327280521,"difficulty":0.0672719479}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Virginia. Anthony's card is shown to Anthony. Anthony's card is shown to Brooke. Brooke's card is shown to Brooke. Brooke's card is shown to Nola. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 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:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Anthony","Brooke","Nola"],"index":20129,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982509017,"difficulty":0.0017490983}
{"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. Douglas's card is shown to Douglas. Joseph's card is shown to Jeffrey. Douglas's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Douglas","Jeffrey"],"index":16312,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994027615,"difficulty":0.0005972385}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Kevin. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Kevin knows whether someone 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 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 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":"Jonathan can now know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kevin","Jonathan"],"index":43264,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9673874974,"difficulty":0.0326125026}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Malcolm's card is shown to Malcolm. Diane's card is shown to Malcolm. Malcolm's card is shown to Diane. Christina's card is shown to Diane. Malcolm's card is shown to Christina. Diane's card is shown to Christina. 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:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Malcolm can now know that Christina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Malcolm","Diane","Christina"],"index":46294,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997923851,"difficulty":0.002076149}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Charles. Charles's card is shown to James. James's card is shown to James. Charles's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Charles can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","James","Gary"],"index":40078,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993501306,"difficulty":0.0006498694}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leo's card is shown to Steven. Leo's card is shown to Leo. It is publicly announced that someone picked a red card. It is publicly announced that Steven does not know whether or not everyone picked a red card. It is publicly announced that Steven does not know whether Steven picked a red card. It is publicly announced that Steven does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (1|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) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Leo can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Steven","Leo"],"index":42710,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994537234,"difficulty":0.0005462766}
{"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 Patricia. Jessie's card is shown to Jessie. Jessie's card is shown to Alicia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alicia can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Jessie","Alicia","Brian"],"index":67436,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993682504,"difficulty":0.0006317496}
{"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 Sheila. Sheila's card is shown to John. John's card is shown to John. John'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 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sheila can now know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sheila","John","Sharon"],"index":65684,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948921204,"difficulty":0.0051078796}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Idell. Idell's card is shown to Adam. Adam's card is shown to Adam. Lillian's card is shown to Adam. Idell's card is shown to Lillian. It is publicly announced that someone picked a red card. It is publicly announced that Lillian does not know whether or not everyone picked a red card. It is publicly announced that Adam knows whether Lillian 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) ] Agentb knows whether (Agentc knows whether 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":"Adam can now know whether Lillian can know whether Lillian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Idell","Adam","Lillian"],"index":64342,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9966391325,"difficulty":0.0033608675}
{"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 Karen. Mildred's card is shown to Mildred. Gary's card is shown to Mildred. Annie's card is shown to Annie. Karen's card is shown to Gary. Mildred'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 Annie picked a red card. It is publicly announced that Mildred picked a black card. It is publicly announced that Mildred knows whether Gary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Annie can now know that Karen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Mildred","Annie","Gary"],"index":62200,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990021586,"difficulty":0.0009978414}
{"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 David. Salvador's card is shown to Gregory. Jeannette's card is shown to Gregory. Jeannette's card is shown to Salvador. Gregory's card is shown to Jeannette. 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: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:2 Agentb:3,4 Agentc:4 Agentd:2 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":["David","Gregory","Salvador","Jeannette"],"index":39181,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960104227,"difficulty":0.0039895773}
{"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 Ruth. Gregory's card is shown to Ruth. Gregory's card is shown to Robert. Ruth's card is shown to Gregory. Ruth'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 Robert picked a red card. It is publicly announced that Stephanie does not know whether Stephanie picked a red card. It is publicly announced that Robert does not know whether Stephanie 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) ] Agentc knows whether (Agentb knows that (1|2|3|4))","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":"Gregory can now know whether Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Robert","Gregory","Stephanie"],"index":27023,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994286895,"difficulty":0.0005713105}
{"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 Doris. Doris's card is shown to Monica. Monica's card is shown to Thanh. It is publicly announced that someone picked a red card. It is publicly announced that Thanh knows whether Monica picked a red card. It is publicly announced that Monica does not know whether Thanh 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) ] (Agenta knows whether (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":"Doris can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Doris","Monica","Thanh"],"index":42718,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932987094,"difficulty":0.0067012906}
{"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 Lawrence. Stanley's card is shown to John. Jessica'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:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stanley can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Stanley","Jessica","John"],"index":23674,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971619844,"difficulty":0.0028380156}
{"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. Wanda's card is shown to Thomas. Wanda's card is shown to Anthony. Thomas'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 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Wanda can know whether Wanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Anthony","Wanda"],"index":34909,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5090569854,"difficulty":1.5090569854}
{"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. Terrance's card is shown to Terrance. Melissa's card is shown to Terrance. 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 Agentb:2,4 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:1 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rose can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Louis","Terrance","Rose","Melissa"],"index":60610,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989405274,"difficulty":0.0010594726}
{"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 Pam. Eileen's card is shown to Eileen. Derek's card is shown to Derek. 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) ] (Agentb knows whether (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":"Eileen can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pam","Eileen","Derek"],"index":64524,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943945408,"difficulty":0.0056054592}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barry's card is shown to Barry. Darren's card is shown to Darren. Darren's card is shown to Sherri. Sherri's card is shown to Sherri. It is publicly announced that someone picked a red card. It is publicly announced that Barry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Barry can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barry","Darren","Sherri"],"index":1635,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9503216743,"difficulty":0.0496783257}
{"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 Sandy. Travis's card is shown to Travis. Travis's card is shown to Jake. It is publicly announced that someone picked a red card. It is publicly announced that Travis does not know whether Maria picked a red card. It is publicly announced that Travis does not know whether Maria 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:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sandy can now know whether Sandy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Sandy","Travis","Jake"],"index":52461,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5903315544,"difficulty":0.4096684456}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mae's card is shown to Cora. Maritza's card is shown to Denise. Cora's card is shown to Maritza. Denise's card is shown to Maritza. Maritza's card is shown to Maritza. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cora can now know whether Mae can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mae","Cora","Denise","Maritza"],"index":34191,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9713780284,"difficulty":0.0286219716}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ana's card is shown to Mildred. Luke's card is shown to Paula. Paula'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:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know that Luke can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Luke","Ana","Paula"],"index":21042,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989681244,"difficulty":0.0010318756}
{"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 Robert. Brenda's card is shown to Brenda. Robert's card is shown to Catherine. Robert's card is shown to Margaret. 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 that (Agentd knows whether 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":"Robert can now know that Margaret can know whether Catherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Brenda","Catherine","Margaret"],"index":31178,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974889755,"difficulty":0.0025110245}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Margaret. Sally's card is shown to Teddy. Teddy's card is shown to Dawn. Dawn's card is shown to Dawn. Sally's card is shown to Dawn. Teddy's card is shown to Sally. 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) ] (Agentd 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":"Sally can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margaret","Teddy","Dawn","Sally"],"index":57207,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993181229,"difficulty":0.0006818771}
{"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 Kathleen. Alma's card is shown to Kathleen. Alma's card is shown to Jessie. Jessie's card is shown to Alma. Alma's card is shown to Alma. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen knows whether Jessie 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) ] (Agenta knows that 1)","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":"Kathleen can now know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Jessie","Alma"],"index":41757,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9843324423,"difficulty":0.0156675577}
{"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 Viola. Hyman's card is shown to Viola. Viola's card is shown to Mark. Mark's card is shown to Mark. Mark's card is shown to Hyman. 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 whether (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":"Mark can now know whether Hyman can know that Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Viola","Mark","Hyman"],"index":57861,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9263889194,"difficulty":0.0736110806}
{"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 Kenneth. Kenneth's card is shown to Maria. Maria's card is shown to Maria. Robert's card is shown to Maria. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know that Maria can know that Maria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Maria","Robert"],"index":29599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953502417,"difficulty":0.0046497583}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Jesus. Linda's card is shown to Ruth. Ruth'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:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Linda can now know whether Ruth can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jesus","Ruth","Linda"],"index":55120,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6252473593,"difficulty":0.3747526407}
{"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 Alex. Aurelia's card is shown to Alex. Carolyn's card is shown to Lois. Lois's card is shown to Lois. Carolyn's card is shown to Aurelia. 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 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:1,4 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lois can now know that Carolyn can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Alex","Lois","Aurelia"],"index":4140,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990178347,"difficulty":0.0009821653}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rafael's card is shown to Rafael. Gertrude's card is shown to Gertrude. Rafael's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Clarence does not know whether Clarence 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":"Gertrude can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rafael","Gertrude","Clarence"],"index":12084,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994488358,"difficulty":0.0005511642}
{"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 Hazel. Hazel's card is shown to Leon. Hazel's card is shown to Sheila. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Hazel can now know whether Hazel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hazel","Jennifer","Leon","Sheila"],"index":32053,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9017612338,"difficulty":1.9017612338}
{"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 Robert does not know whether Robert picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Robert picked a red card. It is publicly announced that Robert 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 that (Agentb knows that (~(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":"Raymond can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Raymond","Robert"],"index":38823,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987693429,"difficulty":0.0012306571}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Madge's card is shown to Madge. Erik's card is shown to Madge. Madge's card is shown to Barbara. Barbara's card is shown to Barbara. David's card is shown to Barbara. Erik's card is shown to Barbara. Madge's card is shown to David. Barbara's card is shown to Erik. 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 (Agentc knows that 3)","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":"Madge can now know that David can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Madge","Barbara","David","Erik"],"index":24240,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979656935,"difficulty":0.0020343065}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eda's card is shown to Eda. Joseph's card is shown to Eda. Jean's card is shown to Eda. Joseph's card is shown to Joseph. Jean's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Eda 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 1) ] (Agentc knows whether 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 1) ] 0","hypothesis":"Jean can now know whether Jean picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eda","Joseph","Jean"],"index":32012,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.831535697,"difficulty":0.168464303}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Ryan. Ryan's card is shown to Marla. Ryan's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marla can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","Marla","Elizabeth","Phillip"],"index":4829,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989702702,"difficulty":0.0010297298}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerri's card is shown to Linda. Linda's card is shown to Jerri. It is publicly announced that someone picked a red card. It is publicly announced that Linda 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)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Linda can now know that Jerri can know that Jerri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Linda","Jerri"],"index":10879,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.731734395,"difficulty":0.268265605}
{"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. Dianne's card is shown to David. Dianne's card is shown to Dianne. It is publicly announced that 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:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"David can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Dianne"],"index":14184,"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). Fred's card is shown to Barbara. Fred's card is shown to Fred. Fred's card is shown to Adam. 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 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 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fred can now know whether Barbara can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Barbara","Fred","Adam"],"index":43209,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9956308603,"difficulty":0.0043691397}
{"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 Sheila. Alexander's card is shown to Scott. Tony's card is shown to Scott. Tony's card is shown to Tony. It is publicly announced that someone picked a red card. It is publicly announced that Scott does not know whether Sheila picked a red card. It is publicly announced that Alexander does not know whether Sheila 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) ] (Agentb knows that 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":"Sheila can now know that Tony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alexander","Sheila","Scott","Tony"],"index":84,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9923651814,"difficulty":0.0076348186}
{"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. Mary's card is shown to Ruby. Ruby's card is shown to Ruby. Ruby's card is shown to Esther. Esther's card is shown to Esther. 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:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Ruby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Ruby","Robert","Esther"],"index":35712,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965118766,"difficulty":0.0034881234}
{"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 Cora. Kimberly's card is shown to Maria. Cora's card is shown to John. Kimberly's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberly can now know that Cora can know whether Kimberly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cora","Maria","Kimberly","John"],"index":20539,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7267801166,"difficulty":0.2732198834}
{"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. Edward's card is shown to Joseph. Alta's card is shown to Joseph. Joseph's card is shown to Edward. Patrica's card is shown to Patrica. Joseph's card is shown to Alta. Patrica's card is shown to Alta. 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:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Edward","Patrica","Alta"],"index":15124,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943777919,"difficulty":0.0056222081}
{"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 Ramona. Ramona's card is shown to Willie. Ramona's card is shown to Carol. Willie's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ramona can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ramona","Willie","Carol"],"index":9433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988974333,"difficulty":0.0011025667}
{"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 Anna. Armando's card is shown to Edwin. Edwin's card is shown to Armando. Armando's card is shown to Armando. 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) ] Agentc knows whether (Agenta knows whether 1)","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":"Armando can now know whether Anna can know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anna","Edwin","Armando"],"index":11939,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9975683093,"difficulty":0.0024316907}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joann's card is shown to Joann. Kim's card is shown to Kim. Kelly's card is shown to Kelly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 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:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joann can now know whether Heather can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","Joann","Kim","Kelly"],"index":45969,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994190931,"difficulty":0.0005809069}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Paul. Elaine's card is shown to Daniel. Paul's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Elaine does not know whether or not everyone picked a red card. It is publicly announced that Elaine 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:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (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":["Elaine","Paul","Daniel"],"index":18764,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985578656,"difficulty":0.0014421344}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Adelia's card is shown to Valerie. Valerie's card is shown to Tracy. Tracy's card is shown to Tracy. Adelia's card is shown to Tracy. Charles's card is shown to Tracy. Tracy's card is shown to Adelia. Charles's card is shown to Adelia. Valerie's card is shown to Charles. Adelia's card is shown to Charles. It is publicly announced that someone 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:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Valerie can now know that Tracy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Valerie","Tracy","Adelia","Charles"],"index":5532,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974105954,"difficulty":0.0025894046}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julio's card is shown to Joseph. Bob's card is shown to Bob. Bob's card is shown to Julio. It is publicly announced that someone picked a red card. It is publicly announced that Bob 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Julio can now know that Julio picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Bob","Julio"],"index":51857,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8208397627,"difficulty":0.1791602373}
{"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 Laura. Justin's card is shown to Justin. Justin's card is shown to Victor. Victor's card is shown to Victor. Victor'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:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Victor can now know that Victor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Justin","Victor","John"],"index":47055,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9861664772,"difficulty":0.0138335228}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Heather. Mary's card is shown to Albert. Virginia's card is shown to Virginia. Heather's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heather can now know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Heather","Albert","Virginia","Mary"],"index":36863,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995106101,"difficulty":0.004893899}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joel's card is shown to Tracy. Joel's card is shown to Mary. John's card is shown to John. Mary's card is shown to Joel. John's card is shown to Joel. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Mary picked a red card. It is publicly announced that Tracy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joel can now know whether John can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracy","Mary","John","Joel"],"index":5752,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994532466,"difficulty":0.0005467534}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dominick's card is shown to Dominick. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether 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&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mary can now know whether Dominick can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dominick","Mary"],"index":27027,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994437099,"difficulty":0.0005562901}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marguerite's card is shown to Marguerite. Glenna's card is shown to Marguerite. Marguerite's card is shown to Thomas. Thomas's card is shown to Thomas. Anita's card is shown to Anita. Marguerite's card is shown to Glenna. Thomas's card is shown to Glenna. 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 Agentc:3 Agentd:1,2 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 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marguerite can now know that Glenna can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marguerite","Thomas","Anita","Glenna"],"index":23454,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993963242,"difficulty":0.0006036758}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Dorothy. Michelle's card is shown to Francis. Francis's card is shown to Michelle. 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 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":"Dorothy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Francis","Michelle"],"index":1307,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989784956,"difficulty":0.0010215044}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roberta's card is shown to Dorothy. John's card is shown to Dorothy. Dorothy's card is shown to James. Dorothy'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:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know whether Roberta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roberta","Dorothy","James","John"],"index":34783,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9938957095,"difficulty":0.0061042905}
{"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. Sonia's card is shown to Sonia. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Theodore does not know whether Kenneth 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 Sonia does not know whether Kenneth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Theodore can now know whether Kenneth can know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Theodore","Sonia","Kenneth"],"index":11577,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973521233,"difficulty":0.0026478767}
{"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 Jerry. David's card is shown to David. James's card is shown to David. Jerry's card is shown to James. David's card is shown to James. James's card is shown to James. David'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:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 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:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that George can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","David","James","George"],"index":17476,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992811084,"difficulty":0.0007188916}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Shirley. David's card is shown to Shirley. David'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 David 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)) ] (Agentb knows that 2)","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":"David can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shirley","David","Margaret"],"index":59929,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7794524431,"difficulty":1.7794524431}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Inez's card is shown to Inez. Inez's card is shown to James. James's card is shown to James. Inez's card is shown to Logan. Logan's card is shown to Logan. It is publicly announced that someone picked a red card. It is publicly announced that Inez does not know whether Logan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Roberta can now know whether Logan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Inez","James","Roberta","Logan"],"index":9926,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9370428324,"difficulty":0.0629571676}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Everett's card is shown to Dolores. Joe's card is shown to Dolores. Dolores's card is shown to Lori. Dolores's card is shown to Joe. Joe's card is shown to Joe. 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 (1&2&3&4))","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":"Everett can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Everett","Dolores","Lori","Joe"],"index":40356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989921451,"difficulty":0.0010078549}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francisco's card is shown to Francisco. Francisco's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether William 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 (Agenta knows whether 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":"William can now know whether Francisco can know whether Francisco picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Francisco","William"],"index":66029,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985855818,"difficulty":0.0014144182}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joey's card is shown to Joey. Joey's card is shown to Thomas. Dorian's card is shown to Thomas. Dorian's card is shown to Dorian. Thomas's card is shown to Ralph. Ralph's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Ralph does not know whether Dorian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Joey can now know whether Dorian can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joey","Thomas","Dorian","Ralph"],"index":34591,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9455100894,"difficulty":0.0544899106}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmel's card is shown to Carmel. Jonathon's card is shown to Carmel. Carmel's card is shown to Jonathon. Jonathon's card is shown to Jonathon. 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) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Jonathon can now know whether Carmel can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carmel","Jonathon"],"index":17522,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999407053,"difficulty":0.000592947}
{"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. Mark's card is shown to Mark. Michael's card is shown to Mark. Virginia's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Carol picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mark can now know that Michael can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Mark","Michael","Virginia"],"index":58294,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7185395956,"difficulty":0.2814604044}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Kenneth. Jack's card is shown to Jack. Anastasia's card is shown to Anastasia. 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:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carolee can now know whether Anastasia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Carolee","Jack","Anastasia"],"index":51852,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7052266598,"difficulty":1.7052266598}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cortney's card is shown to Cortney. Dorothy's card is shown to Cortney. Nicholas's card is shown to Dorothy. Nicholas's card is shown to Nicholas. 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:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 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":["Cortney","Dorothy","Nicholas","Charles"],"index":9512,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989973903,"difficulty":0.0010026097}
{"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. Fred's card is shown to Steven. Daisy's card is shown to Steven. Daisy's card is shown to Frank. Steven's card is shown to Daisy. Fred's card is shown to Daisy. 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:4 Agentc: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:1,2,4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know that Frank can know that Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Fred","Frank","Daisy"],"index":38225,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982424974,"difficulty":0.0017575026}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elisa's card is shown to Elisa. Dean's card is shown to Elisa. Dean's card is shown to Dean. It is publicly announced that someone picked a red card. It is publicly announced that Dean knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Dean can now know that Elisa can know that Elisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elisa","Dean"],"index":40601,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8022732735,"difficulty":1.8022732735}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annett's card is shown to Belinda. Annett's card is shown to Annett. It is publicly announced that someone picked a red card. It is publicly announced that Belinda does not know whether Belinda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 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) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Annett can now know whether Belinda can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Belinda","Annett"],"index":5134,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999430716,"difficulty":0.000569284}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terina's card is shown to Marylou. Bethann's card is shown to Bethann. Marylou's card is shown to Terina. Terina's card is shown to Terina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 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:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terina can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marylou","Bethann","Terina"],"index":45253,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989533424,"difficulty":0.0010466576}
{"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 James. Stanley's card is shown to James. James's card is shown to Stanley. Stanley's card is shown to Stanley. 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 not everyone 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))) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"James can now know whether Stanley can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Stanley"],"index":4704,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999407649,"difficulty":0.000592351}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Jerome. Doreen's card is shown to Louis. Louis's card is shown to George. Louis's card is shown to Doreen. Doreen's card is shown to Doreen. 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 Agentd:2,4 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:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doreen can now know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jerome","Louis","George","Doreen"],"index":28536,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5427087545,"difficulty":1.5427087545}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brett's card is shown to Brett. Nicole's card is shown to Nicole. Ruby's card is shown to Nicole. Ruby's card is shown to Ruby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","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":"Ruby can now know whether Brett picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brett","Nicole","Ruby"],"index":26645,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9867998362,"difficulty":0.0132001638}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Susan. Cindy's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Susan 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 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":"Cindy can now know that Cindy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Susan","Cindy"],"index":15192,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.959964633,"difficulty":0.040035367}
{"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 Leanne. Leanne's card is shown to Patricia. Leanne's card is shown to David. Leanne's card is shown to Suzanne. Suzanne's card is shown to Suzanne. It is publicly announced that someone picked a red card. It is publicly announced that Leanne does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Patricia can now know that Suzanne can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leanne","Patricia","David","Suzanne"],"index":17497,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994174242,"difficulty":0.0005825758}
{"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 Anna. Catherine's card is shown to Gregory. Gregory's card is shown to Lorraine. Anna's card is shown to Catherine. 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 Gregory picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Anna can now know whether Catherine can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anna","Gregory","Lorraine","Catherine"],"index":17893,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8195930123,"difficulty":0.1804069877}
{"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 Lavern. Carla's card is shown to Lavern. James's card is shown to James. Lavern's card is shown to Carla. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 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:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lavern can now know whether Carla picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lavern","James","Carla"],"index":42479,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5874456167,"difficulty":1.5874456167}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beckie's card is shown to Lisa. Lisa's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rachel can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rachel","Beckie","Lisa"],"index":49314,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989847541,"difficulty":0.0010152459}
{"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 Lisa. Lisa's card is shown to Lisa. 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. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Lisa","Annabelle"],"index":11644,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
{"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 Eileen. Jack's card is shown to Valerie. Jack's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Valerie does not know whether Valerie picked a red card. It is publicly announced that Eileen does not know whether Jack picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 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:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jack can now know whether Valerie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eileen","Jack","Valerie","Robert"],"index":31462,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992171526,"difficulty":0.0007828474}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Evelyn. Evelyn's card is shown to Philip. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn knows whether Evelyn picked a red card. It is publicly announced that Evelyn knows whether Philip 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) ] (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 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Evelyn can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Evelyn","Philip"],"index":5858,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994365573,"difficulty":0.0005634427}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felicia's card is shown to Mary. Jean's card is shown to Jean. Ruben's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Felicia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know that Felicia can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Felicia","Mary","Jean","Ruben"],"index":20247,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.871368885,"difficulty":0.128631115}
{"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 Caryl. Richard's card is shown to Joanna. Cecilia's card is shown to Joanna. Caryl's card is shown to Cecilia. Joanna's card is shown to Cecilia. 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 that (Agentc knows that 3)","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":"Richard can now know that Joanna can know that Joanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Caryl","Richard","Joanna","Cecilia"],"index":9219,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977235198,"difficulty":0.0022764802}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenny's card is shown to Michael. Frederick's card is shown to Frederick. Michael's card is shown to Jenny. It is publicly announced that someone picked a red card. It is publicly announced that Jenny does not know whether Frederick 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 whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Michael can now know that Frederick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Frederick","Jenny"],"index":53372,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959775805,"difficulty":0.0040224195}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Israel's card is shown to Natalie. Israel's card is shown to Israel. Dolores's card is shown to Israel. Edith's card is shown to Israel. Israel's card is shown to Edith. Edith's card is shown to Edith. It is publicly announced that someone picked a red card. It is publicly announced that Natalie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Natalie can now know that Israel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Natalie","Israel","Dolores","Edith"],"index":9395,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8370681405,"difficulty":1.8370681405}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aubrey's card is shown to Paula. Robert's card is shown to Brenda. Paula'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:3 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:4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paula","Brenda","Robert","Aubrey"],"index":28986,"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). Lizette's card is shown to Lizette. Alvin's card is shown to Lizette. Lizette's card is shown to Max. Alvin's card is shown to Max. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 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:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alvin can now know that Lizette can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lizette","Alvin","Max"],"index":32038,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994124174,"difficulty":0.0005875826}
{"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. Wendy's card is shown to Eric. Arturo's card is shown to Beatrice. Eric's card is shown to Wendy. It is publicly announced that someone picked a red card. It is publicly announced that Arturo 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:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Wendy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arturo","Eric","Beatrice","Wendy"],"index":19832,"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). Linda's card is shown to Linda. Mildred'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 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Mildred","Sharon","Steve"],"index":57107,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.97356987,"difficulty":0.02643013}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Herbert. Ruth's card is shown to Ruth. Robert's card is shown to Ruth. Herbert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether Herbert picked a red card. It is publicly announced that Ruth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ruth can now know whether Herbert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Herbert","Ruth","Robert"],"index":22495,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7788379192,"difficulty":1.7788379192}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maggie's card is shown to Richard. 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 that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] [ ! (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","Patricia","Maggie"],"index":17178,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993273139,"difficulty":0.006726861}
{"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. Priscilla's card is shown to Priscilla. Leah's card is shown to Elizabeth. Priscilla'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 Leah does not know whether or not everyone picked a red card. It is publicly announced that Priscilla knows whether Priscilla picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Priscilla can now know whether Leah can know whether Priscilla picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leah","Priscilla","Elizabeth"],"index":65363,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980395436,"difficulty":0.0019604564}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Selma's card is shown to Heather. Lisa's card is shown to Lisa. Nora's card is shown to Lisa. Nora's card is shown to Selma. Heather's card is shown to Nora. Lisa's card is shown to Nora. Selma's card is shown to Nora. 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 that (Agentb knows that (1|2|3|4))","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":"Nora can now know that Lisa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","Lisa","Selma","Nora"],"index":22310,"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). Carole's card is shown to Wesley. Carole's card is shown to Carole. Joseph's card is shown to Carole. Wesley's card is shown to Joshua. Carole's card is shown to Joshua. Wesley's card is shown to Joseph. Joshua's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Wesley does not know whether Joshua picked a red card. It is publicly announced that Wesley knows whether Carole picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Carole can now know that Joseph can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wesley","Carole","Joshua","Joseph"],"index":19950,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994284511,"difficulty":0.0005715489}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to Rhonda. Lonnie's card is shown to Rhonda. Rhonda's card is shown to Michael. Michael's card is shown to Michael. Lonnie's card is shown to Michael. William's card is shown to Michael. Michael's card is shown to Lonnie. William's card is shown to Lonnie. Rhonda's card is shown to William. Lonnie'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 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether Lonnie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rhonda","Michael","Lonnie","William"],"index":35153,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994223118,"difficulty":0.0005776882}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamala's card is shown to Jorge. Jorge's card is shown to Jorge. 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:1,2 VALID? [ ! (1|2|3) ] [ ! (~(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 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Pamala can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pamala","Jorge","Luanne"],"index":52393,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994106293,"difficulty":0.0005893707}
{"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 Linda. Shane's card is shown to Shane. It is publicly announced that someone picked a red card. It is publicly announced that Shane does not know whether Linda picked a red card. It is publicly announced that Linda 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 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Shane can now know that Linda can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Linda","Shane"],"index":36203,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.500010252,"difficulty":0.499989748}
{"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 Stephen. Margaret's card is shown to Margaret. Maria's card is shown to Margaret. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Robert picked a red card. It is publicly announced that Stephen does not know whether Margaret picked a red card. It is publicly announced that Maria does not know whether or not everyone picked a red card. It is publicly announced that Margaret does not know whether Robert 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 that 2)","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":"Margaret can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Margaret","Maria","Robert"],"index":36571,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.798142612,"difficulty":0.201857388}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Opal. Ruth's card is shown to Ruth. Kelly's card is shown to Ruth. Opal's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Opal does not know whether Opal picked a red card. It is publicly announced that Ruth picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Ruth can now know that Kelly can know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Opal","Ruth","Kelly"],"index":4717,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9564827085,"difficulty":0.0435172915}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reginald's card is shown to Reginald. Melissa's card is shown to Reginald. Melissa's card is shown to Melissa. Naomi's card is shown to Melissa. Alane's card is shown to Naomi. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Reginald can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alane","Reginald","Melissa","Naomi"],"index":64330,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990133047,"difficulty":0.0009866953}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Melvin. Leo's card is shown to Leo. It is publicly announced that someone picked a red card. It is publicly announced that Leo knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Melvin can now know that Leo can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melvin","Leo"],"index":35229,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994124174,"difficulty":0.0005875826}
{"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 Derrick. Myles's card is shown to Derrick. Mark's card is shown to Mark. Derrick's card is shown to Myles. It is publicly announced that someone picked a red card. It is publicly announced that Derrick 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":"Mark can now know that Myles can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Derrick","Mark","Myles"],"index":4163,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994258881,"difficulty":0.0005741119}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Neal's card is shown to Lisa. Lisa's card is shown to Neal. Lisa's card is shown to Timothy. Neal'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: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":"Lisa can now know whether Timothy can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Neal","Timothy"],"index":51757,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992384911,"difficulty":0.0007615089}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tameka's card is shown to Marvin. Marvin's card is shown to Ryan. Tameka's card is shown to Ryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marvin can now know whether Ryan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marvin","Ryan","Tameka"],"index":26910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974666834,"difficulty":0.0025333166}
{"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 Catherine. Humberto's card is shown to Humberto. Catherine's card is shown to Rosemary. Humberto's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Catherine does not know whether Humberto picked a red card. It is publicly announced that Lawrence knows whether Humberto picked a red card. It is publicly announced that Catherine does not know whether Rosemary picked a red card. It is publicly announced that Humberto 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)) ] Agentc knows whether (Agentd knows that 1)","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":"Rosemary can now know whether Lawrence can know that Catherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Catherine","Humberto","Rosemary","Lawrence"],"index":2856,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9270514846,"difficulty":0.0729485154}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Christine. Shannon's card is shown to Lawrence. Vanessa's card is shown to Vanessa. Lawrence's card is shown to Shannon. Vanessa's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Vanessa does not know whether Lawrence picked a red card. It is publicly announced that Christine knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Shannon can now know that Lawrence can know that Vanessa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Lawrence","Vanessa","Shannon"],"index":35551,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9258621931,"difficulty":0.0741378069}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Cathy. Terri's card is shown to Terri. Cathy's card is shown to Kathleen. Kathleen's card is shown to Kathleen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathleen can now know whether Terri picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cathy","Terri","Kathleen"],"index":26847,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.964158833,"difficulty":0.035841167}
{"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 Karen. Richard's card is shown to Karen. Robin's card is shown to Robin. Kareem's card is shown to Robin. Richard's card is shown to Robin. Robin's card is shown to Kareem. Robin's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Kareem knows whether Robin picked a red card. It is publicly announced that Richard does not know whether Karen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Richard can now know that Karen can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Robin","Kareem","Richard"],"index":66983,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994163513,"difficulty":0.0005836487}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. Frank's card is shown to Victor. Victor's card is shown to Victor. Frank's card is shown to Rebecca. Rebecca's card is shown to Rebecca. It is publicly announced that someone picked a red card. It is publicly announced that Victor knows whether Frank picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Frank can now know whether Victor can know whether Rebecca picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frank","Victor","Rebecca"],"index":46798,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9988797307,"difficulty":1.9988797307}
{"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. James's card is shown to Gerald. 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 Gerald 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 James 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Gerald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gerald","James"],"index":62392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990500808,"difficulty":0.0009499192}
{"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 Fred. Fred's card is shown to Brenda. Brenda's card is shown to Brenda. Fred's card is shown to Larisa. Brenda's card is shown to Larisa. Fred'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 Brenda picked a black card. It is publicly announced that Brenda does not know whether Robert 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)) ] Agentb knows whether (Agentc knows that 1)","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":"Brenda can now know whether Larisa can know that Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fred","Brenda","Larisa","Robert"],"index":55148,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9379214644,"difficulty":0.0620785356}
{"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. Georgene's card is shown to Mary. Mary's card is shown to Georgene. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Benito 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) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Benito can now know that William can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Mary","Benito","Georgene"],"index":42021,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993304014,"difficulty":0.0006695986}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Bonnie. Carolyn's card is shown to Bonnie. Bonnie's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Terry's card is shown to Carolyn. Carolyn's card is shown to Terry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bonnie can now know whether Carolyn can know whether Bonnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Carolyn","Terry"],"index":6842,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980845451,"difficulty":0.0019154549}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Patrick. Wayne's card is shown to Wayne. It is publicly announced that someone picked a red card. It is publicly announced that Patrick 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 (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Wayne can now know whether Patrick can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patrick","Wayne"],"index":17984,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993970394,"difficulty":0.0006029606}
{"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. Beatrice's card is shown to Desmond. Beatrice's card is shown to Beatrice. Georgia's card is shown to Beatrice. Desmond's card is shown to Georgia. It is publicly announced that someone picked a red card. It is publicly announced that Desmond knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Georgia can now know that Beatrice can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Desmond","Beatrice","Georgia"],"index":35202,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993917942,"difficulty":0.0006082058}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carlos's card is shown to Dale. Carlos's card is shown to Carlos. It is publicly announced that someone picked a red card. It is publicly announced that Dale 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)) ] (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":"Dale can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dale","Carlos"],"index":29762,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989540577,"difficulty":0.0010459423}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonio's card is shown to Antonio. Antonio'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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Antonio can now know that Anne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Antonio","Werner","William","Anne"],"index":6120,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965482354,"difficulty":0.0034517646}
{"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. Catherine's card is shown to Catherine. 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:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether Catherine can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Catherine","Flora"],"index":43192,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994545579,"difficulty":0.0005454421}
{"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 Lisa. Carolyn's card is shown to Doris. Carolyn's card is shown to Carolyn. Lisa's card is shown to Anne. 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 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doris can now know whether Carolyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Doris","Carolyn","Anne"],"index":21319,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8173213601,"difficulty":1.8173213601}
{"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 Carolyn. Rita's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows 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":"Carolyn can now know whether Rita can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Rita","Carol"],"index":51301,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991974235,"difficulty":0.0008025765}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keely's card is shown to Lucille. Lucille's card is shown to Keely. It is publicly announced that someone picked a red card. It is publicly announced that Keely does not know whether Keely picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lucille can now know whether Keely can know whether Keely picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lucille","Keely"],"index":36769,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9957619309,"difficulty":0.0042380691}
{"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 Maria. Kenneth's card is shown to Maria. Maria's card is shown to Kenneth. Kelly's card is shown to Kenneth. Maria'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:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maria","Kenneth","Kelly"],"index":26753,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993299246,"difficulty":0.0006700754}
{"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. Reba's card is shown to Joseph. Joseph's card is shown to Joyce. Joyce's card is shown to Reba. 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:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joyce can now know that Joseph can know whether Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Joyce","Reba"],"index":24695,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.716406405,"difficulty":0.283593595}
{"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 Maria. Samantha's card is shown to Ruth. Robin's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Ruth picked a red card. It is publicly announced that Robin picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(4) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Samantha can now know that Robin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Samantha","Maria","Ruth","Robin"],"index":51167,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8380479813,"difficulty":0.1619520187}
{"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 Larry. Yvonne's card is shown to Vernon. Larry's card is shown to Graham. Graham's card is shown to Graham. 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:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vernon can now know that Graham picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Vernon","Graham","Yvonne"],"index":23346,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996437788,"difficulty":0.003562212}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Alan's card is shown to Barbara. Christopher'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:1,3 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Christopher can know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Christopher","Alan"],"index":51351,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973517656,"difficulty":0.0026482344}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eleanor's card is shown to George. Eleanor's card is shown to Carl. Wanda's card is shown to Carl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know that Eleanor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eleanor","George","Carl","Wanda"],"index":56139,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968955517,"difficulty":0.0031044483}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alfred's card is shown to Alfred. Alfred's card is shown to Jason. 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)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Jason can now know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alfred","Jason"],"index":33984,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5581549406,"difficulty":0.4418450594}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Richard. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 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:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Richard can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Richard","Donald"],"index":46419,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9865002036,"difficulty":0.0134997964}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henrietta's card is shown to Anna. Henrietta's card is shown to Kenneth. Anna's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Anna knows whether Henrietta picked a red card. It is publicly announced that Anna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Henrietta can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Henrietta","Anna","Kenneth"],"index":43982,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990025163,"difficulty":0.0009974837}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tammy's card is shown to Betsy. Heather's card is shown to Betsy. Tammy's card is shown to Tammy. Heather's card is shown to Tammy. Betsy's card is shown to Mary. Mary's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Betsy can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betsy","Tammy","Mary","Heather"],"index":14235,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991868138,"difficulty":0.0008131862}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Derek. Douglas's card is shown to Samantha. Samantha's card is shown to Samantha. Derek's card is shown to Brenna. It is publicly announced that someone picked a red card. It is publicly announced that Samantha picked a black card. 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:1 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Derek","Douglas","Samantha","Brenna"],"index":10802,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6861740947,"difficulty":0.3138259053}
{"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 Betty. Betty's card is shown to Geneva. Geneva's card is shown to Geneva. Betty's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether Betty 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:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Betty can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Geneva","Jennifer"],"index":29000,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9911541939,"difficulty":0.0088458061}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Alice. Alice's card is shown to Evelyn. Evelyn'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:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alice can now know that Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alice","Evelyn","Eric"],"index":62149,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932444692,"difficulty":0.0067555308}
{"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. Mary's card is shown to Geraldine. Geraldine's card is shown to Mary. Mary's card is shown to Mary. David's card is shown to Mary. Mary'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 Agentb:1,2,3 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:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Geraldine","Mary","David"],"index":24343,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993997812,"difficulty":0.0006002188}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Maribel. Patricia's card is shown to Laura. Maribel's card is shown to Patricia. Maribel's card is shown to Tobias. Laura's card is shown to Tobias. Patricia's card is shown to Tobias. It is publicly announced that someone picked a red card. It is publicly announced that Tobias knows whether Laura picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Laura can now know whether Tobias can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maribel","Laura","Patricia","Tobias"],"index":19510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5538856387,"difficulty":0.4461143613}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Kimberly. Johnnie's card is shown to Johnnie. It is publicly announced that someone picked a red card. It is publicly announced that Johnnie does not know whether Kimberly 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&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kimberly can now know whether Johnnie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kimberly","Johnnie"],"index":31707,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9520741105,"difficulty":1.9520741105}
{"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 Alfred. Alfred's card is shown to Alfred. Alfred's card is shown to Dawn. Hazel'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 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alfred can now know that Hazel can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bobby","Alfred","Hazel","Dawn"],"index":59273,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988133907,"difficulty":0.0011866093}
{"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 Marvin. Jae's card is shown to Kathleen. Kathleen's card is shown to Jae. Jae's card is shown to Jae. 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 that 2)","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":"Kathleen can now know whether Jae can know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marvin","Kathleen","Jae"],"index":37601,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6700843573,"difficulty":1.6700843573}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodora's card is shown to Lucille. Lucille's card is shown to Theodora. It is publicly announced that someone picked a red card. It is publicly announced that Lucille does not know whether Susan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Susan can now know that Theodora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lucille","Susan","Theodora"],"index":2184,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971290231,"difficulty":0.0028709769}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Homer's card is shown to Kelley. Homer's card is shown to Homer. John's card is shown to John. Homer'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 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Linda can know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelley","Homer","John","Linda"],"index":42753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8450784683,"difficulty":0.1549215317}
{"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 Sarah. Jane's card is shown to Jane. John's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Sarah does not know whether Jane picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Sarah can now know whether Jane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Jane","John"],"index":63131,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9358451366,"difficulty":1.9358451366}
{"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 Ellen. Elisa's card is shown to Perry. Jennifer's card is shown to Elisa. Ellen's card is shown to Jennifer. Elisa's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Perry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 4)","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":"Ellen can now know that Perry can know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ellen","Perry","Elisa","Jennifer"],"index":31539,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5250677466,"difficulty":0.4749322534}
{"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. Gina's card is shown to Gina. Mattie's card is shown to Frances. Cynthia's card is shown to Frances. Gina's card is shown to Frances. 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:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mattie can now know that Cynthia can know that Frances picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mattie","Cynthia","Gina","Frances"],"index":33308,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982476234,"difficulty":0.0017523766}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Daniel. Daniel's card is shown to Lora. Daniel's card is shown to Anne. It is publicly announced that someone picked a red card. It is publicly announced that Lora does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know that Anne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","Lora","Anne"],"index":1642,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8055976629,"difficulty":0.1944023371}
{"premise":"There are four 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 Charles. Joe's card is shown to Anthony. Charles's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether Anthony picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Anthony can now know whether Charles can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Charles","Anthony","Michael"],"index":52824,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5101395249,"difficulty":1.5101395249}
{"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 Marie. Mark's card is shown to Diane. Marie's card is shown to Mark. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marie","Diane","Mark"],"index":7223,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994501472,"difficulty":0.0005498528}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tonya's card is shown to Janet. Jill's card is shown to Jill. Tonya's card is shown to Jill. Tonya's card is shown to Tonya. 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) ] Agentb knows that (Agenta knows whether 3)","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":"Jill can now know that Janet can know whether Tonya picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janet","Jill","Tonya"],"index":19456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6526976824,"difficulty":0.3473023176}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernice's card is shown to Wilson. William's card is shown to Wilson. Wilson's card is shown to Bernice. Wilson's card is shown to William. Bernice's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Bernice does not know whether Bernice 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) ] (Agentc knows that 3)","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":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wilson","Bernice","William","Dorothy"],"index":8766,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944403768,"difficulty":0.0055596232}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Shawna. Angela's card is shown to Jeffrey. Louis's card is shown to Angela. Jeffrey's card is shown to Angela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shawna can now know that Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shawna","Louis","Jeffrey","Angela"],"index":58990,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953477979,"difficulty":0.0046522021}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Lawrence. Joyce's card is shown to Lawrence. Tom's card is shown to Matthew. Matthew's card is shown to Matthew. Joyce's card is shown to Matthew. Lawrence's card is shown to Joyce. Tom's card is shown to Joyce. Joyce's card is shown to Joyce. It is publicly announced that someone picked a red card. It is publicly announced that Matthew 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 that 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":"Matthew can now know whether Tom can know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Tom","Matthew","Joyce"],"index":56358,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9577063918,"difficulty":0.0422936082}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Courtney's card is shown to Neal. Neal's card is shown to Courtney. It is publicly announced that someone picked a red card. It is publicly announced that Courtney does not know whether or not everyone picked a red card. It is publicly announced that Neal knows whether Neal picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Courtney can now know that Neal can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Neal","Courtney"],"index":30016,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971336126,"difficulty":0.0028663874}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Julie. Ana's card is shown to Julie. Kim's card is shown to Kim. Julie's card is shown to Jesus. Ana's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Julie does not know whether or not everyone picked a red card. It is publicly announced that Ana does not know whether Jesus picked a red card. It is publicly announced that Ana does not know whether Jesus 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:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Julie can now know that Ana can know whether Jesus picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Kim","Ana","Jesus"],"index":48812,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9001788497,"difficulty":1.9001788497}
{"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 John. Francisco's card is shown to Stephani. Jane's card is shown to Stephani. Jane's card is shown to Francisco. John's card is shown to Jane. Stephani's card is shown to Jane. Francisco'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:3,4 Agentc:4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Stephani","Francisco","Jane"],"index":50990,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993959665,"difficulty":0.0006040335}
{"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. Rodolfo's card is shown to William. William's card is shown to Roy. Roy's card is shown to Roy. Roy's card is shown to Timothy. Roy's card is shown to Rodolfo. Timothy's card is shown to Rodolfo. 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:1,4 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Timothy can now know whether Rodolfo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Roy","Timothy","Rodolfo"],"index":17600,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9835631847,"difficulty":1.9835631847}
{"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 Dorian. Nick's card is shown to Dorian. Kevin's card is shown to Kevin. Nick's card is shown to Kevin. Dorian's card is shown to Josie. Josie's card is shown to Nick. Nick's card is shown to Nick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Josie can now know whether Nick can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorian","Kevin","Josie","Nick"],"index":21297,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993915558,"difficulty":0.0006084442}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Nicholas. Thomas's card is shown to Nicholas. It is publicly announced that someone picked a red card. It is publicly announced that Nicholas does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Nicholas can now know that Nicholas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nicholas","Wanda","Thomas"],"index":2293,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7230338454,"difficulty":0.2769661546}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cordell's card is shown to Cordell. David's card is shown to David. Cordell's card is shown to Michelle. 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) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know that Michelle can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cordell","David","Michelle"],"index":59910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947249293,"difficulty":0.0052750707}
{"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. Katie's card is shown to David. 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:1,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","James","Katie"],"index":26445,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990180731,"difficulty":0.0009819269}
{"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. Bennett's card is shown to Martin. Luis's card is shown to Martin. Luis's card is shown to Bennett. Luis's card is shown to Luis. 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) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Luis can now know that Bennett can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martin","Bennett","Luis"],"index":53910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993878603,"difficulty":0.0006121397}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Melissa'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 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"David can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Melissa","David"],"index":30407,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7819077373,"difficulty":0.2180922627}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dora's card is shown to Regina. John's card is shown to John. Andy's card is shown to John. Andy's card is shown to Andy. Dora's card is shown to Andy. It is publicly announced that someone picked a red card. It is publicly announced that Andy picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Andy can now know whether Andy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Regina","John","Andy","Dora"],"index":31927,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.978679359,"difficulty":0.021320641}
{"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. James's card is shown to Brenda. Brenda's card is shown to Louis. Louis's card is shown to Delbert. Delbert's card is shown to Delbert. 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) ] (Agenta 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":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Brenda","Louis","Delbert"],"index":28597,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9876616001,"difficulty":0.0123383999}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Franklin's card is shown to Henry. Henry's card is shown to Franklin. Franklin's card is shown to Franklin. Franklin's card is shown to Roger. Roger's card is shown to Roger. 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:2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Roger can now know whether Henry can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Henry","Franklin","Roger"],"index":65774,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994169474,"difficulty":0.0005830526}
{"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 Kathryn. William's card is shown to Kathryn. Robert's card is shown to Robert. Kathryn's card is shown to William. William's card is shown to William. William'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:2 Agentc:1,3 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:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kathryn can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathryn","Robert","William","Anthony"],"index":59197,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968473315,"difficulty":0.0031526685}
{"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 Harris. Amy's card is shown to Lazaro. Lazaro's card is shown to Lazaro. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 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:1 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Harris can now know that Amy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amy","Harris","Lazaro"],"index":1669,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988449812,"difficulty":0.0011550188}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dana's card is shown to James. Erica's card is shown to James. James's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 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:2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dana can now know that James can know whether Dana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Dana","Erica","John"],"index":33076,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9855415225,"difficulty":1.9855415225}
{"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. Helen's card is shown to Alice. Thomas's card is shown to Helen. Helen's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Helen 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:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Thomas can now know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Alice","Helen"],"index":17321,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8251351118,"difficulty":0.1748648882}
{"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 Jason. Donna's card is shown to Donna. Alan's card is shown to Donna. Jason's card is shown to Alan. Donna's card is shown to Alan. Alan's card is shown to Alan. It is publicly announced that someone picked a red card. It is publicly announced that Donna picked a red card. It is publicly announced that Donna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Alan can now know whether Donna can know that Alan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Donna","Alan"],"index":5236,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9200292826,"difficulty":0.0799707174}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Kellee. David's card is shown to Johnny. Johnny'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:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kellee can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Kellee","Johnny","Nancy"],"index":48115,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959152341,"difficulty":0.0040847659}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Terrell. Terrell's card is shown to Christi. Christi'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:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terrell can now know that Christi can know whether Christi picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Terrell","Christi","Daniel"],"index":21059,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.605471015,"difficulty":1.605471015}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jan's card is shown to Aaron. Aaron's card is shown to Jan. Crystal's card is shown to Jan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","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":"Jan can now know whether Aaron picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Aaron","Jan","Shelby","Crystal"],"index":64458,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9470906258,"difficulty":1.9470906258}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Latoya's card is shown to Peggy. Peggy's card is shown to Latoya. It is publicly announced that someone picked a red card. It is publicly announced that Alan does not know whether Peggy picked a red card. It is publicly announced that Alan does not know whether Alan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Alan can now know whether Peggy can know whether Latoya picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alan","Peggy","Latoya"],"index":40785,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983750582,"difficulty":0.0016249418}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luz's card is shown to Teresa. Carlos's card is shown to Teresa. Carlos's card is shown to Luz. Teresa's card is shown to Emanuel. Carlos's card is shown to Carlos. 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)","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":"Teresa can now know whether Teresa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Teresa","Luz","Emanuel","Carlos"],"index":61200,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8446986675,"difficulty":1.8446986675}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pablo's card is shown to Pablo. It is publicly announced that someone picked a red card. It is publicly announced that Pablo does not know whether Andrew picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Pablo can now know whether Pablo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pablo","Kathie","Andrew"],"index":7249,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6888724566,"difficulty":0.3111275434}
{"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 James. James's card is shown to Pamela. Pamela's card is shown to Pamela. 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) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"James can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Pamela"],"index":25072,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.593955636,"difficulty":1.593955636}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jasmine's card is shown to Jasmine. Inez's card is shown to Jasmine. Jasmine's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria knows whether or not nobody 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 whether (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":"Maria can now know that Jasmine can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jasmine","Maria","Inez"],"index":2533,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994077682,"difficulty":0.0005922318}
{"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 Samuel. Samuel's card is shown to Lester. Lee'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:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lee can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lee","Samuel","Lester","James"],"index":33774,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960536957,"difficulty":0.0039463043}
{"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 Melvin. Melvin'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 Melvin knows whether or not everyone picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Mary can now know whether Melvin can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melvin","Mary"],"index":5244,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998559773,"difficulty":0.001440227}
{"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 John. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"John can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Barbara"],"index":20144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994794726,"difficulty":0.0005205274}
{"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 Victor. Ines's card is shown to Victor. Mary's card is shown to Mary. Steven's card is shown to Mary. Victor's card is shown to Ines. Ines's card is shown to Ines. Victor's card is shown to Steven. Ines's card is shown to Steven. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Ines 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) ] Agenta knows that (Agentc 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":"Victor can now know that Ines can know that Victor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victor","Mary","Ines","Steven"],"index":5403,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955675006,"difficulty":0.0044324994}
{"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. Angel's card is shown to Angel. 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 that (Agenta 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":"Angel can now know that James can know whether Cindy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Angel","Cindy"],"index":992,"s-l":"explicit-0","deberta_pred":0,"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). Robert's card is shown to Geraldine. Geraldine's card is shown to German. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Geraldine picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know whether Geraldine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geraldine","German","Robert"],"index":47884,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9918688536,"difficulty":0.0081311464}
{"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 Natasha. Joyce's card is shown to Arthur. Suzanne's card is shown to Arthur. Natasha's card is shown to Joyce. 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. It is publicly announced that Joyce picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Natasha can now know that Arthur can know that Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Natasha","Arthur","Joyce","Suzanne"],"index":27790,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930480123,"difficulty":0.0069519877}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jermaine's card is shown to Jermaine. Robbie's card is shown to Robbie. Jermaine's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mary can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jermaine","Robbie","Mary"],"index":23177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990516305,"difficulty":0.0009483695}
{"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. John's card is shown to John. Paul's card is shown to John. Paul's card is shown to Wayne. 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:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Andrew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","John","Paul","Wayne"],"index":22717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994083643,"difficulty":0.0005916357}
{"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 Larry. Wilmer's card is shown to Larry. Christopher's card is shown to Carey. Carey's card is shown to Wilmer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","Christopher","Carey","Wilmer"],"index":13043,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993745685,"difficulty":0.0006254315}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Wanda. Kathyrn's card is shown to Kathyrn. Luisa's card is shown to Kathyrn. Wanda's card is shown to Jefferson. Wanda's card is shown to Luisa. Luisa's card is shown to Luisa. It is publicly announced that someone picked a red card. It is publicly announced that Kathyrn does not know whether Wanda picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jefferson can now know whether Jefferson picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wanda","Kathyrn","Jefferson","Luisa"],"index":4261,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9781318903,"difficulty":0.0218681097}
{"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 Doris. Mathew's card is shown to Doris. Amy's card is shown to Amy. Doris's card is shown to Mathew. It is publicly announced that someone picked a red card. It is publicly announced that Doris 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 (Agentb knows whether (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":"Doris can now know whether Amy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Amy","Mathew"],"index":42402,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994394183,"difficulty":0.0005605817}
{"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 George. George's card is shown to George. Brady's card is shown to George. George's card is shown to Brady. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know whether William can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Helen","George","Brady"],"index":4629,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9667068124,"difficulty":0.0332931876}
{"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 Pat. Sally's card is shown to Hazel. Jeremy's card is shown to Hazel. Hazel's card is shown to Sally. Hazel's card is shown to Jeremy. 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) ] (Agentc knows that 3)","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":"Sally can now know that Sally picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pat","Hazel","Sally","Jeremy"],"index":3895,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9939272404,"difficulty":0.0060727596}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Loraine's card is shown to Thomas. Paula's card is shown to Thomas. Loraine's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Loraine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Thomas can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","James","Loraine","Paula"],"index":21708,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994737506,"difficulty":0.0005262494}
{"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 Rhonda. Linda's card is shown to Rhonda. Rhonda's card is shown to Linda. Linda's card is shown to Linda. Roy's card is shown to Linda. Rhonda's card is shown to Roy. Linda's card is shown to Roy. Roy'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:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rhonda can now know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rhonda","Linda","Roy"],"index":36681,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9440453053,"difficulty":0.0559546947}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Edwin. Edwin's card is shown to Jesus. 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:1 VALID? [ ! (1|2) ] [ ! (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) ] [ ! (1&2) ] 0","hypothesis":"Edwin can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edwin","Jesus"],"index":22967,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9933951497,"difficulty":0.0066048503}
{"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 Michelle. Michelle'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 Michelle knows whether someone 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)) ] 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) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Patricia can now know that Michelle can know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michelle","Patricia"],"index":60629,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6182066202,"difficulty":0.3817933798}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tomas's card is shown to Miquel. Marilyn's card is shown to Miquel. Miquel'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:1,2 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tomas can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tomas","Marilyn","Miquel","Michael"],"index":4332,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957478642,"difficulty":0.0042521358}
{"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. Tobias's card is shown to Jessie. Alex's card is shown to Tobias. It is publicly announced that someone picked a red card. It is publicly announced that Alex picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Jessie can now know that Alex picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alex","Jessie","Tobias"],"index":63227,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6065052152,"difficulty":1.6065052152}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffany's card is shown to John. John's card is shown to Tiffany. Jessica's card is shown to Tiffany. Tiffany's card is shown to Tiffany. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Tiffany picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Jessica","Tiffany","Jeannette"],"index":22613,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932890534,"difficulty":0.0067109466}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darius's card is shown to Frankie. Darius's card is shown to Darius. Jennie's card is shown to Darius. Frankie's card is shown to Jennie. 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 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennie can now know that Darius can know that Frankie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frankie","Darius","Jennie"],"index":4106,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998110652,"difficulty":0.001889348}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clinton's card is shown to Clinton. Anita's card is shown to Clinton. Frederick's card is shown to Clinton. Anita's card is shown to Anita. Russell's card is shown to Anita. Frederick's card is shown to Frederick. Russell's card is shown to Frederick. Anita's card is shown to Russell. 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) ] (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:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clinton can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clinton","Anita","Frederick","Russell"],"index":25728,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994029999,"difficulty":0.0005970001}
{"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 Erik. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Erik does not know whether Erik picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Erik can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erik","John"],"index":57889,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990384579,"difficulty":0.0009615421}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ramona's card is shown to David. David's card is shown to Ramona. Ramona's card is shown to Ramona. David's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Ramona knows whether Ramona 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 2) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"James can now know whether Ramona can know that Ramona picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Ramona","James"],"index":1134,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9786711335,"difficulty":1.9786711335}
{"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 Susan. Vilma's card is shown to Susan. Andrew's card is shown to Andrew. Susan's card is shown to Vilma. 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 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Andrew can now know that Vilma can know whether Andrew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Andrew","Vilma"],"index":37265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7679641247,"difficulty":0.2320358753}
{"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 Alta. Alta's card is shown to Alice. Antwan's card is shown to Alice. Antwan's card is shown to Antwan. Daniel's card is shown to Antwan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc: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:4 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Antwan can now know whether Alta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alta","Alice","Antwan","Daniel"],"index":3011,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9673164487,"difficulty":0.0326835513}
{"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 Henry. Frances's card is shown to Henry. Guadalupe's card is shown to Karl. Frances's card is shown to Karl. Frances's card is shown to Guadalupe. Henry's card is shown to Frances. It is publicly announced that someone picked a red card. It is publicly announced that Karl knows whether Guadalupe picked a red card. It is publicly announced that Karl knows whether someone picked a red card. It is publicly announced that Karl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentb knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Karl can now know whether Henry can know whether Karl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Henry","Karl","Guadalupe","Frances"],"index":4516,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9969338179,"difficulty":0.0030661821}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leo's card is shown to Leo. Manuel's card is shown to Manuel. Malinda's card is shown to Malinda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leo can now know that Malinda can know that Manuel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leo","Manuel","Malinda"],"index":30048,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974396229,"difficulty":0.0025603771}
{"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. Debra's card is shown to Alice. Alice's card is shown to Ronald. Ronald's card is shown to Ronald. Debra'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 Debra does not know whether or not everyone picked a red card. It is publicly announced that Debra picked a red card. It is publicly announced that Debra 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)) ] Agenta knows whether (Agentc knows whether 4)","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":"Debra can now know whether Ronald can know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Alice","Ronald","Anna"],"index":66504,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987081289,"difficulty":0.0012918711}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laquita's card is shown to Laquita. Carol's card is shown to Laquita. Laquita's card is shown to Carol. Nyla's card is shown to Carol. Nyla's card is shown to Nyla. It is publicly announced that someone picked a red card. It is publicly announced that Carol knows whether someone picked a red card. It is publicly announced that Nyla picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Carol can now know that Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laquita","Carol","Nyla"],"index":9951,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.602624774,"difficulty":0.397375226}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Charla. Cole's card is shown to Cole. Charla's card is shown to Kari. Charla's card is shown to Laura. Cole's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know whether Cole can know that Laura picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charla","Cole","Kari","Laura"],"index":47517,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8383974433,"difficulty":0.1616025567}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tommy's card is shown to Tommy. Henry's card is shown to Tommy. Tommy's card is shown to Margaret. Tommy's card is shown to Henry. Margaret's card is shown to Henry. It is publicly announced that someone picked a red card. It is publicly announced that Tommy does not know whether Margaret picked a red card. It is publicly announced that Margaret knows whether or not everyone picked a red card. It is publicly announced that Henry 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 whether (Agenta 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":"Margaret can now know whether Tommy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tommy","Margaret","Henry"],"index":62760,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999432981,"difficulty":0.000567019}
{"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 Daniel. Paul's card is shown to Paul. Rufus's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that Daniel can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Paul","Rufus"],"index":49361,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993769526,"difficulty":0.0006230474}
{"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. Dale's card is shown to Dale. Michael's card is shown to Dale. Michael's card is shown to Michael. Patricia's card is shown to Tony. 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)) ] (Agentc knows that (1|2|3|4))","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":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Dale","Michael","Tony"],"index":65108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993958473,"difficulty":0.0006041527}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Sonny. Sonny's card is shown to Bryan. Bryan's card is shown to Kimberly. Steve'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 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sonny can now know whether Bryan can know whether Steve picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sonny","Bryan","Kimberly","Steve"],"index":38577,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986932874,"difficulty":0.0013067126}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to William. William's card is shown to William. William's card is shown to Colette. Colette's card is shown to Colette. April's card is shown to Colette. William's card is shown to April. It is publicly announced that someone picked a red card. It is publicly announced that Ryan does not know whether Colette picked a red card. It is publicly announced that Colette 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:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ryan can now know that William can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ryan","William","Colette","April"],"index":1586,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989192486,"difficulty":0.0010807514}
{"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 Samantha. Archie's card is shown to Samantha. Ernest's card is shown to Stephanie. Archie's card is shown to Archie. 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: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:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Samantha can now know whether Archie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samantha","Stephanie","Archie","Ernest"],"index":18750,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993620515,"difficulty":0.0006379485}
{"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. Wanda's card is shown to Patricia. Patricia's card is shown to Wanda. Wanda's card is shown to Wanda. Patricia's card is shown to Suzanne. Daniel's card is shown to Suzanne. Suzanne's card is shown to Daniel. Daniel's card is shown to Daniel. 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 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that Wanda can know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Wanda","Suzanne","Daniel"],"index":35993,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981697798,"difficulty":0.0018302202}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Neil's card is shown to Cara. Evelyn's card is shown to Mary. Evelyn's card is shown to Evelyn. Mary's card is shown to Neil. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn does not know whether or not everyone picked a red card. It is publicly announced that Cara picked a black 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:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Neil can now know that Evelyn can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cara","Mary","Evelyn","Neil"],"index":11035,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7308681607,"difficulty":1.7308681607}
{"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 Michael. Michael's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether Margaret picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Margaret knows whether Michael 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 2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] (Agentb knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] [ ! (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":["Michael","Margaret"],"index":31623,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994530082,"difficulty":0.0005469918}
{"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 Tyrone. Tyrone's card is shown to Debra. Stella's card is shown to Debra. Tyrone's card is shown to Stella. Debra's card is shown to Stella. It is publicly announced that someone picked a red card. It is publicly announced that Tyrone knows whether or not nobody picked a red card. It is publicly announced that Stella does not know whether Stella picked a red card. It is publicly announced that Stella 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)) ] Agentb knows that (Agenta knows that 1)","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":"Debra can now know that Tyrone can know that Tyrone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tyrone","Debra","Stella","Tracy"],"index":61719,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6802810431,"difficulty":1.6802810431}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacey's card is shown to Ellen. Ellen's card is shown to Stacey. Stacey's card is shown to Stacey. Stacey's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Stacey does not know whether or not everyone 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)) ] Agentc 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 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Donna can now know whether Ellen can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellen","Stacey","Donna"],"index":64317,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
{"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 Susan. Susan's card is shown to Anthony. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Susan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Susan","Anthony","Doris"],"index":17775,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994159937,"difficulty":0.0005840063}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Teresa. Denise's card is shown to Teresa. Denise's card is shown to Rodney. Billy's card is shown to Billy. Rodney's card is shown to Denise. Denise's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Billy knows whether someone picked a red card. It is publicly announced that Teresa picked a red card. It is publicly announced that Rodney does not know whether Billy 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) ] Agentd knows whether (Agentc knows whether 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":"Denise can now know whether Billy can know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Teresa","Rodney","Billy","Denise"],"index":64470,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985673428,"difficulty":0.0014326572}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Craig. Tony's card is shown to Tony. Dorine's card is shown to Dorine. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether Dorine 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 Tony does not know whether Dorine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Dorine can now know whether Craig can know whether Dorine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Craig","Tony","Dorine"],"index":48197,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987508059,"difficulty":0.0012491941}
{"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 John. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether John picked a red card. It is publicly announced that John knows whether or not nobody picked a red card. It is publicly announced that David picked a black card. It is publicly announced that John knows whether David 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) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":4,"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) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"John can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","John"],"index":12044,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5088337064,"difficulty":0.4911662936}
{"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 Dustin. Lucy's card is shown to Kelly. 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:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kelly can now know that Dustin can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dustin","Kelly","Lucy","Patricia"],"index":14266,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990159273,"difficulty":0.0009840727}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Courtney's card is shown to Courtney. Jerry's card is shown to Courtney. Heather's card is shown to Joan. Courtney's card is shown to Jerry. Joan's card is shown to Heather. Jerry's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know whether Heather can know whether Courtney picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Courtney","Joan","Jerry","Heather"],"index":32202,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986521602,"difficulty":0.0013478398}
{"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 Lawrence. Robert's card is shown to Lawrence. Joseph's card is shown to Lawrence. Joseph's card is shown to Marie. Lawrence's card is shown to Robert. Marie's card is shown to Joseph. Robert's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentc knows that 1)","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":"Joseph can now know that Robert can know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lawrence","Marie","Robert","Joseph"],"index":47813,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.986586988,"difficulty":0.013413012}
{"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 Melissa. Pete's card is shown to Melissa. Melissa's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Melissa's card is shown to Pete. 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:1 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know that Pete picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melissa","Elizabeth","Pete"],"index":45604,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979935884,"difficulty":0.0020064116}
{"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. Martha's card is shown to Leonard. Martha's card is shown to Jason. Leonard's card is shown to Jason. 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 Martha knows whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Michael can now know that Jason picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Martha","Michael","Leonard","Jason"],"index":16610,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9811313152,"difficulty":0.0188686848}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vicki's card is shown to Flora. Thomas's card is shown to Florence. Flora's card is shown to Florence. Florence's card is shown to Florence. Vicki's card is shown to Florence. Flora's card is shown to Vicki. Vicki's card is shown to Vicki. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Flora can now know whether Thomas can know whether Flora picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Flora","Florence","Vicki"],"index":5439,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984574318,"difficulty":0.0015425682}
{"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 Dwight. Alejandro's card is shown to Dwight. Dwight's card is shown to Gary. Alejandro'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:3,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know that Alejandro picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dwight","Gary","Ronald","Alejandro"],"index":41005,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970107079,"difficulty":0.0029892921}
{"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. Lawrence's card is shown to Linda. Tracy's card is shown to Lawrence. Tracy's card is shown to Tracy. Tracy's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Lawrence does not know whether Brenda picked a red 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) ] [ ! ~(Agentb knows whether 4) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Tracy can now know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Lawrence","Tracy","Brenda"],"index":32538,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5557581782,"difficulty":1.5557581782}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clifford's card is shown to Scott. Mary's card is shown to Clifford. Peter's card is shown to Clifford. Mary's card is shown to Mary. Peter's card is shown to Mary. Clifford's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Clifford picked a red card. It is publicly announced that Mary does not know whether Clifford picked a red card. It is publicly announced that Peter 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 whether (Agentc knows that 3)","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":"Clifford can now know whether Mary can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Clifford","Mary","Peter"],"index":46135,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8015115857,"difficulty":0.1984884143}
{"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 Jared. Dorothy's card is shown to Vasiliki. Vasiliki's card is shown to Vasiliki. Vasiliki's card is shown to Helen. 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 (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":"Vasiliki can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jared","Dorothy","Vasiliki","Helen"],"index":13058,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953149557,"difficulty":0.0046850443}
{"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 Matthew. Ernestine's card is shown to Matthew. Marcos's card is shown to Matthew. Ernestine's card is shown to Larry. Marcos's card is shown to Ernestine. It is publicly announced that someone picked a red card. It is publicly announced that Ernestine knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Matthew can now know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Larry","Ernestine","Marcos"],"index":231,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9606522918,"difficulty":0.0393477082}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ileana's card is shown to Edna. Christopher's card is shown to Edna. Warren's card is shown to Christopher. Christopher's card is shown to Warren. It is publicly announced that someone picked a red card. It is publicly announced that Edna does not know whether Edna picked a red card. It is publicly announced that Edna picked a black card. It is publicly announced that Ileana does not know whether Ileana picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Christopher can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edna","Ileana","Christopher","Warren"],"index":468,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9233108759,"difficulty":0.0766891241}
{"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 Tara. John's card is shown to John. John'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 John picked a black card. It is publicly announced that Karen 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 ] Agentb 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":"John can now know that Tara can know whether Tara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tara","John","Karen"],"index":37047,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7354037762,"difficulty":0.2645962238}
{"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 Hong. Charles's card is shown to Roy. Roy's card is shown to Charles. 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 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Roy can now know that Hong picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hong","Roy","Charles"],"index":39415,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983817339,"difficulty":0.0016182661}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rena's card is shown to Rena. Rena'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 Marie knows whether Marie picked a red card. It is publicly announced that Rena does not know whether Marie 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 whether 2) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Rena can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rena","Marie"],"index":1493,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994570613,"difficulty":0.0005429387}
{"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 Jaqueline. George's card is shown to George. Joseph'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:3 Agentb:2 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:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether Jaqueline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jaqueline","George","Joseph","James"],"index":54708,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.989395678,"difficulty":0.010604322}
{"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 Rhonda. James's card is shown to Rhonda. James's card is shown to James. Rhonda's card is shown to Joseph. James's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rhonda","James","Joseph"],"index":62701,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989529848,"difficulty":0.0010470152}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ina's card is shown to Yolanda. Caleb's card is shown to Yolanda. Yolanda's card is shown to Page. Page's card is shown to Page. Ina's card is shown to Page. Ina's card is shown to Ina. Yolanda's card is shown to Caleb. Ina's card is shown to Caleb. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Yolanda can now know that Ina can know that Caleb picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Yolanda","Page","Ina","Caleb"],"index":13599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975036979,"difficulty":0.0024963021}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Kenneth. Debbie's card is shown to Kenneth. Debbie's card is shown to Gary. Debbie's card is shown to Debbie. It is publicly announced that someone picked a red card. It is publicly announced that Gary does not know whether or not everyone picked a red card. It is publicly announced that Debbie does not know whether Gary picked a red card. It is publicly announced that Debbie 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)) ] (Agentb knows that (1|2|3))","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":"Gary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kenneth","Gary","Debbie"],"index":12907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994354844,"difficulty":0.0005645156}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sabrina's card is shown to Gregory. Michael's card is shown to Gregory. Sabrina's card is shown to Sabrina. Sabrina's card is shown to Sally. 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 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sabrina can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Sabrina","Sally","Michael"],"index":54912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988849759,"difficulty":0.0011150241}
{"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 Robert. Richard's card is shown to Robert. Kenneth's card is shown to Richard. Robert's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Anthony's card is shown to Kenneth. Kenneth'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:1,2 Agentb:3 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know whether Anthony can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Richard","Kenneth","Anthony"],"index":7000,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990763664,"difficulty":0.0009236336}
{"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 Roland. Donnie's card is shown to Roland. Roland's card is shown to Donnie. 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 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Roland","Donnie","Edward"],"index":67478,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993430972,"difficulty":0.0006569028}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmie's card is shown to Cheryl. Debbie's card is shown to Cheryl. Walter's card is shown to Jimmie. Debbie's card is shown to Debbie. 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) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jimmie can now know whether Cheryl can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Walter","Jimmie","Debbie"],"index":46580,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993799925,"difficulty":0.0006200075}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Era's card is shown to Jeffrey. Jeffrey's card is shown to Michael. Michael's card is shown to Michael. Terry's card is shown to Michael. Jeffrey's card is shown to Era. Terry's card is shown to Era. 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 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Terry can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Michael","Terry","Era"],"index":28387,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990516305,"difficulty":0.0009483695}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Darrell. Yvonne's card is shown to Darrell. Yvonne's card is shown to Bret. 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) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Yvonne can now know that Darrell can know whether Bret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darrell","Yvonne","Bret"],"index":66394,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981045723,"difficulty":0.0018954277}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ethel's card is shown to Ethel. Glenn's card is shown to Glenn. Glenn's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Glenn can now know that Ethel can know whether Glenn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ethel","Glenn","Donna"],"index":64324,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.729606688,"difficulty":1.729606688}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Douglas. Thomas's card is shown to Thomas. Rex's card is shown to Thomas. Douglas'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:1 Agentb:2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rex can now know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Douglas","Thomas","Rex","Charles"],"index":24709,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5304313898,"difficulty":1.5304313898}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Eric. Eric's card is shown to Eric. Eric's card is shown to Randy. 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 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Daniel can now know whether Eric can know whether Randy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Eric","Randy"],"index":61836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984200001,"difficulty":0.0015799999}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Merrill's card is shown to Merrill. Larry's card is shown to Larry. Doris's card is shown to Doris. 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:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know whether Merrill picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Merrill","Larry","Shelley","Doris"],"index":43756,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6438894868,"difficulty":0.3561105132}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jane's card is shown to Jane. Truman's card is shown to Jane. Jane's card is shown to Truman. It is publicly announced that someone picked a red card. It is publicly announced that Jane knows whether someone 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)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jane can now know whether Jane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jane","Truman"],"index":15569,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9535514712,"difficulty":0.0464485288}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elmer's card is shown to Elmer. Dorothy's card is shown to Elmer. Elmer'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 Dorothy knows whether someone picked a red card. It is publicly announced that Dorothy 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 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":"Dorothy can now know that Elmer can know whether Elmer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elmer","Dorothy"],"index":47921,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6662372351,"difficulty":1.6662372351}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Christopher. Christopher's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Walter can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christopher","Walter"],"index":65257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994095564,"difficulty":0.0005904436}
{"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 George. Dalila's card is shown to George. Velvet's card is shown to Velvet. Velvet's card is shown to Dalila. 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) ] (Agenta knows whether (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":"George can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Velvet","Dalila"],"index":17649,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944463968,"difficulty":0.0055536032}
{"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 Susan. Jesse's card is shown to Jesse. Mark's card is shown to Jesse. Susan's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Jesse 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 ] (Agenta knows whether (1&2&3))","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":"Susan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Jesse","Mark"],"index":64369,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7927910686,"difficulty":1.7927910686}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Francis. Jerry's card is shown to Francis. Jerry's card is shown to Jerry. Gerald's card is shown to Jerry. Francis's card is shown to Gerald. Jerry's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that Gerald knows whether Jerry 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) ] (Agentc knows that (~(1|2|3)))","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":"Gerald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francis","Jerry","Gerald"],"index":4051,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990465045,"difficulty":0.0009534955}
{"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. Louise's card is shown to Terry. Terry's card is shown to Terry. Yvette's card is shown to Terry. Louise's card is shown to Yvette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Louise can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Louise","Terry","Yvette"],"index":41532,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989797473,"difficulty":0.0010202527}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lesli's card is shown to Harold. April's card is shown to Harold. Harold's card is shown to Anthony. Lesli's card is shown to Anthony. Lesli's card is shown to Lesli. Anthony's card is shown to April. It is publicly announced that someone picked a red card. It is publicly announced that April picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Anthony can now know whether Harold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harold","Anthony","Lesli","April"],"index":15710,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8483694196,"difficulty":0.1516305804}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristy's card is shown to Inez. Ingrid's card is shown to Ingrid. Wayne's card is shown to Ingrid. Kristy's card is shown to Ingrid. Ingrid's card is shown to Wayne. Wayne's card is shown to Kristy. It is publicly announced that someone picked a red card. It is publicly announced that Kristy 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)) ] (Agentc knows that 3)","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":"Wayne can now know that Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Inez","Ingrid","Wayne","Kristy"],"index":63554,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9024978876,"difficulty":1.9024978876}
{"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. Wayne's card is shown to Pauline. Pauline's card is shown to Wayne. It is publicly announced that someone picked a red card. It is publicly announced that Wayne does not know whether Wayne 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 (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Wayne can now know whether Pauline can know that Wayne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pauline","Wayne"],"index":27324,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7458900809,"difficulty":1.7458900809}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Julie. Jeanette's card is shown to Julie. Julie's card is shown to John. John's card is shown to John. Linda's card is shown to John. Jeanette's card is shown to John. Julie's card is shown to Linda. John's card is shown to Jeanette. 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) ] Agentc knows that (Agenta knows whether 2)","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":"Linda can now know that Julie can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","John","Linda","Jeanette"],"index":48086,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7222588658,"difficulty":0.2777411342}
{"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 Robert. Tanya's card is shown to Robert. Gary's card is shown to Robert. Katherine's card is shown to Robert. Robert's card is shown to Tanya. Tanya's card is shown to Tanya. Gary's card is shown to Tanya. Tanya's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether Katherine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Tanya can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Tanya","Gary","Katherine"],"index":20258,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990416169,"difficulty":0.0009583831}
{"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. Rosa's card is shown to Tammy. Rosa's card is shown to Rosa. It is publicly announced that someone picked a red card. It is publicly announced that Tammy 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 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Tammy can now know that Rosa can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tammy","Rosa","James"],"index":67673,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9566821456,"difficulty":0.0433178544}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Miriam. Miriam's card is shown to Beverly. Beverly's card is shown to Beverly. Beverly's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Beverly does not know whether or not everyone 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)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know that Miriam can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Miriam","Beverly","Karen"],"index":61664,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989362359,"difficulty":0.0010637641}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Jane. Jane's card is shown to William. 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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"William can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jane","William"],"index":25562,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994508624,"difficulty":0.0005491376}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heidi's card is shown to Heidi. Ranae's card is shown to Ranae. Heidi'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 Agentb:2 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:1 Agentb:2 Agentc:1 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":["Heidi","Ranae","Thomas"],"index":30002,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993531108,"difficulty":0.0006468892}
{"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 Maria. Maria's card is shown to Emily. Dorene's card is shown to Dorene. It is publicly announced that someone picked a red card. It is publicly announced that Dorene knows whether Dorene 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) ] (Agenta knows whether 3)","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":"Maria can now know whether Dorene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Emily","Dorene"],"index":4371,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9359275103,"difficulty":1.9359275103}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Seth's card is shown to Seth. Seth's card is shown to Matthew. Matthew's card is shown to Matthew. Tammy's card is shown to Matthew. Matthew's card is shown to Tammy. 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) ] Agenta knows whether (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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Seth can now know whether Tammy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Seth","Matthew","Tammy"],"index":19226,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9221842289,"difficulty":0.0778157711}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gretchen's card is shown to Benjamin. Benjamin's card is shown to Kenneth. Kenneth's card is shown to Kristen. Gretchen's card is shown to Kristen. Kristen's card is shown to Gretchen. 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) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristen can now know whether Kenneth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Benjamin","Kenneth","Kristen","Gretchen"],"index":7627,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993919134,"difficulty":0.0006080866}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Verla's card is shown to Robert. Juan's card is shown to Verla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Juan can now know whether Robert can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Juan","Robert","Verla"],"index":11315,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9580473304,"difficulty":0.0419526696}
{"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. Rose's card is shown to Rose. Barbara's card is shown to Daniel. Rose's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Rose picked a red card. It is publicly announced that Anthony knows whether Rose picked a red card. It is publicly announced that Barbara does not know whether Daniel picked a red card. It is publicly announced that Rose 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)) ] Agentb knows whether (Agentd knows that 4)","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":"Rose can now know whether Anthony can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Rose","Daniel","Anthony"],"index":27720,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9118089676,"difficulty":1.9118089676}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hubert's card is shown to Adela. Adela's card is shown to Hubert. Hubert's card is shown to Nettie. It is publicly announced that someone picked a red card. It is publicly announced that Adela picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Nettie 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":"Adela can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harry","Adela","Hubert","Nettie"],"index":8523,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990031123,"difficulty":0.0009968877}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Pauline. William's card is shown to William. Clyde'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:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","William","Clyde","Richard"],"index":40208,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989131689,"difficulty":0.0010868311}
{"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 William. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that 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)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Paul"],"index":58670,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993497014,"difficulty":0.006502986}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harry's card is shown to Arthur. Don's card is shown to Louisa. Harry's card is shown to Don. It is publicly announced that someone picked a red card. It is publicly announced that Don does not know whether Arthur 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) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Arthur can now know whether Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Louisa","Don","Harry"],"index":40623,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8423227668,"difficulty":1.8423227668}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heidi's card is shown to Ronald. Ronald's card is shown to Bradley. Mandy's card is shown to Mandy. It is publicly announced that someone picked a red card. It is publicly announced that Heidi does not know whether Heidi picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta 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) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Bradley can now know that Ronald can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Bradley","Heidi","Mandy"],"index":59553,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994168282,"difficulty":0.0005831718}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lindsay's card is shown to Brooke. William's card is shown to Kathleen. Lindsay's card is shown to Kathleen. Brooke's card is shown to William. 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. It is publicly announced that William picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"William can now know that Brooke can know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brooke","Kathleen","William","Lindsay"],"index":25443,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957717061,"difficulty":0.0042282939}
{"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. Valerie's card is shown to Juan. Juan's card is shown to Valerie. Valerie's card is shown to Valerie. 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 (Agenta 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":"Juan can now know whether Vera can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vera","Juan","Valerie"],"index":49088,"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). Steven's card is shown to Steven. Heather's card is shown to Steven. Larry's card is shown to Heather. 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":"Steven can now know whether Heather can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Heather","Larry"],"index":21592,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994028807,"difficulty":0.0005971193}
{"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 Larry. Ron's card is shown to Larry. Ron's card is shown to Ron. Ron'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 everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Larry can now know that Ron can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Larry","Ron","Michael"],"index":36392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9838584065,"difficulty":0.0161415935}
{"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. Theodore's card is shown to Bobby. Bobby's card is shown to Theodore. 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 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deanna can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deanna","Bobby","Theodore","Mary"],"index":27314,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980980754,"difficulty":0.0019019246}
{"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. Sandy's card is shown to Joseph. Sandy's card is shown to Sandy. Stanley's card is shown to Sandy. Stanley's card is shown to Stanley. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know that Stanley can know that Stanley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Sandy","Stanley"],"index":15283,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5780093074,"difficulty":1.5780093074}
{"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 Kerri. Robert's card is shown to Kerri. Kerri's card is shown to Faye. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Kerri does not know whether Rachel picked a red card. It is publicly announced that Rachel does not know whether Kerri 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 1) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Faye can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rachel","Kerri","Faye","Robert"],"index":63258,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8371124268,"difficulty":0.1628875732}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lauren's card is shown to Lauren. Demetrius's card is shown to Lauren. Lauren's card is shown to Demetrius. It is publicly announced that someone picked a red card. It is publicly announced that Lauren 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 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":"Diana can now know that Lauren can know that Demetrius picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Diana","Lauren","Demetrius"],"index":14132,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7588365078,"difficulty":0.2411634922}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lester's card is shown to Tara. Cecelia's card is shown to Tara. Lester's card is shown to Lester. Tara's card is shown to Cecelia. 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 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tara can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tara","Lester","Cecelia"],"index":2964,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992871881,"difficulty":0.0007128119}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angie's card is shown to James. Gerald's card is shown to James. Angie's card is shown to Angie. Milda's card is shown to Angie. James's card is shown to Milda. Angie's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Milda picked a red card. It is publicly announced that Angie picked a black card. It is publicly announced that James does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Angie can now know that Milda can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Angie","Milda","Gerald"],"index":4116,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.978982091,"difficulty":0.021017909}
{"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 Wilber. Rickey's card is shown to Wilber. Jill's card is shown to Jill. Jill's card is shown to Rickey. Rickey's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Rickey does not know whether or not everyone picked a red card. It is publicly announced that Rickey does not know whether Rickey picked a red card. It is publicly announced that Wilber knows whether Rickey 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 that (Agentc knows whether 3)","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":"Jill can now know that Rickey can know whether Rickey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wilber","Jill","Rickey","Douglas"],"index":50840,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8148599863,"difficulty":1.8148599863}
{"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 Thad. George's card is shown to Thad. Thad's card is shown to Alan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harriet can now know whether Harriet picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thad","Harriet","Alan","George"],"index":19816,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9608873725,"difficulty":0.0391126275}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Travis's card is shown to Travis. Mario's card is shown to Travis. Tayna's card is shown to Travis. Mario's card is shown to Mario. Tayna's card is shown to Tayna. 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 (~(1|2|3)))","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":"Tayna can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Travis","Mario","Tayna"],"index":10820,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989816546,"difficulty":0.0010183454}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Stewart's card is shown to Melissa. Melissa's card is shown to Stewart. It is publicly announced that someone picked a red card. It is publicly announced that Stewart knows whether Stewart picked a red card. It is publicly announced that Stewart picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! 2 ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! 2 ] 0","hypothesis":"Melissa can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Melissa","Stewart"],"index":55790,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9260044694,"difficulty":0.0739955306}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joel's card is shown to Joel. Joel's card is shown to Grace. Grace's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Grace picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Grace 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:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Grace can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joel","Grace"],"index":57795,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9928145409,"difficulty":0.0071854591}
{"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 Mark. Gregory's card is shown to Mark. Mark's card is shown to Gregory. Mark's card is shown to Joshua. Judy's card is shown to Joshua. Gregory's card is shown to Joshua. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 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)) ] (Agentc knows whether (~(1|2|3|4)))","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":"Gregory can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","Judy","Gregory","Joshua"],"index":43855,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994294047,"difficulty":0.0005705953}
{"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 Sara. Judith's card is shown to Judith. 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:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eleanor can now know that Judith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eleanor","Sara","Judith","Michael"],"index":40350,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944850802,"difficulty":0.0055149198}
{"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 Alice. Susan's card is shown to Judith. Carol's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Alice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alice can now know that Susan can know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Susan","Judith","Carol"],"index":39894,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7707189322,"difficulty":0.2292810678}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Thomas. Thomas's card is shown to Barbara. Bryan's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Bryan knows whether Bryan 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) ] (Agentc knows whether (1&2&3))","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":"Bryan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Barbara","Bryan"],"index":39810,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8959762454,"difficulty":0.1040237546}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debbie's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Debbie 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 whether (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":"Debbie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debbie","Thomas"],"index":31989,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994340539,"difficulty":0.0005659461}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Joan. Lindsy's card is shown to Leslie. Lindsy's card is shown to Rhonda. Leslie's card is shown to Rhonda. 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:1,3 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 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joan can now know whether Leslie can know whether Rhonda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lindsy","Joan","Leslie","Rhonda"],"index":7561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985741377,"difficulty":0.0014258623}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rita's card is shown to Rita. Mary's card is shown to Rita. Rita's card is shown to Mary. Courtney's card is shown to Mary. Zachary's card is shown to Courtney. 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 whether 1)","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":"Zachary can now know whether Zachary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Zachary","Rita","Mary","Courtney"],"index":3139,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7825571895,"difficulty":0.2174428105}
{"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. Trenton's card is shown to Thelma. Thelma's card is shown to Trenton. Thelma's card is shown to Kim. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Trenton can now know that Thelma can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thelma","Trenton","Kim"],"index":26866,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9861102104,"difficulty":0.0138897896}
{"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 Jeffrey. Robert's card is shown to Jeffrey. Sarah's card is shown to Jeffrey. Sarah's card is shown to Alice. Alice'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:1,2,4 Agentb:4 Agentc: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:1,2,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffrey","Robert","Alice","Sarah"],"index":57551,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993414283,"difficulty":0.0006585717}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Harold. Harold's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that David does not know whether David 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 whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"David can now know whether Harold can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Harold","Lisa"],"index":37842,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9976664782,"difficulty":0.0023335218}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricky's card is shown to Ricky. Danny's card is shown to Ricky. Billy's card is shown to Ricky. Danny's card is shown to Danny. Billy's card is shown to Danny. Danny's card is shown to Ahmad. Ricky's card is shown to Billy. Danny'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:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Billy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ricky","Danny","Ahmad","Billy"],"index":44210,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989739656,"difficulty":0.0010260344}
{"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. Tracy's card is shown to Barbara. Dora's card is shown to Tracy. Dora's card is shown to Dora. 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:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Tracy","Dora","Michael"],"index":42325,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989307523,"difficulty":0.0010692477}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Idella's card is shown to Stefanie. Jill's card is shown to Stefanie. Idella's card is shown to Jill. Stefanie's card is shown to Jill. It is publicly announced that someone picked a red card. It is publicly announced that Stefanie knows whether or not everyone picked a red card. It is publicly announced that Stefanie does not know whether Jill 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) ] (Agentb 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":"Stefanie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Idella","Stefanie","Jill"],"index":50089,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994663596,"difficulty":0.0005336404}
{"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. Darcie's card is shown to Gregory. Darcie's card is shown to Matthew. Gregory's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Darrell knows whether or not everyone picked a red card. It is publicly announced that Darcie knows whether Darrell picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Darcie can now know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darcie","Darrell","Gregory","Matthew"],"index":47937,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8153125644,"difficulty":0.1846874356}
{"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 Todd. Lisa's card is shown to Janet. Lisa's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Todd picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Janet picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Lisa can now know whether Janet can know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Todd","Janet","Lisa"],"index":27729,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9698556066,"difficulty":0.0301443934}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Stephanie. Carl's card is shown to Margaret. Bryan's card is shown to Margaret. Bryan's card is shown to Bryan. 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 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:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Carl","Margaret","Bryan"],"index":60333,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989777803,"difficulty":0.0010222197}
{"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. Anthony's card is shown to Darrell. Darrell's card is shown to Anthony. Anthony's card is shown to Anthony. Darrell's card is shown to Jeremy. William's card is shown to Jeremy. Jeremy'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 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 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:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darrell can now know whether Jeremy can know whether William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrell","Anthony","Jeremy","William"],"index":21325,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988476038,"difficulty":0.0011523962}
{"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 Yolanda. Robert's card is shown to Robert. Kathryn's card is shown to Robert. Robert's card is shown to Kathryn. Yolanda's card is shown to Ronald. Robert's card is shown to Ronald. 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.","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 ] (Agentc knows that 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":"Kathryn can now know that Ronald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Yolanda","Robert","Kathryn","Ronald"],"index":29962,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7902139425,"difficulty":1.7902139425}
{"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 Jessica. John's card is shown to Jessica. Marvin's card is shown to Jessica. Jessica's card is shown to John. Marvin's card is shown to John. Jessica's card is shown to Marvin. 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) ] (Agentc knows that 1)","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":"John can now know that Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Helen","John","Marvin"],"index":59379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946152568,"difficulty":0.0053847432}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linwood's card is shown to Dodie. Paul's card is shown to Dodie. Dodie's card is shown to Linwood. Linwood's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 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:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Linwood can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dodie","Linwood","Paul"],"index":16459,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993366599,"difficulty":0.0006633401}
{"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. Ora's card is shown to Charles. Anna's card is shown to Charles. Charles's card is shown to Justin. Justin's card is shown to Justin. Justin's card is shown to Anna. Anna's card is shown to Anna. 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:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ora can now know that Justin can know that Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Ora","Justin","Anna"],"index":7824,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972184896,"difficulty":0.0027815104}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alec's card is shown to Kyle. Christina's card is shown to Kyle. Alec's card is shown to Alec. Alec's card is shown to Wendy. Kyle's card is shown to Christina. Wendy's card is shown to Christina. It is publicly announced that someone picked a red card. It is publicly announced that Kyle does not know whether Wendy picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Wendy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Kyle can now know whether Alec picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kyle","Alec","Wendy","Christina"],"index":12633,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7687187791,"difficulty":1.7687187791}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felisha's card is shown to Felisha. Cassandra's card is shown to Felisha. Mary's card is shown to Cassandra. Mary's card is shown to Violet. Cassandra'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:1,2 Agentb:4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Felisha","Cassandra","Violet","Mary"],"index":16243,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993380904,"difficulty":0.0006619096}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janette's card is shown to Teri. Gregory's card is shown to Shirley. Janette'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:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Janette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Teri","Shirley","Janette"],"index":9200,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970538616,"difficulty":0.0029461384}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lindsay's card is shown to Lois. Lois's card is shown to Lindsay. Scott's card is shown to Lindsay. Randal's card is shown to Scott. Lois's card is shown to Randal. Lindsay's card is shown to Randal. It is publicly announced that someone picked a red card. It is publicly announced that Lois does not know whether Randal picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Lindsay can now know that Randal picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lois","Lindsay","Scott","Randal"],"index":20364,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971012473,"difficulty":0.0028987527}
{"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. Gerald's card is shown to Michael. Michael's card is shown to Barbara. Roslyn's card is shown to Gerald. Michael's card is shown to Roslyn. Barbara's card is shown to Roslyn. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Barbara picked a red card. It is publicly announced that Barbara does not know whether Gerald picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Gerald can now know that Barbara can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Barbara","Gerald","Roslyn"],"index":45367,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9710581303,"difficulty":0.0289418697}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Shirley. Kathleen's card is shown to Kathleen. Kathleen's card is shown to Kevin. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Shirley does not know whether Kevin picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Shirley can now know that Kathleen can know whether Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Kathleen","Kevin"],"index":48506,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5840291381,"difficulty":1.5840291381}
{"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 Mary. Florence's card is shown to Mary. Hannah's card is shown to Jessica. Mary's card is shown to Hannah. Hannah's card is shown to Hannah. Florence's card is shown to Florence. It is publicly announced that someone picked a red card. It is publicly announced that Florence knows whether or not everyone picked a red card. It is publicly announced that Jessica does not know whether Mary picked a red card. It is publicly announced that Florence knows whether someone picked a red card. It is publicly announced that Florence does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Hannah can now know that Mary can know that Hannah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Jessica","Hannah","Florence"],"index":38622,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9689721465,"difficulty":0.0310278535}
{"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 Edith. Edith's card is shown to Robert. Michelle's card is shown to Robert. Brian's card is shown to Michelle. Michelle's card is shown to Michelle. 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 whether 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":"Edith can now know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edith","Brian","Robert","Michelle"],"index":30436,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9456396103,"difficulty":1.9456396103}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to David. David's card is shown to Anita. Martha's card is shown to Anita. Anita's card is shown to Anita. It is publicly announced that someone picked a red card. It is publicly announced that Martha knows whether Anita picked a red card. It is publicly announced that David does not know whether Anita picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Martha can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Martha","Anita"],"index":8247,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994064569,"difficulty":0.0005935431}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barton's card is shown to Barton. James's card is shown to Lewis. Lewis's card is shown to James. Barton's card is shown to Clarence. Lewis's card is shown to Clarence. 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 that (Agentc 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":"Barton can now know that James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barton","Lewis","James","Clarence"],"index":48274,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993768334,"difficulty":0.0006231666}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tricia's card is shown to Tricia. Brenda's card is shown to Tricia. Dewey's card is shown to Brenda. Rodney's card is shown to Dewey. Brenda's card is shown to Dewey. 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) ] (Agentb knows that 1)","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":"Rodney can now know that Tricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tricia","Rodney","Brenda","Dewey"],"index":57247,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982361794,"difficulty":0.0017638206}
{"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 Darlene. Jim's card is shown to Jim. Jim's card is shown to Allan. Darlene'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:3 Agentb:2 Agentc:2 Agentd:1 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:3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darlene can now know that Jim can know whether Allan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darlene","Jim","Allan","Billy"],"index":863,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9927143455,"difficulty":0.0072856545}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Michael. Emma's card is shown to Katherine. Katherine's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Katherine does not know whether or not everyone picked a red card. It is publicly announced that Katherine does not know whether or not everyone 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 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Katherine","Steve","Emma"],"index":32606,"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). Richard's card is shown to Benjamin. Lisa's card is shown to Lisa. Richard's card is shown to Lisa. Benjamin's card is shown to Richard. Lisa's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Benjamin can now know whether Lisa can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Benjamin","Lisa","Richard"],"index":60544,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.897993207,"difficulty":0.102006793}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelley's card is shown to Alfredo. Shelley's card is shown to Jack. Alfredo's card is shown to Shelley. 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":"Alfredo can now know whether Shelley can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alfredo","Jack","Shelley"],"index":34503,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992139339,"difficulty":0.0007860661}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tonya's card is shown to Tonya. Anne's card is shown to Tonya. Ruby's card is shown to Tonya. Allyson's card is shown to Allyson. Anne's card is shown to Anne. Allyson's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Allyson does not know whether Ruby picked a red card. It is publicly announced that Tonya knows whether Anne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Ruby can now know that Anne can know whether Ruby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tonya","Allyson","Anne","Ruby"],"index":28566,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7281122208,"difficulty":1.7281122208}
{"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 Brandon. Brian's card is shown to Brian. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Jeremy does not know whether Jeremy 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) ] (Agentb knows whether (~(1|2|3|4)))","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":"Brandon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeremy","Brandon","Brian","Matthew"],"index":2215,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994014502,"difficulty":0.0005985498}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Mark. Mark's card is shown to Nicholas. Mark's card is shown to Isaac. Nicholas's card is shown to Isaac. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Isaac can now know that Nicholas can know that Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Nicholas","Isaac"],"index":5410,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979909658,"difficulty":0.0020090342}
{"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 Edgar. Edgar's card is shown to Luis. Luis's card is shown to Luis. Jodie's card is shown to Luis. Luis's card is shown to Jodie. Melissa's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Melissa picked a red card. It is publicly announced that Edgar 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) ] (Agentd knows that 2)","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":"Melissa can now know that Luis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edgar","Luis","Jodie","Melissa"],"index":8812,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9336034656,"difficulty":0.0663965344}
{"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 Kevin. Kevin's card is shown to Carrie. Carrie's card is shown to Carrie. Kevin's card is shown to Mary. Carrie's card is shown to Tisha. Tisha's card is shown to Tisha. It is publicly announced that someone picked a red card. It is publicly announced that Tisha does not know whether Mary picked a red card. It is publicly announced that Kevin knows whether Mary 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 whether (Agentd knows that 3)","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":"Kevin can now know whether Tisha can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Carrie","Mary","Tisha"],"index":60498,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9730038643,"difficulty":0.0269961357}
{"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 Joan. Gladys's card is shown to Joan. Joan's card is shown to Wallace. Joan's card is shown to Gladys. Gladys's card is shown to Gladys. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gladys can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joan","Wallace","Gladys"],"index":258,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994217157,"difficulty":0.0005782843}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Pauline. Pauline'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 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pauline can now know that Pauline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pauline","Mary","Shirley"],"index":21753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9855750799,"difficulty":0.0144249201}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Denise's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Brenda does not know whether Denise picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Brenda can now know that Denise can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brenda","Denise"],"index":40881,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999073863,"difficulty":0.000926137}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Nina. Nina's card is shown to Sheila. Nina's card is shown to Timmy. 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. It is publicly announced that Nina does not know whether Nina picked a red card. It is publicly announced that Timmy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Timmy can now know whether Nina can know that Sheila picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nina","Sheila","Timmy"],"index":49418,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.955527246,"difficulty":0.044472754}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adina's card is shown to Gary. Paul's card is shown to Gary. Gary's card is shown to Michael. Adina's card is shown to Adina. It is publicly announced that someone picked a red card. It is publicly announced that Michael 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 that (~(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":"Michael can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Michael","Adina","Paul"],"index":62186,"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). Marilyn's card is shown to Angelia. Tony's card is shown to Tony. Tony's card is shown to Marilyn. Marilyn's card is shown to Marilyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc: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:2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tony can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Angelia","Tony","Marilyn"],"index":59813,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999368608,"difficulty":0.000631392}
{"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 Debbie. Gerald's card is shown to Gerald. Debbie'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 Andrew knows whether Debbie picked a red card. It is publicly announced that Gerald does not know whether Debbie 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) ] (Agenta 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":"Debbie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debbie","Gerald","Andrew"],"index":29456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999381423,"difficulty":0.000618577}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emily's card is shown to John. Emily's card is shown to Leroy. John's card is shown to Rosemary. Rosemary's card is shown to Emily. 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 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Leroy can know that Leroy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Leroy","Rosemary","Emily"],"index":32374,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9933850169,"difficulty":1.9933850169}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Anthony. Anthony's card is shown to Marie. Marie's card is shown to Marie. Marie's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 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":"Anthony can now know whether Marie can know that Marie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Antonette","Anthony","Marie","Elizabeth"],"index":20693,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9495604634,"difficulty":0.0504395366}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jorge's card is shown to Gladys. Gladys's card is shown to Jorge. Jorge's card is shown to Jorge. Jorge's card is shown to Herman. 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:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gladys can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gladys","Jorge","Herman"],"index":45623,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9920347333,"difficulty":0.0079652667}
{"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. It is publicly announced that someone picked a red card. It is publicly announced that Vera picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Vera can now know that Cindy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vera","Shirley","Cindy"],"index":21135,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9912881255,"difficulty":0.0087118745}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathaniel's card is shown to Nathaniel. Josphine's card is shown to Nathaniel. Margaret's card is shown to Nathaniel. Margaret's card is shown to Josphine. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know that Josphine can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nathaniel","Josphine","Margaret"],"index":29215,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993218184,"difficulty":0.0006781816}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. John's card is shown to John. 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) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Daniel can now know whether John can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daniel","John"],"index":11981,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8372118473,"difficulty":1.8372118473}
{"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 Karon. Jean'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 that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karon","David","Jean"],"index":23140,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994171858,"difficulty":0.0005828142}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rodney's card is shown to Jorge. Paul's card is shown to Jorge. Rodney's card is shown to Rodney. Rodney's card is shown to Paul. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Jorge does not know whether Jorge picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jorge can now know whether Rodney can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jorge","Rodney","Paul"],"index":50832,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9241300225,"difficulty":1.9241300225}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. William's card is shown to William. 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:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(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) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Maria can now know whether William can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maria","William"],"index":14129,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7471794486,"difficulty":0.2528205514}
{"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 Eleanor. Linda's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Linda picked a red card. It is publicly announced that Eleanor picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Jessie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessie","Eleanor","Linda"],"index":46242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984205961,"difficulty":0.0015794039}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Bobbi. Bobbi's card is shown to Charles. 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:3 Agentb:1 Agentc: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 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bobbi can now know whether Ashley picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bobbi","Charles","Ashley"],"index":24697,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8810706735,"difficulty":0.1189293265}
{"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 Johnnie. It is publicly announced that someone picked a red card. It is publicly announced that Johnnie does not know whether Johnnie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Johnnie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Johnnie","Bill"],"index":38728,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994571805,"difficulty":0.0005428195}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Judy. Judy's card is shown to Amy. Amy's card is shown to Amy. Judy's card is shown to Peggy. Amy's card is shown to Peggy. Peggy's card is shown to Peggy. It is publicly announced that someone picked a red card. It is publicly announced that Peggy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Amy can now know that Peggy can know that Peggy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Judy","Amy","Peggy"],"index":9527,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9237998724,"difficulty":0.0762001276}
{"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 Juan. William's card is shown to Juan. Gerald's card is shown to Gerald. Loyd's card is shown to Gerald. William's card is shown to Gerald. Juan's card is shown to Loyd. Loyd'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 nobody picked a red card. It is publicly announced that William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] Agentc knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Loyd can now know that William can know that Juan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juan","Gerald","Loyd","William"],"index":13488,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9735741615,"difficulty":0.0264258385}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Wayne. Patricia's card is shown to Wayne. John's card is shown to John. John's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Wayne 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 whether 1) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"John can now know that Patricia can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wayne","John","Patricia"],"index":16659,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994071722,"difficulty":0.0005928278}
{"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 Robert. Colette's card is shown to Robert. Jarrett's card is shown to Jarrett. Colette's card is shown to Colette. It is publicly announced that someone picked a red card. It is publicly announced that Colette does not know whether Robert picked a red card. It is publicly announced that Jarrett does not know whether Jeanette picked a red card. It is publicly announced that Colette knows whether someone picked a red card. It is publicly announced that Colette does not know whether Jeanette 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] Agentb knows whether (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Jarrett can now know whether Colette can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Jarrett","Colette","Jeanette"],"index":31482,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9337193966,"difficulty":0.0662806034}
{"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 Carina. Kenneth's card is shown to Carina. Jerry's card is shown to Jerry. Carina's card is shown to Jacquelyn. Kenneth's card is shown to Jacquelyn. It is publicly announced that someone picked a red card. It is publicly announced that Carina does not know whether or not everyone picked a red card. It is publicly announced that Kenneth does not know whether Jacquelyn picked a red card. It is publicly announced that Kenneth does not know whether Jacquelyn 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:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kenneth can now know whether Jerry can know that Carina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carina","Jerry","Kenneth","Jacquelyn"],"index":3288,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8683428764,"difficulty":0.1316571236}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Desiree's card is shown to Desiree. Stacy's card is shown to Timothy. Stacy's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Stacy picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Stacy can now know that Stacy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Desiree","Stacy","Timothy","Robert"],"index":33162,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6059550643,"difficulty":0.3940449357}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randolph's card is shown to William. William's card is shown to Ronald. Ronald's card is shown to Sharon. William's card is shown to Randolph. Randolph's card is shown to Randolph. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether Sharon 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: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 whether (~(1|2|3|4)))","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":"Randolph can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Ronald","Sharon","Randolph"],"index":21539,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994167089,"difficulty":0.0005832911}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Michael. Laura's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Michael picked a red card. It is publicly announced that Laura does not know whether Michael picked a red card. It is publicly announced that Michael 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 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Laura can now know whether Michael can know that Laura picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Laura"],"index":49359,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9893658161,"difficulty":0.0106341839}
{"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. Cindy's card is shown to Charles. Charles's card is shown to Cindy. Cindy's card is shown to Cindy. Kevin's card is shown to Cindy. Charles'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 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that Kevin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Cindy","Kevin"],"index":19148,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9603323936,"difficulty":0.0396676064}
{"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. Roxie's card is shown to Jennifer. Jennifer's card is shown to Roxie. Mary's card is shown to Roxie. Roxie's card is shown to Roxie. 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) ] (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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Mary","Roxie"],"index":57941,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994217157,"difficulty":0.0005782843}
{"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 Christine. Christine's card is shown to Norma. Ashley's card is shown to Eric. Norma's card is shown to Eric. Eric's card is shown to Eric. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Norma can now know whether Norma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ashley","Christine","Norma","Eric"],"index":14955,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8984748721,"difficulty":1.8984748721}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Julie. Ronald's card is shown to John. Julie's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 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:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that Ronald can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julie","John","Ronald"],"index":64095,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988474846,"difficulty":0.0011525154}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jan's card is shown to Marion. Deborah's card is shown to Marion. Marion's card is shown to Jan. Jan's card is shown to Deborah. Deborah's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Deborah picked a red card. It is publicly announced that Marion does not know whether or not everyone picked a red card. It is publicly announced that Marion knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jan can now know that Deborah can know that Jan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marion","Jan","Deborah"],"index":15644,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5796414614,"difficulty":0.4203585386}
{"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. Tammy's card is shown to David. David's card is shown to Tammy. Tammy's card is shown to Tammy. It is publicly announced that someone picked a red card. It is publicly announced that Tammy knows whether someone picked a red card. It is publicly announced that Tammy 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 whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Tammy can now know that David can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Tammy"],"index":29845,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993557334,"difficulty":0.0006442666}
{"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. Doris's card is shown to John. Doris's card is shown to Michael. John's card is shown to Michael. Raymond's card is shown to Michael. John's card is shown to Raymond. Michael'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 Agentb:1 Agentc:1,2,4 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:1 Agentb:1 Agentc:1,2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymond can now know whether John can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doris","John","Michael","Raymond"],"index":7946,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993801117,"difficulty":0.0006198883}
{"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 Melissa. Alvin's card is shown to Melissa. Camille's card is shown to Melissa. Christina's card is shown to Alvin. Camille's card is shown to Alvin. Christina's card is shown to Camille. It is publicly announced that someone picked a red card. It is publicly announced that Alvin does not know whether Melissa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Melissa can now know whether Melissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Melissa","Christina","Alvin","Camille"],"index":58500,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6376388073,"difficulty":1.6376388073}
{"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. Michael's card is shown to Michael. Muriel's card is shown to Muriel. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rose can now know whether Max picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rose","Michael","Max","Muriel"],"index":45273,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9789392948,"difficulty":0.0210607052}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Daniel's card is shown to Brenda. Sheri's card is shown to Nancy. Brenda's card is shown to Daniel. Sheri's card is shown to Daniel. Nancy's card is shown to Sheri. It is publicly announced that someone picked a red card. It is publicly announced that Sheri does not know whether Brenda picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Sheri does not know whether Daniel 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) ] Agentc knows whether (Agentd 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":"Daniel can now know whether Sheri can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Nancy","Daniel","Sheri"],"index":3335,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993915558,"difficulty":0.0006084442}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Jean. Jean's card is shown to Larae. Larae's card is shown to Larae. It is publicly announced that someone picked a red card. It is publicly announced that Jean does not know whether Larae picked a red card. It is publicly announced that Carl does not know whether Carl 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) ] Agentb knows whether (Agenta knows whether 1)","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":"Carl can now know whether Jean can know whether Jean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jean","Carl","Larae"],"index":50954,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977243543,"difficulty":0.0022756457}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beula's card is shown to Beula. Bernice's card is shown to Anthony. Anthony's card is shown to Bernice. Bernice's card is shown to Bernice. It is publicly announced that someone picked a red card. It is publicly announced that Bernice knows whether or not nobody picked a red card. It is publicly announced that Bernice picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] 0","hypothesis":"Beula can now know that Anthony can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beula","Anthony","Bernice"],"index":25244,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994261265,"difficulty":0.0005738735}
{"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 Ericka. Page's card is shown to Ericka. Larry's card is shown to Larry. Marty's card is shown to Larry. Page's card is shown to Marty. Marty's card is shown to Page. It is publicly announced that someone picked a red card. It is publicly announced that Page does not know whether Larry picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Marty can now know whether Page can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ericka","Larry","Marty","Page"],"index":27457,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9778149724,"difficulty":0.0221850276}
{"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 Robert. Robert's card is shown to Ronald. Ronald's card is shown to Ronald. Thomas's card is shown to Ronald. Thomas's card is shown to Thomas. 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:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know that Thomas can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Ronald","Thomas","Kathy"],"index":19602,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989252687,"difficulty":0.0010747313}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherri's card is shown to Nicole. Sherri's card is shown to Kathleen. Dorothy's card is shown to Kathleen. Dorothy's card is shown to Dorothy. 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 Kathleen knows whether Sherri picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kathleen can now know whether Nicole can know that Sherri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicole","Kathleen","Sherri","Dorothy"],"index":46850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9074974656,"difficulty":0.0925025344}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Maria. Rose's card is shown to Maria. Maria'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:2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marvin can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maria","Marvin","Rose","Oscar"],"index":15387,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992631078,"difficulty":0.0007368922}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Blaine's card is shown to Blaine. Robert's card is shown to Blaine. Robert's card is shown to Robert. Max's card is shown to Robert. Robert'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 Blaine picked a red card. It is publicly announced that Blaine does not know whether Max picked a red card. It is publicly announced that Max 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:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Max can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Blaine","Robert","Max"],"index":59578,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992909431,"difficulty":0.0007090569}
{"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. Mildred's card is shown to Richard. Richard's card is shown to Mildred. Mildred'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:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that Albert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Mildred","Albert"],"index":7891,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992743134,"difficulty":0.0007256866}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucille's card is shown to Lucille. Lucille's card is shown to Ryan. It is publicly announced that someone picked a red card. It is publicly announced that Lucille does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 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 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lucille can now know whether Ryan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucille","Ryan","Nicole"],"index":2306,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994354844,"difficulty":0.0005645156}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Carol. Carol's card is shown to Rachel. 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:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Arthur can now know whether Arthur picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Rachel","Arthur"],"index":58257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8809667826,"difficulty":0.1190332174}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Joanne. Walter's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Joanne 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 whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Walter can now know whether Joanne can know whether Joanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joanne","Walter"],"index":49123,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9937108755,"difficulty":0.0062891245}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Marie's card is shown to Angela. Angela's card is shown to Gerald. Gerald's card is shown to Gerald. Angela's card is shown to Diana. Angela'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:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gerald can now know that Angela can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Gerald","Diana","Marie"],"index":43864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9714354277,"difficulty":0.0285645723}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alejandro's card is shown to Helen. Alejandro's card is shown to Mark. Mark's card is shown to Alejandro. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know that Helen can know whether Helen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","Mark","Alejandro"],"index":62643,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5171253085,"difficulty":1.5171253085}
{"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. Rafael's card is shown to Mitzi. Mitzi's card is shown to Mitzi. Tyrone's card is shown to Tyrone. Rafael's card is shown to Richard. Tyrone'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:1 Agentb:1,2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rafael can now know that Mitzi picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rafael","Mitzi","Tyrone","Richard"],"index":18039,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978086352,"difficulty":0.0021913648}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Minnie's card is shown to Minnie. Rick's card is shown to Minnie. Leona's card is shown to Leona. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Minnie can now know that Leona picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Minnie","Leona","Rick"],"index":9209,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976862669,"difficulty":0.0023137331}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heidi's card is shown to Heidi. Deena's card is shown to Michael. Linda's card is shown to Deena. Michael's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Heidi knows whether or not nobody picked a red card. It is publicly announced that Michael 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))) ] Agentd knows that (Agentc knows whether 2)","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":"Linda can now know that Deena can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heidi","Michael","Deena","Linda"],"index":40097,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5469205379,"difficulty":0.4530794621}
{"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 Brandon. Sharon's card is shown to Sharon. Joseph's card is shown to Sharon. Brandon's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Sharon 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 ] (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) ] [ ! 2 ] 0","hypothesis":"Brandon can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brandon","Sharon","Joseph"],"index":2952,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9401951432,"difficulty":0.0598048568}
{"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 Cythia. Aaron's card is shown to Cythia. Joan's card is shown to Joan. Joan's card is shown to Cindy. Cindy's card is shown to Cindy. Aaron's card is shown to Cindy. Cythia's card is shown to Aaron. Joan'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:2,4 Agentb:2 Agentc:2,3,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2,3,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Aaron can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cythia","Joan","Cindy","Aaron"],"index":11658,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993166924,"difficulty":0.0006833076}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alejandro's card is shown to Alejandro. Alejandro's card is shown to Stephanie. Stephanie's card is shown to Stephanie. It is publicly announced that someone picked a red card. It is publicly announced that Alejandro does not know whether or not everyone picked a red card. It is publicly announced that Stephanie picked a black card. It is publicly announced that Stephanie knows whether or not nobody 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)) ] [ ! ~(2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Alejandro can now know whether Stephanie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alejandro","Stephanie"],"index":31687,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994748235,"difficulty":0.0005251765}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Johnny. 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:1 Agentb: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 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Johnny can now know that Lacey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Linda","Jane","Lacey"],"index":53404,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980959296,"difficulty":0.0019040704}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nilsa's card is shown to Jerry. Latoya's card is shown to Bobby. Jerry'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:4 Agentb:3 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:4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know that Latoya picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Bobby","Latoya","Nilsa"],"index":30671,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971495271,"difficulty":0.0028504729}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caroline's card is shown to Nathan. Shannon's card is shown to Shannon. Nathan's card is shown to Donald. Shannon's card is shown to Donald. Shannon's card is shown to Caroline. It is publicly announced that someone picked a red card. It is publicly announced that Shannon picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Caroline can now know that Nathan can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nathan","Shannon","Donald","Caroline"],"index":60513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984916449,"difficulty":0.0015083551}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ola's card is shown to Ola. Angela's card is shown to Ola. Ola's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Ola can now know whether Angela can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ola","Angela"],"index":19113,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992770553,"difficulty":0.0007229447}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Shannon. Sherri's card is shown to Shannon. Sherri's card is shown to Paige. Sherri's card is shown to Kristen. Kristen's card is shown to Sherri. Sherri's card is shown to Sherri. 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:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristen can now know that Shannon can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shannon","Paige","Kristen","Sherri"],"index":53826,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993643165,"difficulty":0.0006356835}
{"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 Diane. Diane's card is shown to Tammy. Tammy's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Diane does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Samuel can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diane","Tammy","Samuel"],"index":36525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9720007777,"difficulty":0.0279992223}
{"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. Brenda's card is shown to James. Bryan's card is shown to James. Brenda's card is shown to Brenda. James'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:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Brenda","Bryan"],"index":45375,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9937791228,"difficulty":0.0062208772}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brett's card is shown to Jannie. Madeline's card is shown to Jannie. Brett's card is shown to Brett. It is publicly announced that someone picked a red card. It is publicly announced that Jannie does not know whether Jannie 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) ] (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) ] 0","hypothesis":"Jannie can now know whether Madeline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jannie","Brett","Madeline"],"index":2327,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9914193153,"difficulty":1.9914193153}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gracie's card is shown to Shannon. Shannon's card is shown to Gracie. It is publicly announced that someone picked a red card. It is publicly announced that Gracie picked a red card. It is publicly announced that Shannon 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) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Shannon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shannon","Gracie"],"index":21931,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994561076,"difficulty":0.0005438924}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Georgiana's card is shown to Daphne. Georgiana's card is shown to Georgiana. Angela's card is shown to Georgiana. Georgiana'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 Agentb:2,3 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:2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Georgiana can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daphne","Georgiana","Angela"],"index":51557,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994383454,"difficulty":0.0005616546}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Jack. Jack's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Julie knows whether someone picked a red card. It is publicly announced that Julie does not know whether Julie 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":"Julie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jack","Julie"],"index":14909,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994269609,"difficulty":0.0005730391}
{"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 Ronald. Ronald's card is shown to Lawrence. Guillermo's card is shown to Lawrence. Guillermo's card is shown to Guillermo. Guillermo's card is shown to Jessica. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lawrence can now know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Lawrence","Guillermo","Jessica"],"index":32872,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9927005172,"difficulty":0.0072994828}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Albert. Billy's card is shown to Carmen. James's card is shown to Carmen. Albert's card is shown to Billy. James's card is shown to Billy. James'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:3 Agentb:3,4 Agentc:1,4 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:3,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Albert can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Carmen","Billy","James"],"index":19078,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983479977,"difficulty":0.0016520023}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eddie's card is shown to Eddie. Gladys'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:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eddie can now know that Gladys can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gladys","Eddie","Joseph"],"index":8240,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992750287,"difficulty":0.0007249713}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sean's card is shown to Lisa. Richard's card is shown to Richard. Richard's card is shown to Karrie. Sean's card is shown to Karrie. Lisa's card is shown to Sean. Richard's card is shown to Sean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Karrie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Richard","Karrie","Sean"],"index":50673,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993077517,"difficulty":0.0006922483}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Edwin. Gertrude's card is shown to Gertrude. Jonathan's card is shown to Gertrude. Lan's card is shown to Lan. Edwin's card is shown to Jonathan. Gertrude'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 Lan picked a red card. It is publicly announced that Gertrude picked a black card. It is publicly announced that Gertrude knows whether Jonathan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Jonathan can now know that Lan can know that Gertrude picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edwin","Gertrude","Lan","Jonathan"],"index":51625,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9636382461,"difficulty":0.0363617539}
{"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 Ricky. Ricky's card is shown to Craig. Craig's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Ricky picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Earl 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 whether (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":"Ricky can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wallace","Ricky","Craig","Earl"],"index":18961,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994072914,"difficulty":0.0005927086}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Scott. Scott's card is shown to Amanda. Christinia's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that Scott 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 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Christinia can now know that Scott can know whether Amanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Christinia","Amanda"],"index":19397,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5220459104,"difficulty":0.4779540896}
{"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 Lisa. 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:3 Agentb: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:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know that Herman can know whether Lisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Herman","Lisa","William"],"index":65942,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9879435301,"difficulty":0.0120564699}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gene's card is shown to Gene. John's card is shown to Gene. Roger's card is shown to Gene. John's card is shown to John. Gene's card is shown to Roger. John's card is shown to Roger. 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:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gene can now know that Roger can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gene","John","Roger"],"index":18916,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9886335135,"difficulty":0.0113664865}
{"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 Mildred. Mathew's card is shown to Darryl. Randy's card is shown to Darryl. Darryl's card is shown to Darryl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3,4 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:1 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mathew can now know that Mildred can know whether Randy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Mathew","Randy","Darryl"],"index":48481,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9871129394,"difficulty":0.0128870606}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valencia's card is shown to Jon. Jon's card is shown to Valencia. Valencia's card is shown to Valencia. Cassandra's card is shown to Valencia. Valencia's card is shown to Cassandra. It is publicly announced that someone picked a red card. It is publicly announced that Cassandra knows whether someone picked a red card. It is publicly announced that Valencia picked a black card. It is publicly announced that Valencia picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] [ ! ~(2) ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Cassandra can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jon","Valencia","Cassandra"],"index":47595,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9813882113,"difficulty":0.0186117887}
{"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 Ruth. Ray's card is shown to Julie. Pamela's card is shown to Julie. Pamela's card is shown to Pamela. 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 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:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Julie can now know whether Pamela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ruth","Ray","Julie","Pamela"],"index":2975,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9739528298,"difficulty":0.0260471702}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelley's card is shown to Shelley. June's card is shown to June. Charles's card is shown to Jeremy. 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:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shelley can now know that Jeremy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shelley","June","Jeremy","Charles"],"index":22923,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993914366,"difficulty":0.0006085634}
{"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. 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 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Margaret can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Margaret","Mary"],"index":54923,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989639521,"difficulty":0.0010360479}
{"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 Luisa. Alma's card is shown to Kathleen. It is publicly announced that someone picked a red card. It is publicly announced that Luisa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agenta 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) ] [ ! 1 ] 0","hypothesis":"Alma can now know whether Luisa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Luisa","Alma","Kathleen"],"index":14847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994569421,"difficulty":0.0005430579}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Jeremy's card is shown to Anthony. Anthony's card is shown to Jeremy. Maurice's card is shown to Jeremy. Stanley's card is shown to Jeremy. Maurice's card is shown to Maurice. Stanley's card is shown to Maurice. Anthony's card is shown to Stanley. 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 Maurice knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Anthony can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anthony","Jeremy","Maurice","Stanley"],"index":56456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994365573,"difficulty":0.0005634427}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwardo's card is shown to Dorothy. Christina's card is shown to Dorothy. Edwardo'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:1,2 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christina can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edwardo","Christina","Dorothy","Glenn"],"index":55016,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999296546,"difficulty":0.000703454}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Vivian. Cynthia's card is shown to Vivian. Vivian's card is shown to Cynthia. Stefanie's card is shown to Cynthia. Leila's card is shown to Cynthia. Stefanie's card is shown to Stefanie. Leila's card is shown to Stefanie. Vivian's card is shown to Leila. 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 Stefanie knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Leila can now know whether Vivian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vivian","Cynthia","Stefanie","Leila"],"index":23720,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9968083501,"difficulty":0.0031916499}
{"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. Josie's card is shown to Mary. Michael's card is shown to Kyle. Mary's card is shown to Josie. Kyle's card is shown to Michael. Josie's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Josie can now know whether Mary can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Kyle","Josie","Michael"],"index":55686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986265898,"difficulty":0.0013734102}
{"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 John. John'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 John knows whether Maria picked a red card. It is publicly announced that Maria knows whether Maria 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 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know that Maria can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Maria"],"index":15673,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9404801726,"difficulty":0.0595198274}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helene's card is shown to Xavier. Shirley's card is shown to Xavier. Ana's card is shown to Xavier. Helene's card is shown to Helene. Helene's card is shown to Shirley. Shirley's card is shown to Shirley. Shirley's card is shown to Ana. 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:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helene can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Xavier","Helene","Shirley","Ana"],"index":30237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994071722,"difficulty":0.0005928278}
{"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 Kenneth. Kenneth's card is shown to Kimberly. Janice's card is shown to Kimberly. Kenneth's card is shown to Janice. Kimberly's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Lawrence 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) ] (Agentc knows that 1)","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":"Lawrence can now know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Kimberly","Lawrence","Janice"],"index":32046,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9939243197,"difficulty":0.0060756803}
{"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 John. John's card is shown to Rosalind. Rosalind's card is shown to Rosalind. 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) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"John can now know that Rosalind picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Rosalind"],"index":44988,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952558875,"difficulty":0.0047441125}
{"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 Gregory. Joyce's card is shown to Gregory. Gregory's card is shown to Kevin. Alan'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:2,3 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know whether Joyce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gregory","Kevin","Joyce","Alan"],"index":44077,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9133848548,"difficulty":1.9133848548}
{"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. Kyle's card is shown to Steven. Steven's card is shown to Kyle. 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 Kyle picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Kyle can now know whether Steven can know whether Kyle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Kyle"],"index":18415,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986482263,"difficulty":0.0013517737}
{"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 John. Lois's card is shown to Lois. William's card is shown to Lois. 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:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether John can know that Lois picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Lois","William"],"index":53840,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9772198796,"difficulty":0.0227801204}
{"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 Annette. Robert's card is shown to Robert. Robert's card is shown to Stephen. Stephen'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:4 Agentb:3 Agentc: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:4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alice","Annette","Robert","Stephen"],"index":56574,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9865925908,"difficulty":0.0134074092}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Greg's card is shown to Greg. Diane's card is shown to Greg. Greg's card is shown to Diane. Charlotte's card is shown to Travis. Diane's card is shown to Travis. Travis's card is shown to Travis. 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) ] Agentc knows whether (Agentb knows that 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":"Diane can now know whether Greg can know that Travis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charlotte","Greg","Diane","Travis"],"index":56441,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9206478596,"difficulty":0.0793521404}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candace's card is shown to James. Lynn's card is shown to Nathaniel. Nathaniel's card is shown to Nathaniel. It is publicly announced that someone picked a red card. It is publicly announced that Candace does not know whether or not everyone picked a red card. It is publicly announced that James picked a red card. It is publicly announced that Lynn picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(2) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(2) ] 0","hypothesis":"Lynn can now know whether Candace picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Candace","Lynn","James","Nathaniel"],"index":24582,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.936091423,"difficulty":0.063908577}
{"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. Robby's card is shown to John. Robby's card is shown to Valerie. Valerie's card is shown to Robby. Christopher's card is shown to Robby. 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:1,4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Valerie can now know that Christopher can know whether Valerie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Valerie","Christopher","Robby"],"index":60304,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6559253335,"difficulty":1.6559253335}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carole's card is shown to Carole. Carole's card is shown to Joan. Carole's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Carole knows whether Carole picked a red card. It is publicly announced that Carole knows whether Carole picked a red card. It is publicly announced that Carole 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 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Patricia can now know whether Carole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carole","Joan","Patricia"],"index":55597,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.98981148,"difficulty":0.01018852}
{"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 Laura. Dorothea's card is shown to Dorothea. Jennifer's card is shown to Dorothea. It is publicly announced that someone picked a red card. It is publicly announced that Laura knows whether or not everyone picked a red card. 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":"Laura can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","Dorothea","Jennifer"],"index":1913,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990654588,"difficulty":0.0009345412}
{"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 Chelsea. Clayton's card is shown to Chelsea. Chelsea's card is shown to Agnes. Clayton's card is shown to Agnes. Agnes's card is shown to James. Clayton's card is shown to James. Chelsea's card is shown to Clayton. 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 that 3)","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":"Agnes can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chelsea","Agnes","James","Clayton"],"index":12990,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984410405,"difficulty":0.0015589595}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nick's card is shown to Helen. Helen's card is shown to Jason. Nick's card is shown to Jason. Jason's card is shown to Nick. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether Helen picked a red card. It is publicly announced that Helen knows whether Nick 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) ] [ ! (Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Helen can now know that Helen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Jason","Nick"],"index":41150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9606612325,"difficulty":0.0393387675}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julius's card is shown to Beverly. Mindy's card is shown to Beverly. Julius's card is shown to Mindy. Beverly's card is shown to Mindy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julius can now know that Beverly can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julius","Beverly","Mindy"],"index":28959,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987969398,"difficulty":0.0012030602}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. John's card is shown to Kathleen. Allen's card is shown to Allen. John's card is shown to Allen. Kathleen'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 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 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":"John can now know whether Allen can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Allen","John"],"index":56414,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984257221,"difficulty":0.0015742779}
{"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 Reed. Tom's card is shown to Reed. Reed's card is shown to Tom. Tom's card is shown to Tom. Melissa's card is shown to Tom. Jeffrey's card is shown to Melissa. 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:1,3 Agentb:2,3,4 Agentc: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:1,3 Agentb:2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tom can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Reed","Tom","Melissa"],"index":4156,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989706278,"difficulty":0.0010293722}
{"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 Melissa. Melissa's card is shown to Martha. Martha's card is shown to Martha. Martha's card is shown to Glenn. Glenn'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:1 Agentb:1,2 Agentc: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:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melissa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Martha","Moon","Glenn"],"index":17837,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989901185,"difficulty":0.0010098815}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Percy's card is shown to Wayne. Marie's card is shown to Wayne. Percy's card is shown to Percy. Wayne's card is shown to Marie. Edith's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Wayne picked a black card. It is publicly announced that Marie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! 3 ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! 3 ] 0","hypothesis":"Wayne can now know whether Percy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","Percy","Marie","Edith"],"index":59349,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9885643125,"difficulty":0.0114356875}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anita's card is shown to Andrew. Andrew's card is shown to Rick. Anita's card is shown to Rick. 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 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Connie can now know whether Connie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Connie","Anita","Rick"],"index":7742,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955685735,"difficulty":0.0044314265}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heidi's card is shown to Mary. Billy's card is shown to Heidi. Billy's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Billy knows whether or not nobody picked a red card. It is publicly announced that Heidi 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 ] (Agenta knows whether 1)","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":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Heidi","Billy","Denise"],"index":13543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9141896367,"difficulty":0.0858103633}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqualine's card is shown to Jacqualine. Randall's card is shown to Jacqualine. Jacqualine's card is shown to Melody. Randall's card is shown to Melody. Melody's card is shown to Margarita. Margarita's card is shown to Margarita. Melody's card is shown to Randall. It is publicly announced that someone picked a red card. It is publicly announced that Melody 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))) ] Agentd knows whether (Agentb knows whether 3)","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":"Randall can now know whether Melody can know whether Margarita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jacqualine","Melody","Margarita","Randall"],"index":58002,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989259839,"difficulty":0.0010740161}
{"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 Carlos. Carlene's card is shown to Robert. Robert's card is shown to Carlene. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Carlos can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carlos","Robert","Carlene"],"index":54972,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9773311019,"difficulty":0.0226688981}
{"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 John. 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 that (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 that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","John"],"index":53417,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994177818,"difficulty":0.0005822182}
{"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. Lisa's card is shown to John. Dorothy's card is shown to John. Augusta's card is shown to Lisa. John's card is shown to Dorothy. John's card is shown to Augusta. Lisa's card is shown to Augusta. Dorothy's card is shown to Augusta. Augusta's card is shown to Augusta. It is publicly announced that someone picked a red card. It is publicly announced that Lisa does not know whether Dorothy 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) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:1 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Augusta can now know whether Lisa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Lisa","Dorothy","Augusta"],"index":24959,"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). Vincent's card is shown to Beverly. Robert's card is shown to Vincent. Delmy's card is shown to Robert. Robert's card is shown to Delmy. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Beverly does not know whether Beverly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Delmy can now know whether Vincent can know whether Delmy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Vincent","Robert","Delmy"],"index":4631,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9976497293,"difficulty":0.0023502707}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annette's card is shown to Gerald. Annette's card is shown to Linda. Annette's card is shown to Annette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 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:4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Linda can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerald","Linda","Robert","Annette"],"index":67416,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9684076905,"difficulty":1.9684076905}
{"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 Barry. Barry's card is shown to Charles. Charles's card is shown to Charles. John's card is shown to Billie. Billie's card is shown to Billie. 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:2 Agentb:1,2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Barry can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barry","Charles","John","Billie"],"index":65521,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932923317,"difficulty":0.0067076683}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristine's card is shown to Cori. Howard's card is shown to Howard. Cori's card is shown to Michele. Howard's card is shown to Michele. Cristine's card is shown to Cristine. 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) ] (Agentd knows whether 2)","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":"Cristine can now know whether Howard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cori","Howard","Michele","Cristine"],"index":44777,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8150131106,"difficulty":0.1849868894}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Julie. Nancy's card is shown to Tonia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tonia can now know whether Julie can know whether Julie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julie","Tonia","Nancy","Jason"],"index":13384,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5044658184,"difficulty":1.5044658184}
{"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 Virginia. Virginia's card is shown to Virginia. Zelma's card is shown to Virginia. Chad's card is shown to Zelma. Sarah's card is shown to Zelma. Sarah's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Sarah 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 whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Zelma can now know whether Chad can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chad","Virginia","Zelma","Sarah"],"index":59049,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.935518682,"difficulty":0.064481318}
{"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 Ryan. Roman's card is shown to Ryan. Mark's card is shown to Mark. Roman's card is shown to Mark. Roman's card is shown to Roman. Amanda's card is shown to Roman. Amanda's card is shown to Amanda. 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 everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Mark can now know that Amanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ryan","Mark","Roman","Amanda"],"index":57973,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9911245704,"difficulty":0.0088754296}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Duane. Stanley's card is shown to Duane. Sol's card is shown to Stanley. Rocky's card is shown to Sol. It is publicly announced that someone picked a red card. It is publicly announced that Duane does not know whether or not everyone picked a red card. It is publicly announced that Stanley knows whether Duane picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Duane can now know that Stanley can know whether Stanley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Duane","Stanley","Rocky","Sol"],"index":48399,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8113360405,"difficulty":0.1886639595}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shantelle's card is shown to Derrick. Mary's card is shown to Derrick. Derrick's card is shown to Shantelle. Derrick's card is shown to Mickey. Shantelle's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Derrick does not know whether Derrick picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Shantelle can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Derrick","Shantelle","Mickey","Mary"],"index":40282,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990109205,"difficulty":0.0009890795}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Bonnie. Bonnie's card is shown to Brittany. Brittany's card is shown to Brittany. Brittany's card is shown to Christi. 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) ] Agenta knows whether (Agentc knows that (1|2|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":"Bonnie can now know whether Christi can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Brittany","Christi"],"index":2237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994223118,"difficulty":0.0005776882}
{"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 Nancy. Marcene's card is shown to Marcene. Nancy's card is shown to Randy. Randy's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that Randy does not know whether Marcene picked a red card. It is publicly announced that Randy knows whether Nancy 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 2) ] [ ! (Agentc knows whether 1) ] (Agentb knows whether 1)","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 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Marcene can now know whether Nancy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Marcene","Randy"],"index":57856,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9751098752,"difficulty":1.9751098752}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Errol's card is shown to Errol. Jean's card is shown to Roger. Jean's card is shown to Lenora. Errol's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Lenora picked a red card. It is publicly announced that Lenora does not know whether Roger 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) ] Agentb knows whether (Agentd knows that 1)","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":"Roger can now know whether Jean can know that Errol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Errol","Roger","Lenora","Jean"],"index":37877,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9133840799,"difficulty":1.9133840799}
{"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 Carmen. Alice's card is shown to Carmen. David's card is shown to David. Alice's card is shown to David. Alice's card is shown to Joseph. David's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether David 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) ] Agentc knows whether (Agentd knows whether 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":"Joseph can now know whether Alice can know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carmen","David","Joseph","Alice"],"index":14906,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998723805,"difficulty":0.001276195}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Elizabeth. Douglas's card is shown to Douglas. Elizabeth's card is shown to Rosa. Rosa's card is shown to Rosa. 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:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know that Rosa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Douglas","Rosa"],"index":32411,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9938515425,"difficulty":0.0061484575}
{"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 Julius. Julius's card is shown to Kenneth. Julius's card is shown to Christy. It is publicly announced that someone picked a red card. It is publicly announced that Julius does not know whether or not everyone picked a red card. It is publicly announced that Julius does not know whether Julius picked a red card. It is publicly announced that Christy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Christy can now know whether Kenneth can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julius","Kenneth","Christy"],"index":23563,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994571805,"difficulty":0.0005428195}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Becky's card is shown to Becky. Kevin's card is shown to Becky. Kevin's card is shown to Kevin. Douglas's card is shown to Douglas. 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 whether (Agentb knows whether (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":"Becky can now know whether Kevin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Becky","Kevin","Douglas"],"index":46989,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7713848352,"difficulty":1.7713848352}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lenora's card is shown to Kathryn. Kathryn's card is shown to Ruth. Ruth's card is shown to Ruth. Kathryn's card is shown to Scott. Ruth's card is shown to Scott. Kathryn's card is shown to Lenora. Lenora's card is shown to Lenora. It is publicly announced that someone picked a red card. It is publicly announced that Ruth picked a black card. It is publicly announced that Ruth does not know whether Lenora 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)) ] Agentb knows whether (Agenta knows that (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":"Ruth can now know whether Kathryn can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Ruth","Scott","Lenora"],"index":35635,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9944850802,"difficulty":0.0055149198}
{"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 Scott. Carolyn's card is shown to Carolyn. 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 Carolyn knows whether Scott 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 that (~(1|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":"Scott can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Scott","Carolyn"],"index":2934,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949132204,"difficulty":0.0050867796}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jewell's card is shown to Charles. Christopher's card is shown to Christopher. Jewell's card is shown to Christopher. Charles's card is shown to Jewell. 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) ] (Agenta knows that 1)","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":"Charles can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Dennis","Christopher","Jewell"],"index":9732,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940683842,"difficulty":0.0059316158}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irving's card is shown to Irving. Laurence's card is shown to Laurence. Douglass's card is shown to Laurence. Douglass's card is shown to Douglass. 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) ] (Agenta knows that 2)","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":"Irving can now know that Laurence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Irving","Laurence","Douglass"],"index":15666,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962294698,"difficulty":0.0037705302}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elmer's card is shown to Janelle. Elmer's card is shown to Elmer. It is publicly announced that someone picked a red card. It is publicly announced that Elmer does not know whether or not everyone picked a red card. It is publicly announced that Janelle knows whether Elmer picked a red card. It is publicly announced that Elmer does not know whether Janelle picked a red card. It is publicly announced that Elmer knows whether or not nobody 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 2) ] [ ! ~(Agentb knows whether 1) ] [ ! (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) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Janelle can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Janelle","Elmer"],"index":42465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994685054,"difficulty":0.0005314946}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candice's card is shown to Candice. Paula's card is shown to Paula. It is publicly announced that someone picked a red card. It is publicly announced that Candice knows whether or not everyone picked a red card. It is publicly announced that Candice picked a black card. It is publicly announced that someone 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)) ] [ ! ~(1) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Candice can now know that Alison can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Candice","Alison","Paula"],"index":20951,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9427280426,"difficulty":0.0572719574}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Sonya. Brenda's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Sonya 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 2) ] (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 2) ] 0","hypothesis":"Sonya can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sonya","Brenda"],"index":65782,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999468863,"difficulty":0.000531137}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Tom. Susan's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Kim 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) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Susan can now know whether Kim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tom","Susan","Kim"],"index":66183,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.987711966,"difficulty":0.012288034}
{"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 Rick. Thomas's card is shown to Rick. Rick's card is shown to Carmelina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carmelina can now know whether Rick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rick","Carmelina","Thomas"],"index":16355,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9621990323,"difficulty":0.0378009677}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricky's card is shown to Ricky. Caroline's card is shown to Darius. It is publicly announced that someone picked a red card. It is publicly announced that Caroline does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Caroline can now know whether Caroline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Caroline","Ricky","Darius"],"index":20802,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8234527111,"difficulty":1.8234527111}
{"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 Christopher. Christopher's card is shown to Ann. James's card is shown to Ann. Ann'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 Christopher does not know whether or not everyone picked a red card. It is publicly announced that James 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 ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Thomas can now know that Christopher can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Thomas","Ann","James"],"index":44972,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998899579,"difficulty":0.001100421}
{"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 Roger. George's card is shown to Roger. Roger'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:1,3 Agentb: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:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know that Roger can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roger","Kevin","George","Timothy"],"index":53028,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993715882,"difficulty":0.0006284118}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathan's card is shown to Stephen. John's card is shown to Stephen. Stephen's card is shown to Irvin. Nathan's card is shown to John. Stephen'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:1,4 Agentb:2 Agentc:1,2,4 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:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nathan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nathan","Stephen","Irvin","John"],"index":47069,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951692224,"difficulty":0.0048307776}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheri's card is shown to Sheri. Denise's card is shown to Victor. Sheri's card is shown to Janelle. Janelle's card is shown to Janelle. 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:1,3 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:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sheri can now know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sheri","Victor","Janelle","Denise"],"index":42973,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917068481,"difficulty":0.0082931519}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to Sheri. Connie's card is shown to Curt. Curt's card is shown to Curt. Charlie's card is shown to Curt. Sheri's card is shown to Charlie. Charlie's card is shown to Charlie. It is publicly announced that someone picked a red card. It is publicly announced that Curt 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) ] 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:1,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Sheri can now know whether Connie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Connie","Sheri","Curt","Charlie"],"index":54755,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994339347,"difficulty":0.0005660653}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Regina's card is shown to Linda. Linda's card is shown to Regina. Jacquelyn's card is shown to Regina. Regina's card is shown to Jacquelyn. It is publicly announced that someone picked a red card. It is publicly announced that Regina 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 whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Linda can now know whether Jacquelyn can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Regina","Jacquelyn"],"index":31799,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9824403524,"difficulty":1.9824403524}
{"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. Rita's card is shown to Michelle. Olga's card is shown to Olga. Leif's card is shown to Olga. Rita's card is shown to Olga. Michelle's card is shown to Leif. Leif's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Rita knows whether or not nobody picked a red card. It is publicly announced that Rita picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Olga can now know whether Michelle can know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Olga","Leif","Rita"],"index":12225,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9709165096,"difficulty":1.9709165096}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glen's card is shown to Glen. Holly's card is shown to Glen. Glen's card is shown to Joseph. Holly's card is shown to Joseph. 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 Glen knows whether or not nobody picked a red card. It is publicly announced that Holly knows whether Joseph 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|2|3))","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":"Glen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Glen","Holly","Joseph"],"index":20401,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994571805,"difficulty":0.0005428195}
{"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. Marsha's card is shown to Marsha. 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: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":"Alice can now know that Marsha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alice","Marsha"],"index":9803,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959290624,"difficulty":0.0040709376}
{"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 James. Larry's card is shown to Gail. James's card is shown to Alexandra. Alexandra's card is shown to Alexandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Gail","Alexandra","Larry"],"index":2777,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988683462,"difficulty":0.0011316538}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Sherry. Michael's card is shown to Sherry. Wayne's card is shown to Wayne. Sherry's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Wayne 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sherry can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherry","Wayne","Michael"],"index":8177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9247772098,"difficulty":0.0752227902}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Jack. Beth's card is shown to Martin. Beth'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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beth can now know that Martin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","Beth","Martin","Cathy"],"index":56179,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984677434,"difficulty":0.0015322566}
{"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 Lee. Nicholas's card is shown to Lee. Tara's card is shown to Lee. Lee's card is shown to Nicholas. Nicholas's card is shown to Nicholas. Lee's card is shown to Tara. 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) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nicholas can now know whether Lee can know whether Nicholas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lee","Nicholas","Tara"],"index":61958,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982224107,"difficulty":0.0017775893}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martine's card is shown to Dorthy. Christopher's card is shown to Martine. Martine's card is shown to Jimmy. Jimmy's card is shown to Jimmy. Martine's card is shown to Christopher. 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) ] (Agentd 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":"Christopher can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dorthy","Martine","Jimmy","Christopher"],"index":22155,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994029999,"difficulty":0.0005970001}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Trisha's card is shown to John. Josephine's card is shown to Josephine. Josephine's card is shown to Maria. 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) ] (Agentb knows whether 1)","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":"John can now know whether Trisha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Trisha","John","Josephine","Maria"],"index":11172,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993811965,"difficulty":0.006188035}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Casey's card is shown to Casey. Seth's card is shown to Casey. Casey's card is shown to Seth. It is publicly announced that someone picked a red card. It is publicly announced that Seth does not know whether or not everyone picked a red card. It is publicly announced that Seth picked a black card. It is publicly announced that Seth knows whether someone 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)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Seth can now know that Casey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Casey","Seth"],"index":5626,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7801541686,"difficulty":1.7801541686}
{"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 Danielle. Anna's card is shown to Mark. Anna's card is shown to Claudia. Claudia's card is shown to Claudia. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Claudia picked a red card. It is publicly announced that Danielle 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:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Anna can now know that Danielle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danielle","Mark","Anna","Claudia"],"index":7699,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9708945751,"difficulty":0.0291054249}
{"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. Crystal's card is shown to Edward. Jimmy's card is shown to Mary. Mary's card is shown to Jimmy. Crystal's card is shown to Crystal. It is publicly announced that someone picked a red card. It is publicly announced that Edward does not know whether Jimmy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 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:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mary can now know that Crystal can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Mary","Jimmy","Crystal"],"index":57456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993490577,"difficulty":0.0006509423}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ariana's card is shown to Thelma. Alix's card is shown to Thelma. Thelma's card is shown to Alix. Alix's card is shown to Alix. Thelma's card is shown to Jeffrey. Ariana's card is shown to Jeffrey. Alix's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thelma can now know whether Alix picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thelma","Ariana","Alix","Jeffrey"],"index":57801,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6050261855,"difficulty":0.3949738145}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Missy. Robert's card is shown to Robert. Jean's card is shown to Robert. Jean's card is shown to Jean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","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":"Robert can now know that Jean picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Missy","Robert","Jean"],"index":9566,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9900553226,"difficulty":0.0099446774}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to Ryan. Myra's card is shown to Diane. Richard's card is shown to Myra. 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 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Myra can now know that Myra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","Diane","Myra","Richard"],"index":40342,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953559637,"difficulty":0.0046440363}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joline's card is shown to Joline. David's card is shown to Joline. David's card is shown to Carrie. Carrie's card is shown to Carrie. 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:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Joline can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joline","David","Carrie"],"index":1860,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
{"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 Jose. Reginia's card is shown to Reginia. Christopher's card is shown to Reginia. Tomasa's card is shown to Tomasa. Jose's card is shown to Christopher. Reginia'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 Tomasa picked a red card. It is publicly announced that Reginia picked a black card. It is publicly announced that Reginia knows whether Christopher picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Jose can now know that Christopher can know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Reginia","Tomasa","Christopher"],"index":22999,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.982363224,"difficulty":1.982363224}
{"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 Charles. Lonnie's card is shown to Lonnie. Kenneth's card is shown to Lonnie. Lonnie's card is shown to Kenneth. Linda'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:4 Agentb:2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether Kenneth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Lonnie","Kenneth","Linda"],"index":61684,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994130135,"difficulty":0.0005869865}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bessie's card is shown to Jessica. Barbara's card is shown to Bessie. It is publicly announced that someone picked a red card. It is publicly announced that Jessica does not know whether Jessica picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Barbara can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Barbara","Carlotta","Bessie"],"index":65907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999432385,"difficulty":0.000567615}
{"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. Megan's card is shown to Christopher. Shirley's card is shown to Shirley. Megan's card is shown to Shirley. Edna's card is shown to Shirley. Edna's card is shown to Edna. It is publicly announced that someone picked a red card. It is publicly announced that Shirley knows whether Megan picked a red card. It is publicly announced that Megan does not know whether Shirley picked a red card. It is publicly announced that Megan does not know whether Shirley picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Megan can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Shirley","Megan","Edna"],"index":56088,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8005000353,"difficulty":0.1994999647}
{"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 Lawrence. Lawrence's card is shown to Nicole. Rebecca's card is shown to Nicole. Nicole's card is shown to Nicole. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rebecca can now know that Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Rebecca","Nicole","Maria"],"index":577,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982162118,"difficulty":0.0017837882}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Michele. Michele's card is shown to Ronald. Kathryn's card is shown to Kathryn. It is publicly announced that someone picked a red card. It is publicly announced that Kathryn picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Michele can now know that Kathryn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michele","Ronald","Kathryn"],"index":31380,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8741513491,"difficulty":0.1258486509}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosie's card is shown to Samuel. Samuel's card is shown to Ralph. Patricia's card is shown to Ralph. Rosie's card is shown to Ralph. Samuel'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:4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","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":"Samuel can now know whether Ralph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Samuel","Ralph","Patricia","Rosie"],"index":51759,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975126982,"difficulty":0.0024873018}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Helen's card is shown to Jonathan. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Jonathan can now know that Helen can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Helen","Jonathan"],"index":17280,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8938529491,"difficulty":0.1061470509}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. Curtis's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Curtis does not know whether Arthur picked a red card. It is publicly announced that Curtis does not know whether Arthur picked a red card. It is publicly announced that Arthur does not know whether or not everyone picked a red card. It is publicly announced that Curtis does not know whether Arthur 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 that (Agenta knows whether 1)","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":"Arthur can now know that Curtis can know whether Curtis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Curtis","Arthur"],"index":1475,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7771441936,"difficulty":0.2228558064}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Amanda. Jessica's card is shown to Amanda. Amanda's card is shown to Jessica. Jessica's card is shown to Jessica. Johnny's card is shown to Jessica. Jessica's card is shown to Johnny. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 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:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amanda can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amanda","Jessica","Johnny"],"index":45963,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994087219,"difficulty":0.0005912781}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Justine. Justine's card is shown to Lois. Lois's card is shown to Lois. Leslie's card is shown to Victor. Victor's card is shown to Victor. 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:2 Agentb:1,2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Justine can now know that Victor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Justine","Lois","Leslie","Victor"],"index":26469,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9835267663,"difficulty":0.0164732337}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenna's card is shown to Guy. Hector's card is shown to Guy. Fatima's card is shown to Guy. Fatima's card is shown to Fatima. It is publicly announced that someone picked a red card. It is publicly announced that Brenna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb: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:2,3,4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Brenna can now know that Brenna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Guy","Brenna","Hector","Fatima"],"index":52866,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.813513875,"difficulty":0.186486125}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sophia's card is shown to Megan. Angel's card is shown to Megan. Annette's card is shown to Megan. Angel's card is shown to Sophia. Angel's card is shown to Annette. Annette's card is shown to Annette. 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) ] Agenta knows that (Agentb knows whether 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":"Megan can now know that Sophia can know whether Annette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Megan","Sophia","Angel","Annette"],"index":60273,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6280258894,"difficulty":1.6280258894}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Gregory. Eunice's card is shown to Gregory. Gregory's card is shown to Mildred. Mildred's card is shown to Mildred. Eunice's card is shown to Mildred. Gregory's card is shown to Eunice. It is publicly announced that someone picked a red card. It is publicly announced that Gregory does not know whether Gregory 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 whether 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":"Eunice can now know whether Eunice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregory","Mildred","Eunice"],"index":61223,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5052964091,"difficulty":0.4947035909}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fred's card is shown to Mary. Mary's card is shown to Fred. Lori's card is shown to Fred. Mary's card is shown to Lori. Lori's card is shown to Lori. 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:1,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lori can now know that Mary can know that Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Fred","Lori"],"index":13894,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982669353,"difficulty":0.0017330647}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dolores's card is shown to Deborah. Deborah's card is shown to Dolores. Felipe's card is shown to Dolores. Deborah's card is shown to Felipe. Felipe's card is shown to Felipe. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Deborah can now know that Felipe can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deborah","Dolores","Felipe"],"index":58966,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993863106,"difficulty":0.0006136894}
{"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 Barbara. Cleo's card is shown to Cleo. It is publicly announced that someone picked a red card. It is publicly announced that Annie does not know whether Barbara picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Barbara can now know whether Annie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annie","Barbara","Cleo"],"index":1542,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7403714061,"difficulty":0.2596285939}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edna's card is shown to Edna. Patricia's card is shown to Edna. Seth's card is shown to Edna. Edna's card is shown to Patricia. Seth's card is shown to Patricia. Edna's card is shown to Seth. 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) ] (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:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"June can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edna","June","Patricia","Seth"],"index":28886,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989903569,"difficulty":0.0010096431}
{"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 Cornell. Myron's card is shown to Anthony. John's card is shown to Anthony. Cornell's card is shown to Myron. Cornell's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Myron knows whether or not everyone picked a red card. It is publicly announced that Anthony knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Cornell can now know whether John can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cornell","Anthony","Myron","John"],"index":19405,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994270802,"difficulty":0.0005729198}
{"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 Emily. Mike's card is shown to Emily. Emily's card is shown to Mike. Felix's card is shown to Mike. Felix's card is shown to Felix. It is publicly announced that someone picked a red card. It is publicly announced that Mike knows whether someone picked a red card. It is publicly announced that Felix picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Emily can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emily","Mike","Felix"],"index":41309,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994747043,"difficulty":0.0005252957}
{"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. Patsy's card is shown to Joe. Joe's card is shown to Patsy. Patsy's card is shown to Patsy. 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) ] Agentc knows that (Agentb knows whether 2)","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":"Patsy can now know that Joe can know whether Joe picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Joe","Patsy"],"index":40872,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8966659904,"difficulty":0.1033340096}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cory's card is shown to Joanne. Terrance's card is shown to Joanne. Cory's card is shown to Terrance. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joanne can now know that Terrance picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joanne","Cory","Terrance"],"index":28818,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997001946,"difficulty":0.002998054}
{"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 Patricia. Janice's card is shown to Patricia. Patricia's card is shown to Pamela. Steven's card is shown to Janice. Patricia's card is shown to Janice. Janice's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Patricia","Pamela","Janice"],"index":32026,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5637430549,"difficulty":1.5637430549}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Bonnie. Bonnie's card is shown to Robert. 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:1 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:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bonnie can now know whether Robert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bonnie","Robert"],"index":26795,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994465709,"difficulty":0.0005534291}
{"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 Richard. Eugene's card is shown to Richard. Richard's card is shown to Carolyn. Richard's card is shown to Eugene. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Richard can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Carolyn","Eugene"],"index":25549,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999404192,"difficulty":0.000595808}
{"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 Jose. Jose's card is shown to Jay. Jay's card is shown to Jay. Sam's card is shown to Jay. Kristin's card is shown to Jay. Jose's card is shown to Kristin. Kristin's card is shown to Kristin. It is publicly announced that someone picked a red card. It is publicly announced that Sam does not know whether or not everyone picked a red card. It is publicly announced that Sam does not know whether Sam picked a red card. It is publicly announced that Jay knows whether Jay picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sam can now know that Jay can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Jay","Sam","Kristin"],"index":65217,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977711439,"difficulty":0.0022288561}
{"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 Wayne. Marvin's card is shown to Wayne. Wayne's card is shown to Robert. Marvin's card is shown to Robert. Robert's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Marvin 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:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Marvin can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wayne","Marvin","Robert","Christine"],"index":58723,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994367957,"difficulty":0.0005632043}
{"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 Adrienne. Allison's card is shown to Julia. Adrienne's card is shown to Allison. Annie's card is shown to Allison. Adrienne's card is shown to Annie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Allison can now know whether Julia can know that Allison picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Adrienne","Julia","Allison","Annie"],"index":628,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7802016735,"difficulty":1.7802016735}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Reginald. Bonita's card is shown to Kyle. Mary's card is shown to Mary. Reginald's card is shown to Bonita. 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:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kyle can now know that Reginald can know whether Kyle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Reginald","Kyle","Mary","Bonita"],"index":56465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9951493144,"difficulty":0.0048506856}
{"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 Helene. Gregory's card is shown to John. Helene's card is shown to Gregory. Ben's card is shown to Ben. 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) ] Agentb knows whether (Agenta 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":"John can now know whether Helene can know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helene","John","Gregory","Ben"],"index":25299,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988874793,"difficulty":0.0011125207}
{"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 Candice. Jayme's card is shown to Cecila. Cecila's card is shown to Bonnie. Candice's card is shown to Jayme. It is publicly announced that someone picked a red card. It is publicly announced that Jayme does not know whether or not everyone picked a red card. It is publicly announced that Cecila picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Cecila can now know whether Candice can know whether Bonnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Candice","Cecila","Bonnie","Jayme"],"index":67077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981014132,"difficulty":0.0018985868}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Bernard. Lina's card is shown to Lina. Bernard's card is shown to Warren. Lina's card is shown to Warren. Jeremy's card is shown to Jeremy. 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 2)","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":"Lina can now know whether Lina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bernard","Lina","Warren","Jeremy"],"index":56300,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6733216643,"difficulty":0.3266783357}
{"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 Eric. Natalie's card is shown to Eric. Natalie's card is shown to Marie. Eric's card is shown to Natalie. Natalie's card is shown to Natalie. It is publicly announced that someone picked a red card. It is publicly announced that Eric does not know whether Eric picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card. It is publicly announced that Natalie picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 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 that (Agentb knows whether (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":"Natalie can now know that Marie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eric","Marie","Natalie"],"index":62979,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6705040336,"difficulty":1.6705040336}
{"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. Harriet's card is shown to Leland. It is publicly announced that someone picked a red card. It is publicly announced that Harriet knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know that Harriet picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harriet","Kenneth","Leland"],"index":9699,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9310543537,"difficulty":0.0689456463}
{"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 Kay. Christine's card is shown to Christine. Bertha's card is shown to Christine. Christine's card is shown to Bertha. It is publicly announced that someone picked a red card. It is publicly announced that Kay 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) ] [ ! 2 ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Christine can now know that Christine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Freeman","Kay","Christine","Bertha"],"index":24680,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7456364632,"difficulty":0.2543635368}
{"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. Kristen's card is shown to Kristen. Kristen's card is shown to Charlotte. It is publicly announced that someone picked a red card. It is publicly announced that Daniel 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 ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Daniel can now know that Patricia can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Kristen","Patricia","Charlotte"],"index":59012,"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). Dale's card is shown to Dale. Leah's card is shown to Dale. Dale's card is shown to Leah. 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 Leah picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Leah can now know whether Dale can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dale","Leah"],"index":23466,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9962764382,"difficulty":0.0037235618}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sylvia's card is shown to Jason. Kevin's card is shown to Jason. Sylvia's card is shown to Sylvia. Jason's card is shown to Kevin. 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 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sylvia can now know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Sylvia","Kevin"],"index":6101,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9564365745,"difficulty":0.0435634255}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rodney's card is shown to Matthew. Matthew's card is shown to Terry. Terry's card is shown to Terry. Rodney's card is shown to Terry. Matthew's card is shown to Rodney. Terry's card is shown to Rodney. Rodney's card is shown to Rodney. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 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:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rodney can now know whether Matthew can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Terry","Rodney"],"index":45752,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994125366,"difficulty":0.0005874634}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Marion. Albert's card is shown to Wayne. Marion'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:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marion can now know whether Albert can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marion","Wayne","Albert"],"index":1947,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9928969741,"difficulty":0.0071030259}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittney's card is shown to Brittney. John's card is shown to Brittney. Brittney's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"John can now know whether Brittney picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brittney","John"],"index":23807,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9909385443,"difficulty":0.0090614557}
{"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. Crystal's card is shown to Barbara. Crystal's card is shown to Crystal. Mark's card is shown to Crystal. Barbara's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Barbara knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Mark can now know that Barbara can know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Barbara","Crystal","Mark"],"index":34620,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6197276115,"difficulty":1.6197276115}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Linda. Bryan's card is shown to Jeremiah. Linda's card is shown to Grant. Grant's card is shown to Grant. 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 whether (Agentc knows that 1)","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":"Linda can now know whether Bryan can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Jeremiah","Bryan","Grant"],"index":1709,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8583707809,"difficulty":1.8583707809}
{"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 Mary. Edwin's card is shown to Mary. Edwin's card is shown to Pamela. 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:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Pamela","Edwin"],"index":59212,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6039940119,"difficulty":1.6039940119}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Alene's card is shown to Brenda. Jose's card is shown to Gregory. Alene's card is shown to Alene. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Alene 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 Gregory 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 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Brenda can now know whether Gregory can know that Brenda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Jose","Gregory","Alene"],"index":28326,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8857743144,"difficulty":0.1142256856}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leanna's card is shown to Leanna. David's card is shown to Leanna. Leanna's card is shown to Vicki. Vicki's card is shown to Vicki. David's card is shown to Vicki. Leanna's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Vicki knows whether or not nobody picked a red card. It is publicly announced that Leanna does not know whether Vicki 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 whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Vicki can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leanna","Vicki","David"],"index":29595,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6752631068,"difficulty":1.6752631068}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glen's card is shown to Glen. Glen's card is shown to Octavio. Glen's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Ron 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 1)","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":"Octavio can now know that Ron picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ron","Glen","Octavio","Alice"],"index":64702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9822973013,"difficulty":0.0177026987}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Virginia. Nathan's card is shown to Virginia. Virginia's card is shown to Lucille. Nathan's card is shown to Lucille. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nathan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virginia","Nathan","Lucille"],"index":25729,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955708385,"difficulty":0.0044291615}
{"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 Nicole. Chantal's card is shown to Nicole. Nicole's card is shown to Joseph. Joseph's card is shown to Chantal. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Jessie 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) ] (Agenta knows that 2)","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":"Jessie can now know that Nicole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessie","Nicole","Joseph","Chantal"],"index":15555,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965769649,"difficulty":0.0034230351}
{"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 Rachael. Joyce's card is shown to Sarah. Lavern's card is shown to Sarah. Rachael's card is shown to Lavern. Sarah's card is shown to Lavern. 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) ] Agentc knows whether (Agenta knows that 2)","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":"Sarah can now know whether Rachael can know that Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachael","Joyce","Sarah","Lavern"],"index":51267,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8981223106,"difficulty":1.8981223106}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Nicole. Nicole's card is shown to Carl. Sara's card is shown to Carl. Nicole's card is shown to Sara. Carl's card is shown to Sara. Sara's card is shown to Petra. It is publicly announced that someone picked a red card. It is publicly announced that Petra 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))) ] Agenta knows whether (Agentc knows that 3)","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":"Nicole can now know whether Sara can know that Sara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicole","Carl","Sara","Petra"],"index":28114,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9112590551,"difficulty":0.0887409449}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erica's card is shown to Matthew. Tanya's card is shown to Matthew. Erica's card is shown to Erica. Tanya's card is shown to Erica. Matthew's card is shown to Tanya. Erica's card is shown to Tanya. Tanya's card is shown to Tanya. It is publicly announced that someone picked a red card. It is publicly announced that Tanya picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Erica can now know that Erica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Erica","Tanya"],"index":3379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5912272334,"difficulty":0.4087727666}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to David. David's card is shown to Ann. Pauline's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Ann 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) ] [ ! 3 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Pauline can now know whether Pauline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","David","Ann","William"],"index":51538,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7065901756,"difficulty":1.7065901756}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Frankie. Harry's card is shown to Harry. Forrest's card is shown to Forrest. Forrest's card is shown to Danielle. 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) ] Agentc knows whether (Agenta knows that 4)","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":"Forrest can now know whether Frankie can know that Danielle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frankie","Harry","Forrest","Danielle"],"index":34966,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.953746736,"difficulty":1.953746736}
{"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 Sean. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sean can now know whether Aaron picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aaron","Sean","Helen","Timothy"],"index":29852,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980541468,"difficulty":0.0019458532}
{"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 Elizabeth. Elizabeth's card is shown to Elizabeth. Gail's card is shown to Elizabeth. Gail's card is shown to Gail. 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 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":"Richard can now know that Elizabeth can know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Elizabeth","Gail"],"index":34545,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7802782655,"difficulty":1.7802782655}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Tamara. Darren's card is shown to Tamara. Tamara's card is shown to Cheryl. Tamara's card is shown to Darren. 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 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Darren can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tamara","Cheryl","Darren"],"index":66107,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990068078,"difficulty":0.0009931922}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to Ryan. Ryan's card is shown to Crystal. Evan's card is shown to Crystal. Crystal's card is shown to Evan. Dustin's card is shown to Evan. It is publicly announced that someone picked a red card. It is publicly announced that Ryan does not know whether Dustin 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)) ] (Agenta knows that (1|2|3|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":"Ryan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ryan","Crystal","Evan","Dustin"],"index":65820,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994445443,"difficulty":0.0005554557}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sally's card is shown to Angela. Sally's card is shown to Sally. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether Angela 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 that (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) ] 0","hypothesis":"Angela can now know that Sally can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Angela","Sally"],"index":22166,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988779426,"difficulty":0.0011220574}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debbie's card is shown to Scott. Delpha's card is shown to Delpha. Debbie's card is shown to Delpha. Debbie's card is shown to Debbie. 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 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Scott can now know whether Delpha can know that Debbie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Delpha","David","Debbie"],"index":7777,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9161696434,"difficulty":0.0838303566}
{"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 Carlos. Patricia's card is shown to Carlos. Carlos's card is shown to George. George's card is shown to George. Carlos's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Carlos knows whether or not nobody 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 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Carlos can now know whether George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carlos","George","Patricia"],"index":33431,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5869328976,"difficulty":0.4130671024}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lia's card is shown to Lia. Sara's card is shown to Lia. Lia's card is shown to Matthew. Matthew's card is shown to Matthew. Matthew's card is shown to Adolfo. Matthew's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:2 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:1,4 Agentb:1,2 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Matthew can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lia","Matthew","Adolfo","Sara"],"index":3828,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988926053,"difficulty":0.0011073947}
{"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 Dana. Dana's card is shown to Amy. Don's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Amy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Dana can now know that Don picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dana","Amy","Don"],"index":41838,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9576960206,"difficulty":0.0423039794}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Patricia'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 Patricia knows whether Patricia picked a red card. It is publicly announced that Patricia does not know whether Eric 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) ] Agentb knows that (Agenta knows that 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":"Eric can now know that Patricia can know that Eric picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Patricia","Eric"],"index":25239,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9665847421,"difficulty":0.0334152579}
{"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. Gary's card is shown to Joan. Gary's card is shown to Gary. Barbara's card is shown to Gary. Clifton's card is shown to Barbara. Barbara'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:1,2 Agentb:2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joan","Gary","Clifton","Barbara"],"index":7406,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999409318,"difficulty":0.000590682}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Manuel. Vernon's card is shown to Dwayne. Dwayne's card is shown to Vernon. 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 that (Agenta knows that (~(1|2|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":"Dwayne can now know that Manuel can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Manuel","Dwayne","Vernon"],"index":10580,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990290403,"difficulty":0.0009709597}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Collin's card is shown to Collin. Bill's card is shown to Collin. Don's card is shown to Wilma. Collin's card is shown to Bill. Wilma's card is shown to Don. Bill's card is shown to Don. 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 whether (Agenta knows that (1&2&3&4))","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":"Don can now know whether Collin can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Collin","Wilma","Bill","Don"],"index":43948,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9818018079,"difficulty":0.0181981921}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kayla's card is shown to William. Michael's card is shown to Michael. Kayla's card is shown to Michael. Kayla's card is shown to Mary. Mary's card is shown to Kayla. 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) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Kayla can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Michael","Mary","Kayla"],"index":2995,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9810732603,"difficulty":0.0189267397}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raquel's card is shown to Hope. David's card is shown to Hope. Hope's card is shown to Raquel. Hope's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","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":"Hope can now know whether Raquel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hope","Raquel","David"],"index":14848,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9818243384,"difficulty":1.9818243384}
{"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. Maurice's card is shown to Josephine. Josephine's card is shown to Chris. Chris's card is shown to Maurice. Maurice's card is shown to Maurice. Maurice's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Josephine can now know whether Maurice can know whether Chris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josephine","Chris","Maurice","Heather"],"index":1070,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998573184,"difficulty":0.001426816}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachel's card is shown to Carolyn. Mary's card is shown to Carolyn. Rachel'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:2,3 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:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rachel can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carolyn","Rachel","Mary"],"index":2321,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999368608,"difficulty":0.000631392}
{"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 Karla. Helen's card is shown to Helen. Helen'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 Karla does not know whether Charles picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 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:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Karla can now know that Charles can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karla","Helen","Charles"],"index":38038,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9853724837,"difficulty":0.0146275163}
{"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. Rosa's card is shown to John. Robert's card is shown to John. John's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rosa can now know that John can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Rosa","Robert"],"index":51647,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5781203508,"difficulty":1.5781203508}
{"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 Michael. Mary's card is shown to Michael. Jean's card is shown to Kerry. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Jean picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Michael can now know whether Kerry can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Kerry","Mary","Jean"],"index":43548,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7240920067,"difficulty":0.2759079933}
{"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 Berta. Troy's card is shown to Berta. Davis's card is shown to Davis. Berta's card is shown to Troy. Thomas's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that Davis picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Davis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Berta","Davis","Thomas","Troy"],"index":36034,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985456467,"difficulty":0.0014543533}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Donna. Donna's card is shown to Becky. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donna can now know whether Fred can know whether Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fred","Donna","Becky","Virginia"],"index":6358,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.834556222,"difficulty":1.834556222}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kerry's card is shown to Robert. Robert's card is shown to Kerry. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Bradley can now know whether Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Bradley","Kerry"],"index":18503,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999440372,"difficulty":0.000559628}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patty's card is shown to Patty. William's card is shown to Patty. Patty's card is shown to William. 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) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Patty can now know that Patty picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patty","William"],"index":24899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9931070209,"difficulty":0.0068929791}
{"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 Jonathan. Diana's card is shown to Diana. Jonathan's card is shown to Troy. Dorothy's card is shown to Troy. Diana's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan does not know whether Diana 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) ] (Agenta knows whether 2)","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":"Jonathan can now know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jonathan","Dorothy","Diana","Troy"],"index":50743,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9766765833,"difficulty":0.0233234167}
{"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 Larraine. Larraine's card is shown to Larraine. Bridget's card is shown to Norman. Kevin's card is shown to Bridget. Larraine's card is shown to Bridget. 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:1,2 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:1,2 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larraine can now know that Kevin can know whether Larraine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Larraine","Norman","Bridget"],"index":34732,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8654347658,"difficulty":0.1345652342}
{"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. Susan's card is shown to Kati. Kati's card is shown to Kati. Michael's card is shown to Kati. Susan's card is shown to Michael. Michael's card is shown to Michael. Susan'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 Agentb:1,2,3 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know that Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","Kati","Michael","Mark"],"index":42959,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957661629,"difficulty":0.0042338371}
{"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 Joseph. Alexander's card is shown to Kelly. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Kelly knows whether Clarence picked a red card. It is publicly announced that Alexander does not know whether Joseph 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) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alexander can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Alexander","Kelly","Clarence"],"index":42159,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962127209,"difficulty":0.0037872791}
{"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 Christopher. Timothy's card is shown to Christopher. Christopher's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Christopher picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Christopher can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christopher","Timothy"],"index":60252,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994663596,"difficulty":0.0005336404}
{"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 Julia. Julia's card is shown to Eddie. It is publicly announced that someone picked a red card. It is publicly announced that Margaret picked a black card. It is publicly announced that Julia knows 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) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Margaret can now know that Julia can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Julia","Eddie"],"index":37318,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989185333,"difficulty":0.0010814667}
{"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 Calvin. Margaret's card is shown to Margaret. Tina's card is shown to Margaret. Calvin's card is shown to Tina. Tina's card is shown to Tina. It is publicly announced that someone picked a red card. It is publicly announced that Tina knows whether Calvin 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) ] (Agentb knows that (~(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":"Margaret can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Calvin","Margaret","Tina"],"index":62839,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999052465,"difficulty":0.000947535}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ellie's card is shown to Ellie. Kenny's card is shown to Ellie. Sylvia's card is shown to Sylvia. Sylvia's card is shown to Kenny. 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 2)","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":"Sylvia can now know that Sylvia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ellie","Sylvia","Kenny"],"index":53942,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9895811081,"difficulty":0.0104188919}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mack's card is shown to Mack. Mack's card is shown to Cameron. Mack's card is shown to Joshua. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Mack does not know whether Joshua picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Cameron can now know that Mack can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mack","Cameron","Joshua"],"index":57380,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994186163,"difficulty":0.0005813837}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janie's card is shown to Larry. Sarah's card is shown to Larry. Sarah's card is shown to Wesley. Larry's card is shown to Janie. Wesley's card is shown to Sarah. Janie'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:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know whether Wesley can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Wesley","Janie","Sarah"],"index":13502,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999363482,"difficulty":0.000636518}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Corey's card is shown to Cynthia. Cynthia's card is shown to Daniel. Daniel's card is shown to Daniel. Corey's card is shown to Daniel. Daniel's card is shown to Corey. Corey's card is shown to Corey. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know that Cynthia can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cynthia","Daniel","Corey"],"index":6006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989302754,"difficulty":0.0010697246}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilma's card is shown to Marie. Janice's card is shown to Marie. Wilma's card is shown to Wilma. Marie's card is shown to Janice. Wilma's card is shown to Janice. Janice's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janice can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marie","Wilma","Janice"],"index":6316,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993884563,"difficulty":0.0006115437}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Nicole. Michael's card is shown to Michael. Katherine's card is shown to Michael. Michael's card is shown to Katherine. Katherine'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:3 Agentb:2,3 Agentc: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:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Nicole can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicole","Michael","Katherine"],"index":11919,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9280747771,"difficulty":0.0719252229}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emerson's card is shown to Emerson. Glenn's card is shown to Emerson. Emerson'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:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emerson can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emerson","Shirley","Glenn","Grace"],"index":55077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999347508,"difficulty":0.000652492}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Michael. Mary's card is shown to Michael. Mary's card is shown to Jeremy. 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) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Jeremy","Mary"],"index":52903,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993944168,"difficulty":0.0006055832}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Letha. Letha's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Jeffrey can now know that Letha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Letha","Jeffrey"],"index":6989,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9246172905,"difficulty":1.9246172905}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Gena's card is shown to Joanne. Eugene's card is shown to Harold. Gena'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:1 Agentb:2 Agentc: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:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joanne can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eugene","Gena","Joanne","Harold"],"index":30508,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993145466,"difficulty":0.0006854534}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Diane. Diane's card is shown to Linda. Diane's card is shown to Angela. 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) ] (Agenta knows that 1)","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":"Diane can now know that Diane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diane","Linda","Angela"],"index":49382,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9961398244,"difficulty":0.0038601756}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Jeremy. Jeremy's card is shown to Wesley. Wesley's card is shown to Wesley. It is publicly announced that someone picked a red card. It is publicly announced that Wesley knows whether Wesley 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 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 2) ] 0","hypothesis":"Wesley can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeremy","Wesley"],"index":39039,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994408488,"difficulty":0.0005591512}
{"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 Lauren. Antonio's card is shown to Timothy. Antonio's card is shown to Antonio. Lauren's card is shown to Maria. Timothy's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Antonio 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)) ] Agentc knows whether (Agentd knows that 2)","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":"Antonio can now know whether Maria can know that Timothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lauren","Timothy","Antonio","Maria"],"index":18848,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9015852809,"difficulty":1.9015852809}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gina's card is shown to Gina. Heather's card is shown to Gina. Gina's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that Gina knows whether or not nobody 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) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Gina can now know whether Heather can know whether Gina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gina","Heather"],"index":49667,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977554679,"difficulty":0.0022445321}
{"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 Wanda. Teresa's card is shown to Teresa. Wanda's card is shown to Jose. Teresa's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Jose 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) ] Agentd knows that (Agenta knows that 3)","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":"Melissa can now know that Wanda can know that Jose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wanda","Teresa","Jose","Melissa"],"index":23823,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946764708,"difficulty":0.0053235292}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chelsea's card is shown to Chelsea. Thomas's card is shown to Chelsea. Chelsea's card is shown to Dorothy. Dorothy's card is shown to Dorothy. Chelsea's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 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:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Chelsea","Dorothy","Thomas"],"index":59113,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989051819,"difficulty":0.0010948181}
{"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 Lillian. Sergio's card is shown to Lillian. Lillian's card is shown to Joy. Lillian's card is shown to Sergio. It is publicly announced that someone picked a red card. It is publicly announced that Lillian picked a red card. It is publicly announced that Joy knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Lillian knows whether Sergio picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Lillian can now know that Sergio can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lillian","Joy","Sergio"],"index":28138,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986172915,"difficulty":0.0013827085}
{"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 Morgan. Vicki's card is shown to Morgan. Morgan's card is shown to Vicki. Vicki's card is shown to Vicki. 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 (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":"Charles can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Morgan","Charles","Vicki"],"index":47658,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994057417,"difficulty":0.0005942583}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Dawn. Ruth's card is shown to Ruth. Cheryl's card is shown to Ruth. Charles's card is shown to Ruth. Charles's card is shown to Cheryl. Cheryl's card is shown to Charles. 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:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Dawn can now know that Cheryl can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dawn","Ruth","Cheryl","Charles"],"index":66446,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994142056,"difficulty":0.0005857944}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alonzo's card is shown to Alonzo. Hattie's card is shown to Alonzo. Alonzo's card is shown to Hazel. Hazel'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:1,2 Agentb:1,3 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:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alonzo can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alonzo","Hattie","Hazel"],"index":8026,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945905209,"difficulty":0.0054094791}
{"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 Kelly. Kelly's card is shown to James. Meta's card is shown to James. James's card is shown to Meta. 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. It is publicly announced that Meta does not know whether Kelly picked a red card. It is publicly announced that Kelly does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kelly can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kelly","James","Meta"],"index":36150,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994344115,"difficulty":0.0005655885}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Tiffany. Tiffany's card is shown to Jackie. Jackie's card is shown to Jackie. Roland's card is shown to Roland. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tiffany can now know whether Tiffany picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tiffany","Jackie","Roland"],"index":49681,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5143606067,"difficulty":0.4856393933}
{"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 Patricia. Marc's card is shown to Patricia. Debra's card is shown to Debra. Debra's card is shown to Marc. 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 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Debra can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Frances","Debra","Marc"],"index":34676,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993621707,"difficulty":0.0006378293}
{"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 Miriam. David's card is shown to Rebecca. Miriam's card is shown to David. 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 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Miriam","Rebecca","David"],"index":12993,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5240505934,"difficulty":0.4759494066}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Martin. Martin's card is shown to Richard. Richard's card is shown to Richard. Kevin's card is shown to Richard. Martin's card is shown to Kevin. Richard'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 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Martin can now know that Kevin can know that Martin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martin","Richard","Kevin"],"index":51854,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944492579,"difficulty":0.0055507421}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to David. Evelyn's card is shown to Evelyn. Evelyn's card is shown to Elaine. It is publicly announced that someone picked a red card. It is publicly announced that Elaine picked a red card. It is publicly announced that Bobby knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Bobby can now know that David can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Evelyn","Bobby","Elaine"],"index":5157,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982281327,"difficulty":0.0017718673}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Judith. Laura's card is shown to Laura. Laura's card is shown to Geri. It is publicly announced that someone picked a red card. It is publicly announced that Laura does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc: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:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Laura can now know whether Judith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judith","Laura","Geri"],"index":19614,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8267656565,"difficulty":0.1732343435}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Victor. Victor's card is shown to Kim. Kim's card is shown to Kim. Victor's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Kim knows whether Kim 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 2) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Evelyn can now know whether Victor can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Victor","Kim","Evelyn"],"index":25628,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9747728705,"difficulty":0.0252271295}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cherlyn's card is shown to Nick. Nick's card is shown to Cherlyn. Shirley's card is shown to Cherlyn. Nick's card is shown to Shirley. Cherlyn's card is shown to Shirley. 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 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":"Cherlyn can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nick","Cherlyn","Shirley"],"index":43888,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994021654,"difficulty":0.0005978346}
{"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 Edwin. William's card is shown to William. Annette's card is shown to Annette. 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 whether 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":"William can now know whether Edwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edwin","William","Annette"],"index":8389,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975341558,"difficulty":0.0024658442}
{"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 Graham. Christopher's card is shown to Richard. Graham's card is shown to Christopher. Christopher's card is shown to Christopher. Christopher's card is shown to Rhonda. 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:3 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Graham can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Graham","Richard","Christopher","Rhonda"],"index":38084,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994283319,"difficulty":0.0005716681}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelvin's card is shown to Thomas. Kelvin's card is shown to Kelvin. It is publicly announced that someone picked a red card. It is publicly announced that Kelvin knows whether or not nobody picked a red card. It is publicly announced that Kelvin 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))) ] [ ! ~(Agentb knows whether (1&2)) ] (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))) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Kelvin can now know that Kelvin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thomas","Kelvin"],"index":65714,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6216364503,"difficulty":1.6216364503}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lana's card is shown to Elizabeth. Elizabeth's card is shown to Lana. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Elizabeth picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (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":"Elizabeth can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","Lana"],"index":12394,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994314313,"difficulty":0.0005685687}
{"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 Glenn. Ruby's card is shown to Glenn. Glenn's card is shown to Juan. Juan's card is shown to Juan. Gordon's card is shown to Ruby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruby can now know that Glenn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Glenn","Juan","Ruby","Gordon"],"index":52148,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977983832,"difficulty":0.0022016168}
{"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 Brenda. Verna's card is shown to Verna. Douglas's card is shown to Verna. Brenda's card is shown to Douglas. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Douglas knows whether Brenda picked a red card. It is publicly announced that Douglas knows whether Verna picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Douglas can now know that Brenda can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brenda","Verna","Douglas"],"index":59844,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994177818,"difficulty":0.0005822182}
{"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 Kevin. Kevin's card is shown to Joyce. Joyce's card is shown to Joyce. 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 Joyce knows whether Joyce picked a red card. It is publicly announced that Kevin knows whether Kevin 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) ] (Agenta knows that (1&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":"Kevin can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kevin","Joyce"],"index":34128,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9933755994,"difficulty":0.0066244006}
{"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 Brian. Ralph's card is shown to Brian. Miguel's card is shown to Miguel. Miguel's card is shown to Lori. Ralph's card is shown to Lori. Ralph's card is shown to Ralph. 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. 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 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lori can now know that Ralph can know that Lori picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Miguel","Lori","Ralph"],"index":46237,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7255437374,"difficulty":0.2744562626}
{"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. Serena's card is shown to David. David's card is shown to Serena. Serena's card is shown to Serena. Adam's card is shown to Serena. David's card is shown to Adam. Serena's card is shown to Adam. Adam's card is shown to Adam. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Adam can now know whether Adam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Serena","Adam"],"index":45306,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8920806646,"difficulty":0.1079193354}
{"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 Chester. 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 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Tommy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tommy","Chester"],"index":3289,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989578724,"difficulty":0.0010421276}
{"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 Robert. David's card is shown to Robert. Anna's card is shown to Octavia. David's card is shown to Octavia. David's card is shown to Anna. Robert's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Octavia knows whether Anna picked a red card. It is publicly announced that Octavia knows whether someone picked a red card. It is publicly announced that Octavia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentc knows that (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Anna can now know that David can know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Octavia","Anna","David"],"index":22989,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9880644679,"difficulty":1.9880644679}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nellie's card is shown to Virgil. Louis's card is shown to Virgil. Nellie's card is shown to Nellie. Nellie's card is shown to Louis. Louis's card is shown to Louis. It is publicly announced that someone picked a red card. It is publicly announced that Virgil does not know whether Virgil picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Nellie can now know whether Virgil can know that Louis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Virgil","Nellie","Louis"],"index":31547,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9494909048,"difficulty":1.9494909048}
{"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 Chris. Thomas's card is shown to Chris. Jerry's card is shown to Jessica. Thomas'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:2,3 Agentb:4 Agentc: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:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know whether Jessica can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chris","Jessica","Thomas","Jerry"],"index":64006,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848337173,"difficulty":0.0151662827}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clara's card is shown to Lashanda. Linda's card is shown to Lashanda. Clara's card is shown to Linda. Michael's card is shown to Linda. 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:1,3 Agentb:1,4 Agentc: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:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clara can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clara","Lashanda","Linda","Michael"],"index":15540,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942030311,"difficulty":0.0057969689}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julio's card is shown to Michael. Michael's card is shown to Michael. Michael's card is shown to Beverly. Beverly's card is shown to Denis. Denis's card is shown to Denis. 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:1,2 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Julio can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julio","Michael","Beverly","Denis"],"index":42543,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.986196816,"difficulty":0.013803184}
{"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 Deanna. Brandon's card is shown to Brandon. Tanya's card is shown to John. Deanna'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:4 Agentb:3 Agentc:1,2 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:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandon can now know whether Deanna can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tanya","Deanna","Brandon","John"],"index":5325,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993935823,"difficulty":0.0006064177}
{"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 Lawrence. Anna's card is shown to Phillip. Phillip's card is shown to Anna. 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)) ] Agentc knows that (Agentb knows whether 2)","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":"Anna can now know that Phillip can know whether Phillip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lawrence","Phillip","Anna"],"index":52351,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6848420501,"difficulty":1.6848420501}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wendy's card is shown to Wendy. Wendy's card is shown to Martin. Amanda's card is shown to Martin. Amanda's card is shown to Amanda. Dale's card is shown to Amanda. Martin's card is shown to Dale. It is publicly announced that someone picked a red card. It is publicly announced that Dale does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Dale can now know that Amanda can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wendy","Martin","Amanda","Dale"],"index":28351,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9292667508,"difficulty":0.0707332492}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Jennifer. Sandra's card is shown to Sandra. Andrea's card is shown to Andrea. Andrea's card is shown to Therese. Therese's card is shown to Therese. It is publicly announced that someone picked a red card. It is publicly announced that Therese does not know whether Jennifer picked a red card. It is publicly announced that Jennifer does not know whether Jennifer picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Therese can now know whether Jennifer can know whether Sandra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Sandra","Andrea","Therese"],"index":20553,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988740087,"difficulty":0.0011259913}
{"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 James. James'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 James does not know whether or not everyone picked a red card. It is publicly announced that Charles picked a black card. It is publicly announced that Charles knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Charles can now know whether James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Charles"],"index":34922,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9870485663,"difficulty":0.0129514337}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eve's card is shown to Joseph. Cami's card is shown to Joseph. Eve's card is shown to Cami. Kenneth's card is shown to Cami. Cami's card is shown to Kenneth. 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:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eve can now know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Eve","Cami","Kenneth"],"index":66749,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9662625194,"difficulty":1.9662625194}
{"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 Larry. Charles's card is shown to Charles. Karen's card is shown to Charles. Karen's card is shown to Amy. Amy's card is shown to Karen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd: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:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know whether Charles can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Charles","Amy","Karen"],"index":3341,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993934631,"difficulty":0.0006065369}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Doris. Janet's card is shown to Janet. Kathleen's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Doris can now know that Janet can know whether Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Janet","Kathleen"],"index":10867,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9890294075,"difficulty":1.9890294075}
{"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 Leland. Leland's card is shown to Julius. Carlos's card is shown to Julius. Leland's card is shown to Carlos. It is publicly announced that someone picked a red card. It is publicly announced that Carlos does not know whether Kevin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Carlos can now know whether Julius can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leland","Julius","Carlos","Kevin"],"index":35756,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989824891,"difficulty":0.0010175109}
{"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 Erika. Erika's card is shown to Jennifer. 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 knows whether or not nobody picked a red card. It is publicly announced that Jennifer does not know whether Jennifer 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 whether 2) ] (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Erika can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Erika","Jennifer"],"index":25668,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994383454,"difficulty":0.0005616546}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. William's card is shown to Curtis. William's card is shown to Dean. William's card is shown to Mary. Mary'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 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dean can now know whether Curtis can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Curtis","Dean","Mary","William"],"index":9009,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9405843616,"difficulty":0.0594156384}
{"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 Sherman. Sherman's card is shown to William. William's card is shown to Patrice. Patrice's card is shown to Patrice. 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 that (Agentb 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":"Sherman can now know that William can know whether Sherman picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sherman","William","Patrice"],"index":12314,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7775333524,"difficulty":1.7775333524}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherman's card is shown to Lynn. Joanna's card is shown to Joanna. Sherman's card is shown to Joanna. Lynn's card is shown to Sherman. Joanna's card is shown to Sherman. Sherman's card is shown to Sherman. It is publicly announced that someone picked a red card. It is publicly announced that Joanna does not know whether or not everyone picked a red card. It is publicly announced that Sherman knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Sherman can now know that Lynn can know whether Lynn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lynn","Joanna","Sherman"],"index":4444,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5873601437,"difficulty":0.4126398563}
{"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. Steven's card is shown to Sharon. Lillie's card is shown to Lillie. 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:1,3 Agentb:2 Agentc:3 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:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know whether Sharon can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Lillie","Steven"],"index":52217,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8330318332,"difficulty":0.1669681668}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Bryan. Harold's card is shown to Bryan. Clifford's card is shown to Bryan. Clifford's card is shown to Paul. Bryan's card is shown to Harold. Paul's card is shown to Clifford. Harold's card is shown to Clifford. It is publicly announced that someone picked a red card. It is publicly announced that Harold 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) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Harold can now know whether Clifford can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bryan","Paul","Harold","Clifford"],"index":13556,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.990911305,"difficulty":0.009088695}
{"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. Grace's card is shown to Grace. Mary's card is shown to Grace. Lisa's card is shown to Mary. Lisa's card is shown to Bret. Grace's card is shown to Bret. 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:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Grace","Mary","Bret"],"index":42110,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.928185761,"difficulty":0.071814239}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Alice. Alice's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Alice knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Kelly can now know that Alice can know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alice","Kelly"],"index":61090,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9370346665,"difficulty":1.9370346665}
{"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 Agustin. Jamel's card is shown to Larry. Fanny's card is shown to Fanny. 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) ] Agenta knows whether (Agentb knows that 3)","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":"Agustin can now know whether Larry can know that Jamel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Agustin","Larry","Jamel","Fanny"],"index":66665,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9030269384,"difficulty":1.9030269384}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stanley's card is shown to Stanley. Daniel's card is shown to Stanley. Alicia's card is shown to Alicia. Stanley's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Alicia does not know whether Stanley 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 that (Agentb knows that 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":"Daniel can now know that Alicia can know that Daniel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stanley","Alicia","Daniel"],"index":3884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960636497,"difficulty":0.0039363503}
{"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 Ricardo. Laura's card is shown to Laura. Laura'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:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 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":"Laura can now know whether Robin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ricardo","Laura","Robin"],"index":26021,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967773557,"difficulty":0.0032226443}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kendall's card is shown to Janet. Janet's card is shown to Joshua. Kendall's card is shown to Joshua. Janet's card is shown to Kendall. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Janet 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 3)","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":"Kendall can now know whether Kendall picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janet","Joshua","Kendall"],"index":32995,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5234607458,"difficulty":1.5234607458}
{"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 Rebecca. Rita's card is shown to Rebecca. Jeanette's card is shown to Rebecca. Patricia's card is shown to Jeanette. 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 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rebecca can now know whether Rita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Rebecca","Rita","Jeanette"],"index":41694,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9161158204,"difficulty":0.0838841796}
{"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 Harold. Maureen's card is shown to Harold. Amanda's card is shown to Amanda. Maureen's card is shown to Amanda. Harold's card is shown to Maureen. Amanda's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Harold 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) ] Agentc knows whether (Agentb knows whether 1)","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":"Maureen can now know whether Amanda can know whether Harold picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Amanda","Maureen","Jeffrey"],"index":40626,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983591437,"difficulty":0.0016408563}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terry's card is shown to Emily. Emily's card is shown to Earl. 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 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emily can now know that Emily picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Emily","Earl","Terry","Ruth"],"index":20060,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9884753227,"difficulty":0.0115246773}
{"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 Cody. Cody's card is shown to Charles. Charles's card is shown to Charles. Cody's card is shown to Russell. Russell's card is shown to Russell. It is publicly announced that someone picked a red card. It is publicly announced that Cody does not know whether Russell picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Alton can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cody","Charles","Alton","Russell"],"index":13713,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993724227,"difficulty":0.0006275773}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffery's card is shown to Jeffery. Joanne's card is shown to Joanne. Joan's card is shown to Joanne. Joanne's card is shown to Joan. 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 Joan does not know whether Joan 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) ] (Agentc 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":"Joan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffery","Joanne","Joan"],"index":33640,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990156889,"difficulty":0.0009843111}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Donald. Debra's card is shown to Shelley. Donald's card is shown to Tom. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether Shelley can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Donald","Shelley","Tom"],"index":56688,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993025064,"difficulty":0.0006974936}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jim's card is shown to Jim. Jim's card is shown to Carrie. Emanuel's card is shown to Carrie. Jim's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Jim does not know whether Emanuel picked a red card. It is publicly announced that Kelly knows whether or not everyone picked a red card. It is publicly announced that Jim does not know whether Carrie 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) ] Agenta knows whether (Agentc knows that 1)","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":"Jim can now know whether Kelly can know that Jim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jim","Carrie","Kelly","Emanuel"],"index":55411,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9301676154,"difficulty":0.0698323846}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leticia's card is shown to Natalie. Leisha's card is shown to Natalie. Leisha's card is shown to Leticia. Leisha's card is shown to Leisha. It is publicly announced that someone picked a red card. It is publicly announced that Leisha 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:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Leisha can now know that Natalie can know whether Natalie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Natalie","Leticia","Leisha"],"index":20898,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5707316995,"difficulty":0.4292683005}
{"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 Margaret. Patrick's card is shown to Margaret. Patrick's card is shown to Patrick. Enrique's card is shown to Enrique. 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 that 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":"Margaret can now know that Patrick can know that Enrique picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Patrick","Enrique"],"index":62510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974907637,"difficulty":0.0025092363}
{"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 Mary. Debra's card is shown to Debra. Dan's card is shown to Debra. Mary's card is shown to Dan. Debra's card is shown to Dan. It is publicly announced that someone picked a red card. It is publicly announced that Debra picked a black card. It is publicly announced that Mary knows whether Mary 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)) ] (Agenta knows whether (~(1|2|3)))","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":"Mary can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Debra","Dan"],"index":21663,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993979931,"difficulty":0.0006020069}
{"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 Thelma. Matthew's card is shown to Matthew. Eldon's card is shown to Matthew. Matthew'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 Thelma 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) ] (Agentb knows whether 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":"Matthew can now know whether Eldon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thelma","Matthew","Eldon"],"index":15282,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8817844987,"difficulty":0.1182155013}
{"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. Lasonya's card is shown to Billy. Billy's card is shown to Lasonya. Howard's card is shown to Lasonya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Howard can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Billy","Howard","Lasonya"],"index":33821,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952072501,"difficulty":0.0047927499}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Cheryl. Mike's card is shown to Cheryl. Mike's card is shown to Mike. Stanley's card is shown to Mike. Anna's card is shown to Stanley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 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:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know that Cheryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Cheryl","Mike","Stanley"],"index":32030,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979026318,"difficulty":0.0020973682}
{"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 Darlene. Scott's card is shown to Darlene. Darlene's card is shown to Scott. Tasha's card is shown to Tasha. It is publicly announced that someone picked a red card. It is publicly announced that Tasha picked a black card. It is publicly announced that Scott does not know whether Darlene picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Gary can now know whether Darlene can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Darlene","Scott","Tasha"],"index":30460,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994495511,"difficulty":0.0005504489}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Buddy. Buddy's card is shown to Jaime. Jaime's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Johnny knows whether Johnny picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Johnny can now know whether Buddy can know whether Johnny picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnny","Buddy","Jaime","Donald"],"index":15841,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980573058,"difficulty":0.0019426942}
{"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 Jessica. Loretta's card is shown to Jessica. Leonel's card is shown to Jessica. Xavier's card is shown to Jessica. Xavier's card is shown to Leonel. Xavier's card is shown to Xavier. It is publicly announced that someone picked a red card. It is publicly announced that Xavier picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Leonel can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Loretta","Leonel","Xavier"],"index":23345,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990543723,"difficulty":0.0009456277}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Kelly. Mark's card is shown to Anthony. Anthony's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Kelly 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:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Kelly can now know that Kelly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kelly","Anthony","Roy","Mark"],"index":58911,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9679570198,"difficulty":0.0320429802}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Byron's card is shown to Byron. Kevin's card is shown to Byron. Byron's card is shown to Kevin. Jesus's card is shown to Kevin. Byron's card is shown to Jesus. Kevin's card is shown to Jesus. Arthur's card is shown to Jesus. Byron's card is shown to Arthur. Kevin's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Byron does not know whether Arthur picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1,2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1,2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Jesus can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Byron","Kevin","Jesus","Arthur"],"index":59529,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994204044,"difficulty":0.0005795956}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Jason. Jason's card is shown to Mario. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Jason knows whether or not nobody picked a red card. It is publicly announced that Jason does not know whether James 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 that (Agenta knows whether 1)","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":"Mario can now know that Jason can know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Mario","James"],"index":51390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9393590689,"difficulty":0.0606409311}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ismael's card is shown to Ismael. Ismael'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 Andrew picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Ismael can now know that Andrew can know whether Andrew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ismael","Andrew"],"index":37301,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.955082953,"difficulty":0.044917047}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Helen. Gerald's card is shown to Robert. Robert's card is shown to Robert. Robert'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:2,3 Agentc: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:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gerald can now know whether Gerald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Gerald","Robert","Stephen"],"index":29590,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.701459229,"difficulty":0.298540771}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelyn's card is shown to Bradley. Daniel's card is shown to Bradley. Bradley's card is shown to Angelyn. Nancy's card is shown to Angelyn. Daniel's card is shown to Angelyn. 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) ] (Agenta knows that 3)","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":"Bradley can now know that Nancy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bradley","Angelyn","Nancy","Daniel"],"index":53124,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963105321,"difficulty":0.0036894679}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Michael. Wayne's card is shown to Matthew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Matthew can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Matthew","Wayne"],"index":4154,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966266155,"difficulty":0.0033733845}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodore's card is shown to Theodore. Virginia's card is shown to Virginia. Theodore's card is shown to Flora. Virginia's card is shown to Flora. Alice's card is shown to Flora. Theodore'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 Flora does not know whether Flora picked a red card. It is publicly announced that Virginia does not know whether Flora 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) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Virginia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Theodore","Virginia","Flora","Alice"],"index":18360,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989728928,"difficulty":0.0010271072}
{"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 Catherine. George's card is shown to Catherine. Andreas's card is shown to Scott. George's card is shown to Scott. Catherine's card is shown to Andreas. George's card is shown to Andreas. Catherine's card is shown to George. Scott'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:1,4 Agentb:3,4 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andreas can now know that Catherine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Scott","Andreas","George"],"index":9728,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988784194,"difficulty":0.0011215806}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ebony's card is shown to Ebony. Bryan's card is shown to Ebony. Ebony's card is shown to Bryan. 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 Bryan picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Bryan can now know whether Ebony can know whether Ebony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ebony","Bryan"],"index":53999,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9962902069,"difficulty":0.0037097931}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernestina's card is shown to Amber. Amber's card is shown to Emanuel. Loren's card is shown to Emanuel. Ernestina's card is shown to Emanuel. Amber's card is shown to Loren. Loren's card is shown to Loren. 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 whether 1)","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":"Loren can now know whether Amber picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amber","Emanuel","Loren","Ernestina"],"index":52474,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8499743938,"difficulty":0.1500256062}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Gonzalo. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Thomas knows whether someone picked a red card. It is publicly announced that 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)) ] Agenta knows that (Agentb knows that (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":"Gonzalo can now know that Thomas can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gonzalo","Thomas"],"index":10844,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930231571,"difficulty":0.0069768429}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. Gregory's card is shown to Howard. Howard's card is shown to Howard. Jerome's card is shown to Howard. Gregory's card is shown to Jerome. 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:1 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jerome can now know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregory","Howard","Jerome"],"index":18810,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954079986,"difficulty":0.0045920014}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Armando's card is shown to Armando. Mattie's card is shown to Armando. Charles's card is shown to Charles. Mattie's card is shown to Mattie. 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:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mattie can now know whether Armando can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Armando","Charles","Mattie"],"index":48769,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9444281459,"difficulty":1.9444281459}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelby's card is shown to Shelby. Robert's card is shown to Shelby. Diane's card is shown to Diane. Robert's card is shown to Ann. Shelby's card is shown to Robert. Diane's card is shown to Robert. Robert'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:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 3)","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":"Robert can now know that Shelby can know whether Ann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shelby","Diane","Ann","Robert"],"index":54227,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9936118722,"difficulty":0.0063881278}
{"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 Christopher. Christopher's card is shown to Dennis. Alice's card is shown to Dennis. Dennis's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card. It is publicly announced that Christopher knows whether Alice 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) ] [ ! (Agenta knows whether 3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Alice can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christopher","Dennis","Alice"],"index":23711,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994530082,"difficulty":0.0005469918}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to Harry. Harry's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Jesus does not know whether or not everyone picked a red card. It is publicly announced that Jesus 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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Jesus can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harry","Jesus"],"index":35961,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999456346,"difficulty":0.000543654}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tisha's card is shown to Deborah. Deborah's card is shown to Tisha. Judith's card is shown to Tisha. Alice's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether Deborah picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Deborah can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Tisha","Alice","Judith"],"index":62686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999422431,"difficulty":0.000577569}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leisha's card is shown to Cynthia. Cynthia's card is shown to Maria. Leisha's card is shown to Maria. Francisca's card is shown to Maria. Cynthia's card is shown to Francisca. It is publicly announced that someone picked a red card. It is publicly announced that Leisha does not know whether Leisha picked a red card. It is publicly announced that Leisha does not know whether Maria picked a red card. It is publicly announced that Cynthia 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 that 1)","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":"Leisha can now know that Maria can know that Cynthia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Maria","Leisha","Francisca"],"index":36862,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953586459,"difficulty":0.0046413541}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mae's card is shown to Ann. Ronald's card is shown to Warren. Mae's card is shown to Ronald. Ronald'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:4 Agentc:2,4 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:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mae can now know whether Mae picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ann","Mae","Warren","Ronald"],"index":24268,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8035194278,"difficulty":1.8035194278}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darren's card is shown to Darren. Thelma's card is shown to Darren. Ashley's card is shown to Ashley. Thelma's card is shown to Ashley. Ashley's card is shown to Charles. Charles's card is shown to Charles. Darren's card is shown to Thelma. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Thelma picked a red card. It is publicly announced that Darren does not know whether Ashley 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) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Thelma can now know whether Ashley can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darren","Ashley","Charles","Thelma"],"index":47462,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8424884677,"difficulty":0.1575115323}
{"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 Melody. Manuel's card is shown to Melody. Manuel'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:2,3 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruby can now know whether Summer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melody","Ruby","Manuel","Summer"],"index":36826,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977688789,"difficulty":0.0022311211}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felipa's card is shown to Felipa. Barbara's card is shown to Felipa. Janet's card is shown to Felipa. Felipa's card is shown to Barbara. Barbara's card is shown to Barbara. Janet's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Felipa knows whether Felipa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Barbara can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Felipa","Barbara","Janet"],"index":27383,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9181787968,"difficulty":0.0818212032}
{"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 Myron. Myron's card is shown to Myron. Denise's card is shown to Joseph. Myron's card is shown to Joseph. Denise's card is shown to Cassandra. Myron's card is shown to Cassandra. It is publicly announced that someone picked a red card. It is publicly announced that Myron does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Denise can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Denise","Myron","Joseph","Cassandra"],"index":14655,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993363023,"difficulty":0.0006636977}
{"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. Adam's card is shown to Charlotte. Kathleen's card is shown to Adam. Charlotte's card is shown to Adam. 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 (Agenta knows whether 1)","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":"Charlotte can now know that Kathleen can know whether Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Barbara","Charlotte","Adam"],"index":57238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9822339416,"difficulty":0.0177660584}
{"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 Melanie. Sharon's card is shown to Joe. Shirley's card is shown to Sharon. Joe'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:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melanie can now know whether Joe can know whether Melanie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Melanie","Joe","Sharon"],"index":47592,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9976142645,"difficulty":0.0023857355}
{"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 Kendra. John's card is shown to Kendra. Christine's card is shown to Christine. Kendra's card is shown to John. Christine's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kendra can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kendra","Christine","John"],"index":26646,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963394403,"difficulty":0.0036605597}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mai's card is shown to Theresa. Theresa's card is shown to Mai. Mai's card is shown to Mai. It is publicly announced that someone picked a red card. It is publicly announced that Mai knows whether Mai picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Theresa can now know that Mai picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Theresa","Mai"],"index":64693,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9348800778,"difficulty":0.0651199222}
{"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. Robert's card is shown to Michael. Michael's card is shown to Michael. Robert's card is shown to Justin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 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:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Justin can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Michael","Justin"],"index":4043,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993853569,"difficulty":0.0006146431}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holly's card is shown to Holly. Holly's card is shown to Gregory. Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Gregory knows whether Gregory 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 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 2) ] 0","hypothesis":"Holly can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Holly","Gregory"],"index":30785,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994551539,"difficulty":0.0005448461}
{"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 Hazel. Sally's card is shown to Opal. Sally's card is shown to Sally. Opal's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Sally does not know whether or not everyone picked a red card. It is publicly announced that Hazel picked a black card. It is publicly announced that Sally does not know whether Opal picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sally can now know whether Opal can know that Hazel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hazel","Opal","Sally","Virginia"],"index":32964,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9216912389,"difficulty":0.0783087611}
{"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 Jose. Bernice's card is shown to Michael. Jose's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bernice can now know that Jose can know that Bernice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bernice","Jose","Michael"],"index":9997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997538805,"difficulty":0.002461195}
{"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 Marjorie. Marjorie's card is shown to David. David's card is shown to David. Sandy's card is shown to David. Mildred's card is shown to David. David's card is shown to Sandy. Marjorie's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Sandy does not know whether Marjorie picked a red card. It is publicly announced that Marjorie knows whether 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:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Mildred can now know whether Sandy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marjorie","David","Sandy","Mildred"],"index":33286,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994130135,"difficulty":0.0005869865}
{"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. Brian's card is shown to Daniel. Aaron's card is shown to Angie. It is publicly announced that someone picked a red card. It is publicly announced that Aaron picked a black card. It is publicly announced that Angie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 4 ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 4 ] 0","hypothesis":"Daniel can now know that Angie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Aaron","Brian","Angie"],"index":42046,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7831219435,"difficulty":1.7831219435}
{"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 Joseph. John's card is shown to John. John's card is shown to Carol. Carol's card is shown to Carol. Carol'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 Agentb:2 Agentc:2,3 Agentd:3 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:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","John","Carol","Charles"],"index":67668,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980177879,"difficulty":0.0019822121}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Orlando's card is shown to Orlando. Alexander's card is shown to Orlando. Orlando's card is shown to Alexander. It is publicly announced that someone picked a red card. It is publicly announced that Alexander does not know whether Alexander picked a red card. It is publicly announced that Orlando knows whether Alexander picked a red card. It is publicly announced that Orlando 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Orlando can now know that Alexander can know whether Alexander picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Orlando","Alexander"],"index":48663,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9517096877,"difficulty":1.9517096877}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Nancy. Nancy's card is shown to Kristopher. Ma's card is shown to Kristopher. Kristopher's card is shown to Kristopher. Nancy's card is shown to Andrew. Andrew'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 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ma can now know that Kristopher can know whether Kristopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Ma","Kristopher","Andrew"],"index":61565,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6078113914,"difficulty":0.3921886086}
{"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. Ralph's card is shown to Robert. Robert's card is shown to Ralph. Ralph's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Ralph knows whether or not nobody picked a red card. It is publicly announced that Ralph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] 0","hypothesis":"Jane can now know that Ralph can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jane","Robert","Ralph"],"index":13289,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994459748,"difficulty":0.0005540252}
{"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. Louis's card is shown to Louis. Etta's card is shown to Louis. Beverly's card is shown to Christopher. Beverly's card is shown to Etta. Etta's card is shown to Etta. It is publicly announced that someone picked a red card. It is publicly announced that Louis does not know whether Beverly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Beverly can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beverly","Louis","Christopher","Etta"],"index":660,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990481734,"difficulty":0.0009518266}
{"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. Leona's card is shown to Leona. Jennifer's card is shown to Mary. Leona'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 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leona 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":["Jennifer","Leona","Mary"],"index":14052,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993353486,"difficulty":0.0006646514}
{"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 Elizabeth. Robert's card is shown to Elizabeth. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card. It is publicly announced that Jessica knows whether Jessica 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) ] (Agenta knows that 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":"Elizabeth can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Jessica","Robert"],"index":24893,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9868946075,"difficulty":0.0131053925}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joey's card is shown to Joey. Loren's card is shown to Joey. Joey's card is shown to Loren. 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 Joey picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Joey can now know that Loren can know that Joey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joey","Loren"],"index":24557,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7714239955,"difficulty":0.2285760045}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Kathy. Albert's card is shown to William. Kathy's card is shown to Michael. 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:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathy","William","Michael","Albert"],"index":29794,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993084669,"difficulty":0.0006915331}
{"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 Beatrice. Beatrice's card is shown to Theresa. Theresa's card is shown to Rich. Rich's card is shown to Rich. 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) ] (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 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Beatrice","Theresa","Rich"],"index":44266,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948923588,"difficulty":0.0051076412}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amalia's card is shown to Amalia. Enrique's card is shown to Amalia. Carmen's card is shown to Amalia. Carmen's card is shown to Enrique. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc: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:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amalia can now know whether Carmen can know whether Amalia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amalia","Enrique","Carmen"],"index":5505,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9965054989,"difficulty":0.0034945011}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Benjamin's card is shown to Benjamin. Phyllis's card is shown to Phyllis. It is publicly announced that someone picked a red card. It is publicly announced that Phyllis 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) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Benjamin can now know that Phyllis can know that Phyllis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Benjamin","Phyllis"],"index":14672,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5222741961,"difficulty":1.5222741961}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Warren's card is shown to Jeremy. Warren's card is shown to Warren. It is publicly announced that someone picked a red card. It is publicly announced that Warren knows whether Jeremy 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|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":"Warren can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeremy","Warren"],"index":2931,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994328618,"difficulty":0.0005671382}
{"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 Patricia. Patricia's card is shown to Mary. Dale's card is shown to Mary. Patricia's card is shown to Dale. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Dale 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) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Patricia can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Mary","Dale"],"index":31127,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919141531,"difficulty":0.0080858469}
{"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 Norman. Norman's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Kenneth's card is shown to Matthew. 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 someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know whether Norman picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norman","Lena","Kenneth","Matthew"],"index":67535,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9233053923,"difficulty":0.0766946077}
{"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 Karen. Karen's card is shown to Arthur. Arthur's card is shown to Arthur. Karen's card is shown to Daniel. Arthur's card is shown to Daniel. Karen's card is shown to Robin. Robin's card is shown to Robin. It is publicly announced that someone picked a red card. It is publicly announced that Arthur picked a black card. It is publicly announced that Arthur does not know whether Robin 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 whether (Agentd knows that (~(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":"Karen can now know whether Robin can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Arthur","Daniel","Robin"],"index":26351,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992903471,"difficulty":0.0007096529}
{"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. Chad's card is shown to John. Jennifer's card is shown to Chad. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether Chad picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Chad can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","John","Chad"],"index":39835,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9756161571,"difficulty":0.0243838429}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandy's card is shown to Christina. Brandy's card is shown to Brandy. James's card is shown to Brandy. Christina's card is shown to Lisa. Lisa's card is shown to Lisa. Christina'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:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christina","Brandy","Lisa","James"],"index":34574,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989976287,"difficulty":0.0010023713}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Arthur. Arthur'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 Deborah picked a red card. 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 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta 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) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Deborah can now know whether Arthur can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arthur","Deborah"],"index":66587,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9826418161,"difficulty":0.0173581839}
{"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 Alejandro. Alejandro's card is shown to Linda. William's card is shown to Irene. It is publicly announced that someone picked a red card. It is publicly announced that Linda 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) ] [ ! 3 ] (Agenta knows that 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) ] [ ! 3 ] 0","hypothesis":"William can now know that Irene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Alejandro","Linda","Irene"],"index":64192,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9903820157,"difficulty":0.0096179843}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Christopher. Christopher's card is shown to Katherine. Donald's card is shown to Katherine. 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 whether 1)","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":"Barry can now know whether Barry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barry","Christopher","Donald","Katherine"],"index":48702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99084723,"difficulty":0.00915277}
{"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 Eric. Eric's card is shown to Alfredo. Alfredo's card is shown to Carol. Carol's card is shown to Carol. Carol'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:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eric can now know that Carol can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Alfredo","Carol","Mary"],"index":15593,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998056829,"difficulty":0.001943171}
{"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 Cindy. Craig's card is shown to Craig. Craig's card is shown to Dusty. It is publicly announced that someone picked a red card. It is publicly announced that Craig knows whether or not everyone picked a red card. It is publicly announced that Cindy does not know whether Dusty picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Craig can now know whether Dusty can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cindy","Craig","Dusty","Warren"],"index":15901,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994564652,"difficulty":0.0005435348}
{"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 Edward. Mark's card is shown to Edward. Joan's card is shown to Joan. Joan's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Edward 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 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Joan can now know whether Mark can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Joan","Mark"],"index":57572,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.990426898,"difficulty":0.009573102}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Anne. Maxine's card is shown to Anne. Mario's card is shown to Anne. Maxine's card is shown to Maxine. Mario'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:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anne can now know that Maxine can know whether Anne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anne","Maxine","Mario"],"index":39848,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7353191376,"difficulty":1.7353191376}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ian's card is shown to Richard. Theresa's card is shown to Richard. Richard's card is shown to Raymond. Ian's card is shown to Raymond. Ian's card is shown to Ian. Richard's card is shown to Theresa. Ian's card is shown to Theresa. 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 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Theresa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Raymond","Ian","Theresa"],"index":20775,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999380827,"difficulty":0.000619173}
{"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 Corey. Alva's card is shown to Sonia. Whitney's card is shown to Alva. Alva's card is shown to Whitney. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd: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:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sonia can now know whether Alva can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Corey","Sonia","Alva","Whitney"],"index":60684,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.954164207,"difficulty":0.045835793}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristopher's card is shown to Cristopher. Cristopher's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Cristopher does not know whether or not everyone 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 that (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 (1&2)) ] 0","hypothesis":"Cristopher can now know that Thomas can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cristopher","Thomas"],"index":3041,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.750846386,"difficulty":1.750846386}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Julie. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Margaret does not know whether Julie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (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":"Julie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Julie","Margaret"],"index":44368,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9924371839,"difficulty":1.9924371839}
{"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 Veronica. Dana's card is shown to Veronica. Veronica's card is shown to John. Dana's card is shown to Joan. 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 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Joan can now know that Veronica can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Veronica","John","Joan","Dana"],"index":9495,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993054867,"difficulty":0.0006945133}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Robert. Barry's card is shown to Robert. Angela's card is shown to Angela. Barry's card is shown to Angela. Barry's card is shown to Barry. Larry's card is shown to Barry. Larry's card is shown to Larry. 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 everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Barry can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Angela","Barry","Larry"],"index":23868,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9971985817,"difficulty":0.0028014183}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Samuel. Phillip's card is shown to Phillip. 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) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Samuel can now know whether Phillip can know whether Phillip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Samuel","Phillip"],"index":66055,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9902627468,"difficulty":0.0097372532}
{"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 Loretta. It is publicly announced that someone picked a red card. It is publicly announced that Floyd picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Floyd can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Floyd","Kent","Bonnie","Loretta"],"index":66814,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990436435,"difficulty":0.0009563565}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lottie's card is shown to Michael. Michael's card is shown to Linda. Lottie's card is shown to Linda. 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:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Lottie","Linda"],"index":38238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9923189282,"difficulty":0.0076810718}
{"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 Daphne. Daphne's card is shown to Daphne. Jon's card is shown to Daphne. Earl's card is shown to Earl. Steven's card is shown to Jon. It is publicly announced that someone picked a red card. It is publicly announced that Daphne knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Earl can now know whether Jon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Daphne","Earl","Jon"],"index":11079,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919717312,"difficulty":0.0080282688}
{"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. Sonya's card is shown to Mark. Melissa's card is shown to Mark. Patty's card is shown to Melissa. Mark's card is shown to Melissa. Sonya's card is shown to Melissa. 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:2,3,4 Agentb:1,2,3,4 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:2,3,4 Agentb:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know whether Patty can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patty","Mark","Sonya","Melissa"],"index":40666,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9931897521,"difficulty":0.0068102479}
{"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 Teresa. Tom's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Teresa can now know whether Tom picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Teresa","James","Tom"],"index":9615,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9621303678,"difficulty":0.0378696322}
{"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. Walter's card is shown to Dawn. William'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:1 Agentb:3 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:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dawn can now know that William can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Dawn","Walter"],"index":16348,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990234375,"difficulty":0.0009765625}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Clarence's card is shown to Angela. Angela's card is shown to Carl. Angela's card is shown to Clarence. 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:1,3 Agentb:1 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:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clarence can now know whether Angela can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Carl","Clarence"],"index":31621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994143248,"difficulty":0.0005856752}
{"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 Muriel. Christine's card is shown to Teresa. Christine's card is shown to Christine. Teresa's card is shown to Rose. 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 Muriel picked a black card. It is publicly announced that Christine does not know whether Teresa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Teresa can now know that Muriel can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Muriel","Teresa","Christine","Rose"],"index":20267,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998247385,"difficulty":0.001752615}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemarie's card is shown to Rosemarie. Ruby's card is shown to David. David's card is shown to Ruby. Ruby's card is shown to Ruby. Rosemarie's card is shown to Jack. It is publicly announced that someone picked a red card. It is publicly announced that Jack knows whether Rosemarie 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 whether (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":"Jack can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rosemarie","David","Ruby","Jack"],"index":14645,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994423985,"difficulty":0.0005576015}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Meredith's card is shown to Kathryn. Kathryn's card is shown to Meredith. Meredith's card is shown to Meredith. It is publicly announced that someone picked a red card. It is publicly announced that Kathryn does not know whether Kathryn picked a red card. It is publicly announced that Kathryn does not know whether Kathryn 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 that 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":"Kathryn can now know whether Meredith can know that Meredith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathryn","Meredith"],"index":62416,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8764243722,"difficulty":0.1235756278}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Beverly. Sherri's card is shown to Beverly. Sherri's card is shown to Sherri. It is publicly announced that someone picked a red card. It is publicly announced that Beverly knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Beverly can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Beverly","Sherri"],"index":2368,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994261265,"difficulty":0.0005738735}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luisa's card is shown to Luisa. Kari's card is shown to Luisa. Kari's card is shown to Paula. Kari's card is shown to Rick. Luisa's card is shown to Kari. It is publicly announced that someone picked a red card. It is publicly announced that Luisa knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Luisa can now know whether Kari can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Luisa","Paula","Rick","Kari"],"index":63379,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993702769,"difficulty":0.0006297231}
{"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 Leonora. Leonora's card is shown to Leonora. Robin's card is shown to Leonora. 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) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leonora can now know that Robin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Leonora","Robin"],"index":59390,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965788722,"difficulty":0.0034211278}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margo's card is shown to Guy. Margo's card is shown to Margo. William's card is shown to William. 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:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Margo can now know whether William can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Guy","Margo","William"],"index":61738,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993928671,"difficulty":0.0006071329}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. George's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Betty can now know that George can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Betty","George"],"index":1028,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990369081,"difficulty":0.0009630919}
{"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. Andrew's card is shown to Rita. Marie's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Marie does not know whether Rita picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Marie can now know whether Andrew can know whether Andrew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Marie","Rita"],"index":42789,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983432293,"difficulty":0.0016567707}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernice's card is shown to Bernice. Shauna's card is shown to Bernice. Bernice's card is shown to Brooks. Brooks's card is shown to Brooks. Shauna's card is shown to Brooks. Bernice's card is shown to Shauna. 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 (Agentb knows whether (~(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":"Shauna can now know that Brooks can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bernice","Brooks","Shauna"],"index":2396,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993213415,"difficulty":0.0006786585}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Matthew. Ronald's card is shown to Matthew. Frank's card is shown to Frank. Matthew's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Matthew can now know whether Frank can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Frank","Ronald"],"index":22570,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993690848,"difficulty":0.0006309152}
{"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 Herman. Herman's card is shown to Glenn. Glenn's card is shown to Glenn. Herman'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 Herman does not know whether Glenn picked a red card. It is publicly announced that Glenn 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:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Geneva can now know whether Glenn can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Herman","Glenn","Geneva","Betty"],"index":39192,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994452596,"difficulty":0.0005547404}
{"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 Geraldine. Jose's card is shown to Rickey. Jose's card is shown to Jose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rickey can now know whether Jay can know that Jay picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jay","Geraldine","Rickey","Jose"],"index":2539,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9918968081,"difficulty":1.9918968081}
{"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 Marcela. Marcela's card is shown to Adrian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marcela can now know whether Adrian can know that Adrian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marcela","Adrian","Evelyn"],"index":14417,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8591666222,"difficulty":1.8591666222}
{"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. Jessie's card is shown to Christopher. Jessie's card is shown to Arthur. Christopher's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Jessie knows 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 (Agentc knows that 1)","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":"Jessie can now know that Arthur can know that Jessie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jessie","Christopher","Arthur"],"index":37292,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9684479237,"difficulty":0.0315520763}
{"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 Brian. Brian's card is shown to Brian. Jason's card is shown to Brian. Brian'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 LAW Top OBS Agenta:1,2,3 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:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tim","Brian","Jason"],"index":14414,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993615746,"difficulty":0.0006384254}
{"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. Denise's card is shown to John. Mary's card is shown to Denise. Kevin's card is shown to Kevin. Denise'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:1,2 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Denise","Kevin","Mary"],"index":63730,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959378242,"difficulty":0.0040621758}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Bryan. Martha's card is shown to Bryan. Alfred's card is shown to Bryan. Alfred's card is shown to Martha. Bryan's card is shown to Alfred. 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) ] Agenta knows that (Agentc knows whether 2)","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":"Bryan can now know that Alfred can know whether Martha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bryan","Martha","Alfred"],"index":28198,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786325097,"difficulty":0.0213674903}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Herbert. Herbert's card is shown to Howard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Howard can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Herbert","Howard","Justin"],"index":66585,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994142056,"difficulty":0.0005857944}
{"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. Daniel's card is shown to James. Keith's card is shown to Daniel. 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) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know that James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Victor","James","Daniel"],"index":3164,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989970326,"difficulty":0.0010029674}
{"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 Robert. Latonya's card is shown to Robert. Mandi's card is shown to Ella. Ella's card is shown to Latonya. Robert's card is shown to Mandi. It is publicly announced that someone picked a red card. It is publicly announced that Ella 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)) ] (Agentc 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":"Latonya can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Ella","Latonya","Mandi"],"index":66161,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9771313071,"difficulty":0.0228686929}
{"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 Wallace. Sharon's card is shown to Robert. Wallace'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 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sharon can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wallace","Robert","Sharon","Mary"],"index":23132,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984915257,"difficulty":0.0015084743}
{"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 Matthew. Matthew's card is shown to Suzanne. Suzanne's card is shown to Suzanne. It is publicly announced that someone picked a red card. It is publicly announced that Suzanne picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Matthew can now know whether Suzanne can know that Suzanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Matthew","Suzanne"],"index":26946,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9836747646,"difficulty":0.0163252354}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherri's card is shown to Austin. Austin's card is shown to Sherri. Sherri's card is shown to Sherri. Austin's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that Austin does not know whether Austin 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:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Sherri can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Austin","Sherri","Lisa"],"index":14025,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994519353,"difficulty":0.0005480647}
{"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 Adan. Joyce's card is shown to Adan. Joyce's card is shown to Scott. Scott'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:1 Agentb:1,4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Adan can now know whether Joyce can know that Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Adan","Scott","Joyce"],"index":24694,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9546125531,"difficulty":1.9546125531}
{"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. Carol's card is shown to Amy. Clara's card is shown to Amy. Amy's card is shown to Clara. It is publicly announced that someone picked a red card. It is publicly announced that Carol knows 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) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Clara can now know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Amy","Clara"],"index":27075,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9539158344,"difficulty":0.0460841656}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ida's card is shown to Angela. Angela's card is shown to Lenard. Lenard's card is shown to Lenard. Lenard's card is shown to Ida. It is publicly announced that someone picked a red card. It is publicly announced that Ida picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Angela can now know that Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Lenard","Ida"],"index":37997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9134801626,"difficulty":0.0865198374}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Florine. Jared's card is shown to Teresa. Jonathan's card is shown to Teresa. Jonathan's card is shown to Jared. Teresa's card is shown to Jonathan. Jonathan'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 Jared picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (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:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jonathan can now know that Jared can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Florine","Teresa","Jared","Jonathan"],"index":4752,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994101524,"difficulty":0.0005898476}
{"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 Barbara. Michael's card is shown to Darwin. Darwin's card is shown to Darwin. Darwin's card is shown to Katrina. 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 3)","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":"Barbara can now know that Darwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Michael","Darwin","Katrina"],"index":19881,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958070517,"difficulty":0.0041929483}
{"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 Charles. Charles's card is shown to Eric. Max's card is shown to Eric. Charles's card is shown to Max. It is publicly announced that someone picked a red card. It is publicly announced that Charlie knows whether Charles 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:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Charles can now know that Eric can know that Eric picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Charlie","Eric","Max"],"index":67012,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6902606487,"difficulty":0.3097393513}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kerry's card is shown to Kerry. George's card is shown to George. Gretchen's card is shown to Gretchen. It is publicly announced that someone picked a red card. It is publicly announced that Gretchen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Gretchen can now know that Kerry can know whether Kerry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kerry","George","Gretchen"],"index":27678,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8397693634,"difficulty":0.1602306366}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rod's card is shown to Randall. Randall's card is shown to David. 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:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rod can now know that Randall can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rod","Randall","David"],"index":53258,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987083673,"difficulty":0.0012916327}
{"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 Franklin. Emily's card is shown to Emily. Franklin's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Franklin's card is shown to Nicole. Emily's card is shown to Nicole. It is publicly announced that someone picked a red card. It is publicly announced that Nicole knows whether someone picked a red card. It is publicly announced that Kenneth does not know whether Nicole picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] Agenta knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Franklin can now know whether Kenneth can know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Franklin","Emily","Kenneth","Nicole"],"index":64888,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6208515167,"difficulty":0.3791484833}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lottie's card is shown to Lottie. Johnny's card is shown to Lottie. Lottie's card is shown to Johnny. 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) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Johnny can now know that Lottie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lottie","Johnny"],"index":40379,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9820140004,"difficulty":1.9820140004}
{"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 Gregory. Gregory's card is shown to Tiffany. It is publicly announced that someone picked a red card. It is publicly announced that Gregory knows whether Gregory picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Gregory can now know that Tiffany can know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gregory","Tiffany"],"index":66110,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9307919741,"difficulty":1.9307919741}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Tracey. Tracey's card is shown to Willie. Willie's card is shown to Willie. Willie's card is shown to Alan. Alan'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:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Willie can now know that Tracey can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tracey","Willie","Alan"],"index":26215,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988887906,"difficulty":0.0011112094}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betsy's card is shown to Betsy. Margaret's card is shown to Betsy. Stephanie's card is shown to Margaret. Stephanie's card is shown to Stephanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know that Stephanie can know whether Betsy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betsy","Margaret","Stephanie"],"index":1005,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9173128009,"difficulty":0.0826871991}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristen's card is shown to Kristen. Charles's card is shown to Kristen. Kristen'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 Kristen knows whether or not nobody 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) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Kristen can now know whether Charles can know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kristen","Charles"],"index":2137,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9963645339,"difficulty":0.0036354661}
{"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 Keith. Ciera's card is shown to Cynthia. Keith's card is shown to Ciera. Fred's card is shown to Ciera. Keith'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:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ciera can now know whether Keith can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Cynthia","Ciera","Fred"],"index":43593,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992575049,"difficulty":0.0007424951}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Todd. Martin's card is shown to Martin. Martin'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:1 Agentb:2 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:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Todd can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Todd","Martin","Robert"],"index":65087,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981439114,"difficulty":0.0018560886}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cherie's card is shown to Cherie. Brenda's card is shown to Cherie. Cherie's card is shown to Brenda. Morris's card is shown to Brenda. Cherie's card is shown to Morris. 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":"Brenda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cherie","Brenda","Morris"],"index":63252,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943828583,"difficulty":0.0056171417}
{"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. Kimberly's card is shown to Harry. Harry's card is shown to Harry. Kimberly's card is shown to Elizabeth. Harry's card is shown to Elizabeth. 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 Kimberly does not know whether Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Elizabeth can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kimberly","Harry","Elizabeth"],"index":35282,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994438291,"difficulty":0.0005561709}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Martha. Martha's card is shown to Jonathan. Jonathan's card is shown to Renee. Donna's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jonathan can now know that Renee can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Martha","Jonathan","Renee","Donna"],"index":19529,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993728995,"difficulty":0.0006271005}
{"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. Robert's card is shown to Amanda. Amanda's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that Amanda knows whether Amanda picked a red card. It is publicly announced that Robert does not know whether Amanda 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 whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Robert can now know whether Amanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Amanda"],"index":32801,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9209545851,"difficulty":1.9209545851}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Chris. Donovan's card is shown to Pamela. Pamela's card is shown to Pamela. 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:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Chris can now know whether Donovan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donovan","Chris","Pamela"],"index":54947,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994245768,"difficulty":0.0005754232}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Harold. Douglas's card is shown to Harold. Harold's card is shown to Douglas. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Douglas can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harold","Douglas","John"],"index":45143,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980825186,"difficulty":0.0019174814}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terrie's card is shown to Terrie. Terrie's card is shown to Rebecca. Rebecca's card is shown to Rebecca. Wayne's card is shown to Rebecca. Terrie's card is shown to Barbara. Barbara's card is shown to Barbara. Barbara's card is shown to Wayne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 Agentc:1,3 Agentd:3 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:1,2,4 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terrie can now know whether Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terrie","Rebecca","Barbara","Wayne"],"index":7954,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970266223,"difficulty":0.0029733777}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Normand's card is shown to Sherri. Verna's card is shown to Sherri. Maria's card is shown to Normand. Normand's card is shown to Normand. Normand's card is shown to Verna. 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 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know whether Normand can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sherri","Maria","Normand","Verna"],"index":53376,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992620349,"difficulty":0.0007379651}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Helen. Christopher's card is shown to Helen. Christopher's card is shown to Carl. Carl's card is shown to Christopher. Carol's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Carl does not know whether Carol picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Helen can now know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Carl","Christopher","Carol"],"index":40779,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5289462209,"difficulty":0.4710537791}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Van's card is shown to Pam. Arnold's card is shown to Pam. Mark's card is shown to Van. Arnold's card is shown to Van. Pam's card is shown to Mark. Mark's card is shown to Mark. Arnold's card is shown to Arnold. It is publicly announced that someone picked a red card. It is publicly announced that Arnold does not know whether Van picked a red card. It is publicly announced that Mark does not know whether Van 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) ] (Agentc knows whether 2)","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":"Mark can now know whether Van picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pam","Van","Mark","Arnold"],"index":16387,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8225349784,"difficulty":1.8225349784}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Simon's card is shown to Sylvia. Sylvia's card is shown to Simon. Simon's card is shown to Israel. Sylvia's card is shown to John. Simon's card is shown to John. Israel'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:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Simon can now know that Simon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sylvia","Simon","Israel","John"],"index":66830,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949982166,"difficulty":0.0050017834}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Tom. Jenny's card is shown to Tom. Gilbert's card is shown to Tom. Tom's card is shown to Jenny. Gilbert's card is shown to Jenny. Gilbert's card is shown to Gilbert. 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 2)","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":"Gilbert can now know that Jenny picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tom","Jenny","Gilbert"],"index":59880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976041913,"difficulty":0.0023958087}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annamaria's card is shown to Larhonda. Larhonda's card is shown to Alice. Cameron's card is shown to Annamaria. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know that Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cameron","Larhonda","Alice","Annamaria"],"index":43583,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9874271154,"difficulty":0.0125728846}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geoffrey's card is shown to Karen. Karen's card is shown to Christina. Christina's card is shown to Christina. Geoffrey's card is shown to Christina. Christina's card is shown to Geoffrey. Geoffrey's card is shown to Geoffrey. 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:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Geoffrey can now know whether Christina can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Christina","Geoffrey"],"index":4941,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9872374535,"difficulty":1.9872374535}
{"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 Kristin. 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:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Emma can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emma","Kristin","Matthew","Mary"],"index":36130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9927353859,"difficulty":0.0072646141}
{"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 Chase. Adam's card is shown to Virginia. Robert's card is shown to Virginia. Chase's card is shown to Adam. 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. It is publicly announced that Adam picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Adam can now know that Chase can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chase","Virginia","Adam","Robert"],"index":23437,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9844167829,"difficulty":0.0155832171}
{"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 Juan. Esther's card is shown to Summer. Ralph's card is shown to Summer. Juan's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Juan knows whether Juan 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) ] (Agentb knows whether (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":"Summer can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Summer","Esther","Ralph"],"index":56925,"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). William's card is shown to Brian. James's card is shown to Brian. William'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:2 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","William","James"],"index":36295,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988667965,"difficulty":0.0011332035}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Stephanie. Harold's card is shown to Harold. Harold's card is shown to Virginia. 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 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:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harold can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephanie","Harold","Virginia","Mattie"],"index":54375,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994083643,"difficulty":0.0005916357}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Mark. Joseph's card is shown to Mark. Cynthia'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:1,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Cynthia","Mark","Joseph"],"index":9858,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989743233,"difficulty":0.0010256767}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Barbara. Heather's card is shown to Barbara. Ray's card is shown to Annie. Barbara's card is shown to Annie. Heather's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ray can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ray","Barbara","Annie","Heather"],"index":13196,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977807403,"difficulty":0.0022192597}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shu's card is shown to Shu. Tracy's card is shown to Shu. Shu's card is shown to Mary. Shu's card is shown to Tracy. Tracy's card is shown to Tracy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shu can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shu","Mary","Tracy"],"index":8841,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999361217,"difficulty":0.000638783}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cruz's card is shown to Cruz. Kathleen's card is shown to Cruz. Jarod's card is shown to Cruz. Cruz's card is shown to Kathleen. Jane's card is shown to Jane. Cruz's card is shown to Jarod. Jane's card is shown to Jarod. 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:3 Agentd:1,3 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:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kathleen can now know that Jarod picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cruz","Kathleen","Jane","Jarod"],"index":46159,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970865846,"difficulty":0.0029134154}
{"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 Nellie. John's card is shown to Lisette. Nellie's card is shown to Lisette. Lisette's card is shown to Lisette. 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) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nellie can now know whether John can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Nellie","Lisette"],"index":13505,"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). Deborah's card is shown to Deborah. Claudia's card is shown to Beth. Deborah's card is shown to Claudia. 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:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Deborah can now know whether Beth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deborah","Beth","Claudia","Joann"],"index":53629,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9494460821,"difficulty":0.0505539179}
{"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 James. Jason's card is shown to Jason. James's card is shown to Joey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 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:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carlos","James","Jason","Joey"],"index":48308,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989796281,"difficulty":0.0010203719}
{"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 Robert. Robert's card is shown to Elizabeth. Elizabeth's card is shown to Christine. Clarence's card is shown to Christine. Christine's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth knows whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","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":"Robert can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Elizabeth","Christine","Clarence"],"index":58037,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.987187624,"difficulty":0.012812376}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Paul. Harold's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Harold knows whether Paul 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 (Agentb knows that (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":"Paul can now know whether Harold can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Harold"],"index":17525,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994282126,"difficulty":0.0005717874}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Adam. Morris's card is shown to Adam. Morris's card is shown to Morris. 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 Morris does not know whether or not everyone picked a red card. It is publicly announced that Morris does not know whether Adam picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Adam can now know whether Morris can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Adam","Morris"],"index":12951,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994545579,"difficulty":0.0005454421}
{"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. Arthur's card is shown to Justin. Justin's card is shown to Charles. Robert's card is shown to Charles. Arthur's card is shown to Charles. Robert's card is shown to Robert. Arthur's card is shown to Robert. Justin's card is shown to Arthur. Arthur's card is shown to Arthur. 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 whether 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":"Arthur can now know whether Arthur picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Justin","Charles","Robert","Arthur"],"index":15871,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7921651006,"difficulty":0.2078348994}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Enid's card is shown to Enid. Kenneth's card is shown to Enid. Enid's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Enid's card is shown to Alice. Kenneth's card is shown to Alice. Daniel's card is shown to Daniel. 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 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Enid","Kenneth","Alice","Daniel"],"index":59840,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994069338,"difficulty":0.0005930662}
{"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. Michael's card is shown to Michael. Darren's card is shown to Michael. Michael's card is shown to Darren. 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 whether 1)","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":"Herbert can now know whether Herbert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Herbert","Michael","Darren"],"index":1713,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6965878606,"difficulty":0.3034121394}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Nicholas. Anthony's card is shown to Nicholas. Lisa's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Lisa can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Nicholas","Anthony"],"index":3780,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994577765,"difficulty":0.0005422235}
{"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 Tonya. Tonya's card is shown to David. David's card is shown to David. Tonya'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:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tonya can now know that David can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tonya","David","William"],"index":7587,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999329567,"difficulty":0.000670433}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Verna's card is shown to Verna. Antoinette's card is shown to Antoinette. Ann's card is shown to Antoinette. Ann's card is shown to Ann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Verna can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Verna","Antoinette","Ann"],"index":38860,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944617152,"difficulty":0.0055382848}
{"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. James's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether someone picked a red card. It is publicly announced that Paul does not know whether Paul 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) ] Agentb knows that (Agenta knows that 2)","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":"Paul can now know that James can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Paul","Jerry"],"index":1130,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9743697047,"difficulty":0.0256302953}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Constance's card is shown to Kevin. Constance's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 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:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that Kevin can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","James","Constance"],"index":36558,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993534684,"difficulty":0.0006465316}
{"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 James. Shirley's card is shown to James. Ira's card is shown to Ira. James'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 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shirley can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Ira","Shirley"],"index":46264,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989861846,"difficulty":0.0010138154}
{"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. Ronald's card is shown to Michael. Peter's card is shown to Ronald. Ronald's card is shown to Alison. Alison's card is shown to Peter. Peter's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Ronald does not know whether Alison picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Michael can now know that Ronald can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Ronald","Alison","Peter"],"index":32163,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993420243,"difficulty":0.0006579757}
{"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 Michael. Michael's card is shown to Janice. Janice's card is shown to Janice. 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 Nellie does not know whether Nellie 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) ] (Agenta knows whether (~(1|2|3)))","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":"Nellie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nellie","Michael","Janice"],"index":42724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994613528,"difficulty":0.0005386472}
{"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 Daniel. Harry's card is shown to Thomas. Daniel's card is shown to Shellie. Harry's card is shown to Shellie. Thomas'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 Harry picked a red card. It is publicly announced that Daniel 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)) ] Agenta knows that (Agentb knows whether 3)","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":"Daniel can now know that Thomas can know whether Shellie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Thomas","Shellie","Harry"],"index":24424,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7385239005,"difficulty":0.2614760995}
{"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. Robert's card is shown to Anthony. Robert's card is shown to Stephanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Stephanie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Robert","Stephanie"],"index":53566,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9896019101,"difficulty":0.0103980899}
{"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 Lynne. Lynne's card is shown to Caitlyn. Caitlyn's card is shown to Caitlyn. Steve's card is shown to Caitlyn. Caitlyn's card is shown to Steve. 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) ] (Agenta knows that 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":"Lynne can now know that Steve picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynne","Caitlyn","Steve"],"index":16888,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9634224772,"difficulty":0.0365775228}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Kim. Pamela's card is shown to Kim. Rita's card is shown to Kelly. Rita's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Kim picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Kelly can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kim","Pamela","Kelly","Rita"],"index":6611,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8386051059,"difficulty":1.8386051059}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Kevin. Sandra's card is shown to Sandra. Stephanie's card is shown to Sandra. Kevin's card is shown to Stephanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sandra can now know that Kevin can know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Sandra","Stephanie"],"index":48747,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.852321744,"difficulty":0.147678256}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Filiberto's card is shown to Filiberto. Filiberto's card is shown to Virginia. Virginia's card is shown to Virginia. Virginia's card is shown to Joyce. It is publicly announced that someone picked a red card. It is publicly announced that Joyce knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Virginia can now know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Filiberto","Virginia","Joyce"],"index":67310,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9908969998,"difficulty":0.0091030002}
{"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 Carol. Gordon's card is shown to Gordon. It is publicly announced that someone picked a red card. It is publicly announced that Carol picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] Agenta knows that (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":"Carol can now know that Gordon can know whether Gordon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carol","Gordon"],"index":55822,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8953787088,"difficulty":0.1046212912}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delia's card is shown to Haywood. Haywood's card is shown to Freddie. Freddie's card is shown to Freddie. Haywood's card is shown to Delia. Freddie's card is shown to Delia. It is publicly announced that someone picked a red card. It is publicly announced that Freddie knows whether Freddie picked a red card. It is publicly announced that Haywood does not know whether Freddie 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) ] (Agentc knows that (~(1|2|3)))","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":"Delia can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Haywood","Freddie","Delia"],"index":19611,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990391731,"difficulty":0.0009608269}
{"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 David. Katherine's card is shown to David. David's card is shown to Robert. Robert's card is shown to Robert. Katherine's card is shown to Robert. David's card is shown to Katherine. Christopher's card is shown to Katherine. 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 Katherine picked a red card. It is publicly announced that Christopher does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"David can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Robert","Katherine","Christopher"],"index":38859,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9822922945,"difficulty":0.0177077055}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kayla's card is shown to Kayla. Edward's card is shown to Kayla. Kayla's card is shown to Edward. Edward's card is shown to Edward. Edward's card is shown to Noreen. Noreen's card is shown to Noreen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kayla can now know whether Edward can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kayla","Edward","Noreen"],"index":34816,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994155169,"difficulty":0.0005844831}
{"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 John. John's card is shown to Larry. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether Larry picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"John can now know whether Larry can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Larry"],"index":67155,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999432385,"difficulty":0.000567615}
{"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 Vanessa. Lawrence's card is shown to Thomas. Vanessa's card is shown to James. Vanessa'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:4 Agentc:1 Agentd: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:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vanessa can now know that Thomas can know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vanessa","Thomas","James","Lawrence"],"index":64924,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983935952,"difficulty":0.0016064048}
{"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. Tamara's card is shown to Nancy. Nancy's card is shown to Melissa. Melissa's card is shown to Melissa. Nancy's card is shown to Tamara. 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) ] (Agenta 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":"Nancy can now know whether Tamara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Melissa","Tamara"],"index":34548,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.984870851,"difficulty":1.984870851}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Burton's card is shown to Marc. Burton's card is shown to Burton. Joel's card is shown to Burton. 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 that (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":"Marc can now know that Burton can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marc","Burton","Joel"],"index":51809,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9859765768,"difficulty":0.0140234232}
{"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. Lela's card is shown to James. James's card is shown to Erin. Erin's card is shown to Lela. Lela's card is shown to Lela. It is publicly announced that someone picked a red card. It is publicly announced that James picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb 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":"Erin can now know whether Erin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Erin","Lela"],"index":30891,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8353001475,"difficulty":1.8353001475}
{"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 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.","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":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Rosemary"],"index":10329,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990577102,"difficulty":0.0009422898}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerome's card is shown to Jerome. Dennis's card is shown to Jerome. Jerome's card is shown to Henry. Dennis's card is shown to Dennis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dennis can now know whether Henry can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jerome","Henry","Dennis"],"index":60621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990926981,"difficulty":0.0009073019}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charisse's card is shown to Charles. Charles's card is shown to Charisse. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Charisse","Crystal"],"index":38046,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988926053,"difficulty":0.0011073947}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Angela's card is shown to David. Angela's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Emely does not know whether David picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Brenda does not know whether Brenda 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) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Brenda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emely","Brenda","David","Angela"],"index":67139,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9785917401,"difficulty":0.0214082599}
{"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. Catherine's card is shown to Evelyn. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn picked a red card. It is publicly announced that Evelyn 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)) ] (Agentb 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":"Evelyn can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Catherine","Evelyn"],"index":31006,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994674325,"difficulty":0.0005325675}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Britany. Britany's card is shown to Frank. Deann's card is shown to Deann. Deann's card is shown to Lauren. It is publicly announced that someone picked a red card. It is publicly announced that Lauren does not know whether Frank 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 whether (Agenta knows that (1|2|3|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":"Frank can now know whether Britany can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Britany","Frank","Deann","Lauren"],"index":5419,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994207621,"difficulty":0.0005792379}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maxwell's card is shown to Gerald. Gerald's card is shown to Maxwell. Maxwell's card is shown to Maxwell. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Gerald can now know that Maxwell can know that Gerald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gerald","Maxwell"],"index":11216,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961107373,"difficulty":0.0038892627}
{"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. John's card is shown to William. Florence's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 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:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","John","Florence"],"index":14238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.992349267,"difficulty":0.007650733}
{"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. Elizabeth's card is shown to Robin. Graciela's card is shown to Elizabeth. Robin's card is shown to Graciela. Robin's card is shown to Rudolph. Elizabeth's card is shown to Rudolph. 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:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Graciela can now know whether Graciela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robin","Elizabeth","Graciela","Rudolph"],"index":39790,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6741012931,"difficulty":0.3258987069}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Dwight. 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 that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dwight can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dwight","Carl","Kathleen"],"index":50460,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989798665,"difficulty":0.0010201335}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mauricio's card is shown to Lora. Lora's card is shown to Mauricio. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Lora can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lora","Mauricio"],"index":42486,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.988319397,"difficulty":0.011680603}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kareem's card is shown to Kareem. Patricia's card is shown to Patricia. Joyce's card is shown to Steven. Kareem's card is shown to Steven. Patricia'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:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joyce can now know that Kareem can know whether Kareem picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Kareem","Patricia","Steven"],"index":4320,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.641346395,"difficulty":1.641346395}
{"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 Robert. Dean's card is shown to Robert. Jason's card is shown to Jason. Dean's card is shown to Dean. It is publicly announced that someone picked a red card. It is publicly announced that Dean does not know whether Robert picked a red card. It is publicly announced that Jason does not know whether Raul picked a red card. It is publicly announced that Dean knows whether someone picked a red card. It is publicly announced that Dean does not know whether Raul 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Dean can now know whether Robert can know that Raul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Jason","Dean","Raul"],"index":45973,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8648099303,"difficulty":0.1351900697}
{"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 Clay. Jason's card is shown to Adela. Adela's card is shown to Joshua. Adela'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:4 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","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":"Clay can now know that Joshua picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clay","Adela","Joshua","Jason"],"index":32279,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983831644,"difficulty":0.0016168356}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Mark. Mark's card is shown to Kathleen. Judy's card is shown to Kathleen. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Kathleen can now know that Mark can know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Kathleen","Judy"],"index":29074,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5493003726,"difficulty":0.4506996274}
{"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. William's card is shown to Susan. Ethan's card is shown to Susan. Ethan's card is shown to Ethan. Ethan's card is shown to Ann. Ann's card is shown to Ann. 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) ] (Agentb knows whether 1)","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":"Susan can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Susan","Ethan","Ann"],"index":62521,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8941711187,"difficulty":1.8941711187}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ethel's card is shown to David. Ethel's card is shown to Ethel. 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) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"David can now know that Ethel can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Ethel"],"index":21863,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994012117,"difficulty":0.0005987883}
{"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 Joshua. Ann's card is shown to Francisco. Joshua's card is shown to Ann. Ann's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Ann 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:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Ann can now know whether Joshua can know whether Francisco picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joshua","Francisco","Ann"],"index":65879,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989460111,"difficulty":0.0010539889}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Lois. Gwendolyn's card is shown to Gwendolyn. It is publicly announced that someone picked a red card. It is publicly announced that Lois does not know whether or not everyone picked a red card. It is publicly announced that Gwendolyn 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 whether (Agenta 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":"Gwendolyn can now know whether Lois can know that Gwendolyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lois","Gwendolyn"],"index":42821,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8349606991,"difficulty":0.1650393009}
{"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 Thomas. Rebecca's card is shown to Lynn. Kendra's card is shown to Kendra. Thomas's card is shown to Rebecca. It is publicly announced that someone picked a red card. It is publicly announced that Lynn does not know whether Thomas picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Thomas picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Thomas can now know whether Lynn can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Lynn","Kendra","Rebecca"],"index":57696,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987427592,"difficulty":0.0012572408}
{"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. Clayton's card is shown to Betty. Betty's card is shown to Clayton. Barbara's card is shown to Clayton. William's card is shown to Clayton. Barbara's card is shown to Barbara. William's card is shown to Barbara. Betty's card is shown to William. 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 Barbara knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Barbara can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Clayton","Barbara","William"],"index":29996,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942071438,"difficulty":0.0057928562}
{"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 Jeffrey. Christina's card is shown to Jeffrey. Doris's card is shown to Mary. Mary's card is shown to Mary. Mary'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 Doris 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 that 1)","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":"Doris can now know that Jeffrey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffrey","Doris","Mary","Christina"],"index":18999,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9912840128,"difficulty":0.0087159872}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Jean. Jean's card is shown to Joey. Jean's card is shown to Robert. Joey's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Jean knows whether Jean 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) ] (Agenta knows whether 1)","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) ] 0","hypothesis":"Jean can now know whether Jean picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jean","Joey","Robert"],"index":63017,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.973906219,"difficulty":0.026093781}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Lacie's card is shown to Angela. Cheryl's card is shown to Angela. Chassidy's card is shown to Cheryl. 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 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Angela can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chassidy","Angela","Lacie","Cheryl"],"index":18921,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989129305,"difficulty":0.0010870695}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Walter's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Walter knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Walter can now know that Donald can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donald","Walter"],"index":55877,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9061483741,"difficulty":1.9061483741}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kendra's card is shown to Philip. Sidney's card is shown to Philip. Micheal's card is shown to Kendra. Philip's card is shown to Sidney. Sidney's card is shown to Micheal. 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) ] Agentd knows whether (Agentc knows that 1)","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":"Micheal can now know whether Sidney can know that Philip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Philip","Kendra","Sidney","Micheal"],"index":14262,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9315169454,"difficulty":1.9315169454}
{"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 Patricia. Patricia's card is shown to Nicole. Adam's card is shown to Adam. 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 that (Agentb knows whether 3)","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":"Patricia can now know that Nicole can know whether Adam picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Nicole","Adam","Shawn"],"index":27157,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7636412978,"difficulty":1.7636412978}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Cassandra. Cassandra's card is shown to Cassandra. Jose's card is shown to Cassandra. Ronald's card is shown to Jose. Cassandra's card is shown to Jose. 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 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cassandra can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Cassandra","Jose"],"index":53936,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989439845,"difficulty":0.0010560155}
{"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 Jessica. Kerry's card is shown to Kimberly. It is publicly announced that someone picked a red card. It is publicly announced that Jessica picked a black card. It is publicly announced that Jessica does not know whether Kimberly picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jessica can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kerry","Jessica","Kimberly"],"index":21723,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994630218,"difficulty":0.0005369782}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. Clifford's card is shown to Clifford. 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) ] (Agentb knows whether (1&2&3&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":"Clifford can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Curtis","Clifford","Michael","Martha"],"index":734,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9929305315,"difficulty":0.0070694685}
{"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 Minerva. Minerva's card is shown to Edward. Minerva's card is shown to Anna. Edward's card is shown to Anna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anna can now know whether Edward can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Minerva","Edward","Anna"],"index":37061,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994034767,"difficulty":0.0005965233}
{"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 James. James's card is shown to John. John's card is shown to John. Ida's card is shown to John. James's card is shown to Alan. Ida's card is shown to Alan. 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 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:4 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether John can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","John","Ida","Alan"],"index":34943,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999309659,"difficulty":0.000690341}
{"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. Corrine's card is shown to Robert. Tammy's card is shown to Robert. Robert's card is shown to Corrine. Robert's card is shown to Tammy. It is publicly announced that someone picked a red card. It is publicly announced that Tammy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 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:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Corrine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Corrine","Tammy"],"index":33789,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990447164,"difficulty":0.0009552836}
{"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 James. James's card is shown to Amber. Amber's card is shown to Amber. Nichol's card is shown to Amber. Amber's card is shown to Nichol. Joaquin's card is shown to Joaquin. It is publicly announced that someone picked a red card. It is publicly announced that Joaquin 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 Agentb:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agenta knows that 2)","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":"James can now know that Amber picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Amber","Nichol","Joaquin"],"index":38963,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6930367351,"difficulty":0.3069632649}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Barbara's card is shown to Lola. Lola's card is shown to Lola. 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 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Barbara can now know that Lola can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barbara","Lola"],"index":26597,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7723222971,"difficulty":0.2276777029}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Joseph. Mable's card is shown to Mable. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (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":"Joseph can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Mable","Roland"],"index":46344,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951620698,"difficulty":0.0048379302}
{"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 Cassandra. Cassandra's card is shown to Sarah. Sarah's card is shown to Sarah. Matthew's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Cassandra does not know whether Robert picked a red card. It is publicly announced that Matthew picked a red card. It is publicly announced that Sarah does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 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)) ] (Agentb knows that 3)","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":"Sarah can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cassandra","Sarah","Robert","Matthew"],"index":34968,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8818668127,"difficulty":0.1181331873}
{"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 Carrie. Carrie's card is shown to Mark. Mark's card is shown to Marquis. Robert's card is shown to Marquis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know whether Robert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carrie","Mark","Robert","Marquis"],"index":30120,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993483424,"difficulty":0.0006516576}
{"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 John. Larry's card is shown to Larry. Patricia's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Linda can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","John","Larry","Patricia"],"index":36599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9915508032,"difficulty":0.0084491968}
{"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. Margart's card is shown to Jennifer. Jennifer's card is shown to Margart. Matthew's card is shown to Margart. Jennifer's card is shown to Barbara. Margart'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:1,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether Margart can know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Matthew","Margart","Barbara"],"index":30681,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998747468,"difficulty":0.001252532}
{"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 Francine. Francine's card is shown to Amanda. Amanda's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that Francine does not know whether Amanda 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 whether (Agentb 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":"Francine can now know whether Amanda can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Francine","Amanda"],"index":66146,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.98171103,"difficulty":1.98171103}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Odell. David's card is shown to David. Odell's card is shown to James. Odell's card is shown to Randall. David's card is shown to Randall. 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) ] Agentc knows whether (Agenta knows whether 3)","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":"James can now know whether Odell can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Odell","David","James","Randall"],"index":11628,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9918640852,"difficulty":0.0081359148}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqueline's card is shown to Tamara. Jacqueline's card is shown to Jacqueline. Tamara's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jacqueline can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tamara","Jacqueline","Robert"],"index":30148,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967239499,"difficulty":0.0032760501}
{"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 Matthew. Anne's card is shown to Anne. Anne'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:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Matthew can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Matthew","Anne","John"],"index":62714,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981665611,"difficulty":0.0018334389}
{"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 Elizabeth. Mary's card is shown to William. Mary's card is shown to Mary. 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:2 Agentb:3 Agentc: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:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","William","Mary"],"index":10730,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998599112,"difficulty":0.001400888}
{"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. Delbert's card is shown to Stephen. Delbert's card is shown to Delbert. Amanda's card is shown to Delbert. Stephen's card is shown to Amanda. Delbert's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that Amanda knows whether Delbert 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 3)","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":"Delbert can now know that Amanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephen","Delbert","Amanda"],"index":62405,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9872186184,"difficulty":0.0127813816}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Coral's card is shown to Andrea. Andrea's card is shown to Coral. It is publicly announced that someone picked a red card. It is publicly announced that Coral 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)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Andrea can now know that Coral can know whether Andrea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrea","Coral"],"index":13883,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8634062409,"difficulty":0.1365937591}
{"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 Calvin. Joseph's card is shown to Calvin. Randall's card is shown to Calvin. Joseph's card is shown to Joseph. Randall's card is shown to Randall. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Calvin can now know that Randall picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Calvin","Joseph","Randall"],"index":14300,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973276854,"difficulty":0.0026723146}
{"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 Shannon. Harold's card is shown to Harold. Harold's card is shown to Christine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harold can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shannon","Harold","Christine","Delores"],"index":28332,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989810586,"difficulty":0.0010189414}
{"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 Larry. Daniel's card is shown to Herman. Herman's card is shown to Herman. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether Larry picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","James","Daniel","Herman"],"index":13076,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8677440286,"difficulty":0.1322559714}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tim's card is shown to Julia. Fred's card is shown to Tim. It is publicly announced that someone picked a red card. It is publicly announced that Earl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Earl can now know that Julia can know that Julia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julia","Earl","Tim","Fred"],"index":48520,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9830649495,"difficulty":0.0169350505}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dillon's card is shown to Marva. Marva's card is shown to Ruthie. Katie's card is shown to Dillon. Marva's card is shown to Katie. Ruthie's card is shown to Katie. It is publicly announced that someone picked a red card. It is publicly announced that Ruthie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Marva can now know that Katie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marva","Ruthie","Dillon","Katie"],"index":33329,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989821315,"difficulty":0.0010178685}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Marion. Marjorie's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Marion knows whether or not nobody 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))","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":"Marion can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marion","Marjorie"],"index":55800,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994231462,"difficulty":0.0005768538}
{"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 John. John'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 Christopher picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that John knows 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) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Christopher can now know whether John can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Christopher"],"index":3566,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9947240949,"difficulty":0.0052759051}
{"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 Debra. Michael's card is shown to Debra. Debra's card is shown to Robert. Robert's card is shown to Robert. Michael's card is shown to Robert. Debra's card is shown to Michael. Robert'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:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Debra can now know that Michael can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debra","Robert","Michael"],"index":6310,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958561063,"difficulty":0.0041438937}
{"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 Joseph. Joseph's card is shown to Lois. Lois's card is shown to Lois. Tina's card is shown to Lois. Lois's card is shown to Tina. Tina's card is shown to Tina. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lois can now know whether Tina can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Lois","Tina"],"index":32100,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9842748046,"difficulty":0.0157251954}
{"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 Sara. Allen's card is shown to Sara. Sara's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Timothy does not know whether Timothy picked a red card. It is publicly announced that Sara 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 whether (~(1|2|3)))","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":"Timothy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sara","Timothy","Allen"],"index":16400,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993927479,"difficulty":0.0006072521}
{"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. Louise's card is shown to Alma. Alma's card is shown to Alma. Steven's card is shown to Alma. 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 Agentb:1,2,3 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:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know whether Alma can know that Alma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Louise","Alma","Steven"],"index":32532,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6458678842,"difficulty":1.6458678842}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lasonya's card is shown to Lasonya. Lori's card is shown to Lasonya. Richard's card is shown to Lasonya. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lori can now know that Lori picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lasonya","Lori","Richard"],"index":21947,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9827210307,"difficulty":0.0172789693}
{"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. Evette's card is shown to Evette. Wanda's card is shown to Wanda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Evette","Wanda"],"index":5018,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993625283,"difficulty":0.0006374717}
{"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 Robert. Larry's card is shown to Larry. Robert's card is shown to Lee. It is publicly announced that someone picked a red card. It is publicly announced that Lee does not know whether Lee 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 whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Larry can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Larry","Lee"],"index":6525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9863305092,"difficulty":0.0136694908}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yan's card is shown to Yan. Yan's card is shown to Patti. Patti's card is shown to Patti. It is publicly announced that someone picked a red card. It is publicly announced that Patti knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Yan does not know whether Patti 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":"Yan can now know that Patti can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Yan","Patti"],"index":37965,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6851365566,"difficulty":0.3148634434}
{"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 Debbie. Julie's card is shown to Debbie. Annette's card is shown to Annette. Debbie's card is shown to Julie. Annette'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:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debbie","Annette","Julie"],"index":7104,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998967886,"difficulty":0.001032114}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rick's card is shown to Carol. Jaime's card is shown to Jaime. Rick's card is shown to Jaime. Cindy's card is shown to Jaime. Cindy's card is shown to Rick. Rick's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Rick does not know whether Rick 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 whether (Agentc knows that 1)","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":"Cindy can now know whether Rick can know that Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Jaime","Rick","Cindy"],"index":53839,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.84882164,"difficulty":0.15117836}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnnie's card is shown to Johnnie. Maria's card is shown to Johnnie. Johnnie's card is shown to Tina. Tina'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:1,3 Agentb:1 Agentc:2,3 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 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tina can now know that Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Johnnie","Tina","Maria"],"index":16076,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948764443,"difficulty":0.0051235557}
{"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 Wayne. Leana's card is shown to Leana. Wayne's card is shown to Norman. Leana's card is shown to Robin. It is publicly announced that someone picked a red card. It is publicly announced that Wayne does not know whether Leana picked a red card. It is publicly announced that Robin knows whether Leana picked a red card. It is publicly announced that Wayne does not know whether Norman picked a red card. It is publicly announced that Leana 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)) ] Agentc knows whether (Agenta knows whether 4)","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":"Norman can now know whether Wayne can know whether Robin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","Leana","Norman","Robin"],"index":10236,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986352324,"difficulty":0.0013647676}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leona's card is shown to Leona. Anthony's card is shown to Leona. Leona's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shirley can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leona","Shirley","Anthony"],"index":8882,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993002415,"difficulty":0.0006997585}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Milton's card is shown to Milton. Pedro's card is shown to Pedro. Milton's card is shown to Shirley. Pedro's card is shown to Josh. It is publicly announced that someone picked a red card. It is publicly announced that Milton does not know whether Pedro picked a red card. It is publicly announced that Josh knows whether Pedro picked a red card. It is publicly announced that Milton does not know whether Shirley picked a red card. It is publicly announced that Pedro 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)) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc: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":"Milton can now know that Shirley can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Milton","Pedro","Shirley","Josh"],"index":7134,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9856851101,"difficulty":0.0143148899}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Saul's card is shown to Angela. Marcela's card is shown to Angela. Saul's card is shown to Josephine. Josephine's card is shown to Marcela. Marcela's card is shown to Marcela. It is publicly announced that someone picked a red card. It is publicly announced that Marcela picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Saul can now know that Josephine can know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Saul","Josephine","Marcela"],"index":18998,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9849328399,"difficulty":0.0150671601}
{"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 Maria. Maria's card is shown to Christopher. Christopher's card is shown to Christopher. Maria's card is shown to Richard. Christopher'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 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","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":"Maria can now know that Darla picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Christopher","Darla","Richard"],"index":64448,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985697269,"difficulty":0.0014302731}
{"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 Lucile. Louise's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Daniel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Daniel can now know whether Lucile can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucile","Daniel","Louise"],"index":52553,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8700281382,"difficulty":0.1299718618}
{"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 Jessica. Laura's card is shown to Jessica. Barbara's card is shown to Laura. Laura's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessica","Laura","Barbara"],"index":58907,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949352145,"difficulty":0.0050647855}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Roy. Brandon's card is shown to Brandon. Roy's card is shown to Lawrence. Brandon's card is shown to Annetta. It is publicly announced that someone picked a red card. It is publicly announced that Roy does not know whether Brandon picked a red card. It is publicly announced that Annetta knows whether Brandon picked a red card. It is publicly announced that Roy does not know whether Lawrence picked a red card. It is publicly announced that Brandon 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)) ] Agenta knows that (Agentc 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":"Roy can now know that Lawrence can know whether Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roy","Brandon","Lawrence","Annetta"],"index":2311,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8034885526,"difficulty":0.1965114474}
{"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 Harold. Jennifer's card is shown to Harold. Harold's card is shown to Jennifer. Ray's card is shown to Jennifer. Jennifer's card is shown to Ray. Harold's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer picked a black card. It is publicly announced that Harold does not know whether Teresa 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) ] Agenta knows whether (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":"Harold can now know whether Teresa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Jennifer","Ray","Teresa"],"index":2721,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999302268,"difficulty":0.000697732}
{"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 John. John's card is shown to Lisa. Tracy's card is shown to Lisa. John's card is shown to Tracy. Tracy's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Tracy can now know that Lisa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Lisa","Tracy"],"index":26671,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993652701,"difficulty":0.0006347299}
{"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 Tim. James's card is shown to Jeannie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tim can now know whether Lee can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tim","Lee","Jeannie","James"],"index":20690,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.980581522,"difficulty":0.019418478}
{"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 Carolyn. Carolyn's card is shown to Alexis. Alexis's card is shown to Alexis. Alexis's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc: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:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether Alexis can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Alexis","Richard"],"index":28452,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993938208,"difficulty":0.0006061792}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elton's card is shown to Clarence. Clarence's card is shown to Grover. Grover's card is shown to Grover. Clarence's card is shown to Elton. Grover's card is shown to Elton. It is publicly announced that someone picked a red card. It is publicly announced that Grover knows whether Grover picked a red card. It is publicly announced that Clarence does not know whether Grover 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) ] (Agenta knows whether (1|2|3))","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":"Clarence can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clarence","Grover","Elton"],"index":9371,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994459748,"difficulty":0.0005540252}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emanuel's card is shown to Juanita. Erica's card is shown to Juanita. Ruth's card is shown to Juanita. Juanita's card is shown to Erica. Erica's card is shown to Erica. Erica'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:2,3,4 Agentb:1,3 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:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emanuel can now know whether Juanita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Emanuel","Erica","Ruth"],"index":19470,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7010813951,"difficulty":1.7010813951}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alfred's card is shown to Alfred. Lela's card is shown to Alfred. Georgianna's card is shown to Alfred. Alfred's card is shown to Kathleen. Lela's card is shown to Kathleen. Georgianna's card is shown to Lela. Alfred's card is shown to Georgianna. Lela's card is shown to Georgianna. 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 whether (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":"Kathleen can now know whether Alfred can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfred","Kathleen","Lela","Georgianna"],"index":9428,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848874807,"difficulty":0.0151125193}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristi's card is shown to Kyong. Kyong's card is shown to Kristi. It is publicly announced that someone picked a red card. It is publicly announced that Kyong 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 whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Kristi can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kyong","Kristi"],"index":6868,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7173641324,"difficulty":0.2826358676}
{"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 Cassie. Cassie's card is shown to Linda. Janice's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that Janice does not know whether Linda picked a red card. It is publicly announced that Cassie does not know whether Cassie 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 2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Janice can now know that Cassie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cassie","Linda","Janice"],"index":38896,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994165897,"difficulty":0.0005834103}
{"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 Nicholas. 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 Nicholas picked a red card. It is publicly announced that David does not know whether Nicholas 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) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Nicholas can now know whether David can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nicholas","David"],"index":65208,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9741520882,"difficulty":0.0258479118}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Prudence's card is shown to Prudence. Helen's card is shown to Prudence. Darrell's card is shown to Prudence. Helen's card is shown to Helen. Darrell's card is shown to Helen. Prudence's card is shown to Darrell. Helen's card is shown to Darrell. 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) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Helen can now know that Darrell can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Prudence","Helen","Darrell"],"index":19447,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992732406,"difficulty":0.0007267594}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Christopher's card is shown to Barbara. Barbara's card is shown to Christopher. Christopher's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Barbara 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 that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Barbara can now know that Christopher can know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barbara","Christopher"],"index":3837,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9747530818,"difficulty":0.0252469182}
{"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 Arthur. Jared's card is shown to Nora. Nora's card is shown to Jared. It is publicly announced that someone picked a red card. It is publicly announced that Nora does not know whether Arthur picked a red card. It is publicly announced that Nora 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 (Agentb 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":"Arthur can now know that Nora can know whether Jared picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Arthur","Nora","Jared"],"index":65246,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9203265309,"difficulty":0.0796734691}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Gladys. James's card is shown to James. Janet's card is shown to James. Gladys's card is shown to Janet. 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. It is publicly announced that James picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Janet can now know that Gladys can know that Janet picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gladys","James","Janet"],"index":3218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9719681144,"difficulty":0.0280318856}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maryjane's card is shown to Maryjane. Kristy's card is shown to Maryjane. Charles's card is shown to Maryjane. Charles's card is shown to Bradley. Maryjane's card is shown to Kristy. Bradley's card is shown to Charles. Kristy's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Kristy 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) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Kristy can now know that Charles can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maryjane","Bradley","Kristy","Charles"],"index":47170,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985528588,"difficulty":0.0014471412}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Emma. Emma's card is shown to Janice. Arthur's card is shown to Janice. Janice's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Emma 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 that (Agentb knows whether 1)","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":"Emma can now know that Janice can know whether Emma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emma","Janice","Arthur"],"index":34981,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.892663002,"difficulty":0.107336998}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tabetha's card is shown to Tabetha. Tabetha's card is shown to George. George's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Tabetha knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Denise can now know whether George can know whether Tabetha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tabetha","George","Denise","Mary"],"index":35312,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990556836,"difficulty":0.0009443164}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glen's card is shown to Janice. Margaret's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that Glen knows whether Margaret picked a red card. It is publicly announced that Glen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! 1 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! 1 ] 0","hypothesis":"Glen can now know whether Glen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Glen","Janice","Margaret"],"index":65021,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9609564543,"difficulty":0.0390435457}
{"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. Brian's card is shown to Brian. Brian's card is shown to Andrew. Linda'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:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Brian","Andrew","William"],"index":7756,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7796804309,"difficulty":0.2203195691}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jo's card is shown to Jo. Jo's card is shown to Norine. Norine's card is shown to Julio. 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) ] Agentc knows that (Agentb 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":"Julio can now know that Norine can know that Julio picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jo","Norine","Julio"],"index":64920,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980314374,"difficulty":0.0019685626}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harriet's card is shown to Harriet. Taylor's card is shown to Harriet. Harriet's card is shown to Taylor. Taylor's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Harriet 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 Agentc: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:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Linda can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harriet","Taylor","Linda"],"index":67170,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984745383,"difficulty":0.0015254617}
{"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 Dale. Laura's card is shown to Dana. Dorothy's card is shown to Dana. Dale's card is shown to Laura. Dale's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Laura knows whether or not everyone picked a red card. It is publicly announced that Dana knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Dale can now know that Dana can know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dale","Dana","Laura","Dorothy"],"index":35455,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9537006617,"difficulty":0.0462993383}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Joe. Carolyn's card is shown to Joe. Carolyn's card is shown to Robin. Carolyn's card is shown to Carolyn. 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. It is publicly announced that Carolyn does not know whether Robin 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 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)) ] (Agenta knows that (1|2|3))","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":"Joe can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joe","Robin","Carolyn"],"index":8852,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994490743,"difficulty":0.0005509257}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Santo's card is shown to Santo. Santo's card is shown to Marsha. It is publicly announced that someone picked a red card. It is publicly announced that Marsha does not know whether Marsha picked a red card. It is publicly announced that Santo 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 whether (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":"Santo can now know whether Marsha can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Santo","Marsha"],"index":63940,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990946054,"difficulty":0.0009053946}
{"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 Eva. Margaret's card is shown to Eva. Kenneth's card is shown to Kenneth. Carol's card is shown to Margaret. Eva's card is shown to Margaret. 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:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Eva picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Eva","Kenneth","Margaret"],"index":64218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969991446,"difficulty":0.0030008554}
{"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 Yvonne. Elsie's card is shown to Nicholas. Nicholas's card is shown to Elsie. Elsie's card is shown to Elsie. Yvonne's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Donna knows whether Yvonne 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) ] (Agenta knows whether 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":"Yvonne can now know whether Donna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Yvonne","Nicholas","Elsie","Donna"],"index":3517,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971334934,"difficulty":0.0028665066}
{"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 Virginia. Virginia's card is shown to Mary. Jacob's card is shown to Vicki. Vicki's card is shown to Vicki. It is publicly announced that someone picked a red card. It is publicly announced that Virginia does not know whether Virginia picked a red card.","smcdel_problem":"VARS 1,2,3,4 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 3)","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":"Mary can now know that Jacob can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Virginia","Jacob","Mary","Vicki"],"index":33365,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981513619,"difficulty":0.0018486381}
{"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 Martin. Martin's card is shown to Deborah. Martin's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Steve does not know whether Steve picked a red card. It is publicly announced that Deborah knows whether or not everyone picked a red card. It is publicly announced that Deborah 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 ] (Agentb knows that (1&2&3))","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":"Deborah can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Martin","Deborah","Steve"],"index":33965,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964398742,"difficulty":0.0035601258}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catarina's card is shown to Catarina. Dan's card is shown to Dan. It is publicly announced that someone picked a red card. It is publicly announced that Bonnie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Dan can now know that Dan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Catarina","Dan","Bonnie"],"index":26306,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8082428575,"difficulty":0.1917571425}
{"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. Kellie's card is shown to Guadalupe. Guadalupe's card is shown to Kellie. Kellie's card is shown to Kellie. Linda's card is shown to Kellie. Kellie's card is shown to Linda. Linda's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 Agentd: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 Agentb:1,2,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Guadalupe can now know that Kellie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Guadalupe","Kellie","Linda","Jennifer"],"index":36729,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.994002521,"difficulty":0.005997479}
{"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 Rocky. Malcolm's card is shown to Erna. Paul's card is shown to Erna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 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:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Malcolm can now know that Malcolm picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Malcolm","Rocky","Erna","Paul"],"index":38041,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940328002,"difficulty":0.0059671998}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Billie. Billie's card is shown to Juanita. Juanita's card is shown to Juanita. It is publicly announced that someone picked a red card. It is publicly announced that Billie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Juanita can now know that Juanita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Billie","Juanita"],"index":10324,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.696727097,"difficulty":0.303272903}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Melvin. Jesse's card is shown to Melvin. Melvin's card is shown to Jesse. Jesse's card is shown to Jesse. Yvonne's card is shown to Jesse. Jesse's card is shown to Yvonne. Yvonne's card is shown to Brandi. 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 whether 3)","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":"Melvin can now know whether Yvonne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melvin","Jesse","Yvonne","Brandi"],"index":29936,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7295969725,"difficulty":1.7295969725}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Mary. Andre's card is shown to James. Mary's card is shown to Alvin. Andre's card is shown to Alvin. James's card is shown to Andre. Andre's card is shown to Andre. It is publicly announced that someone picked a red card. It is publicly announced that Andre picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 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)) ] Agentc knows that (Agentd knows that 3)","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":"Alvin can now know that Andre can know that Alvin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","James","Alvin","Andre"],"index":41463,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6174641252,"difficulty":0.3825358748}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Ronald. Ronald's card is shown to Jennifer. Ronald's card is shown to Jon. Jennifer's card is shown to Jon. It is publicly announced that someone picked a red card. It is publicly announced that Ronald knows whether Ronald 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) ] (Agentc knows whether 2)","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) ] 0","hypothesis":"Jon can now know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ronald","Jennifer","Jon"],"index":63454,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9173111916,"difficulty":0.0826888084}
{"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 Josephine. Josephine's card is shown to Everett. It is publicly announced that someone picked a red card. It is publicly announced that Everett knows whether Josephine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Josephine can now know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Josephine","Everett","Cynthia"],"index":33299,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9856984019,"difficulty":1.9856984019}
{"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 Jennifer. Jennifer's card is shown to Jose. Jose's card is shown to Jeanine. It is publicly announced that someone picked a red card. It is publicly announced that Jeanine knows whether Jose picked a red card. It is publicly announced that Jose does not know whether Jeanine 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) ] (Agenta knows that 1)","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":"Jennifer can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Jose","Jeanine"],"index":58982,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9710308313,"difficulty":0.0289691687}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonita's card is shown to Bonita. Bonita's card is shown to Susan. Susan's card is shown to Susan. Susan's card is shown to Brenda. Bonita's card is shown to Lee. It is publicly announced that someone picked a red card. It is publicly announced that Bonita does not know whether Lee 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) ] (Agentb knows that (~(1|2|3|4)))","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":"Susan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bonita","Susan","Brenda","Lee"],"index":11905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990246296,"difficulty":0.0009753704}
{"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 Ann. Ann'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 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ann can now know that Cathy can know whether Cathy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ann","Cathy","Angela"],"index":42006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9733980298,"difficulty":0.0266019702}
{"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 Crystal. Crystal's card is shown to Rebecca. Francis's card is shown to Rebecca. Crystal's card is shown to Francis. Francis's card is shown to Francis. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Crystal can now know that Rebecca can know whether Rebecca picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Crystal","Rebecca","Francis"],"index":62296,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7894194126,"difficulty":1.7894194126}
{"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 Sarah. Lemuel's card is shown to Lemuel. Shannon's card is shown to Lemuel. Sarah's card is shown to Shannon. 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 whether 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":"Sarah can now know that Lemuel can know whether Lemuel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Lemuel","Shannon"],"index":32984,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7970950603,"difficulty":1.7970950603}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shayne's card is shown to Lottie. David's card is shown to Shayne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shayne can now know that Lottie can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lottie","Shayne","David"],"index":6559,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980533123,"difficulty":0.0019466877}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hal's card is shown to Hal. Hal's card is shown to Tanya. Tanya's card is shown to Tanya. Hal's card is shown to Ann. Tanya's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Tanya does not know whether Ann picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Larry can now know that Tanya can know whether Hal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hal","Tanya","Larry","Ann"],"index":19285,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7277581096,"difficulty":1.7277581096}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracy's card is shown to Josie. 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 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Josie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Josie","Trish","Tracy"],"index":44515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953733087,"difficulty":0.0046266913}
{"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 Dennis. Xuan's card is shown to Dennis. Dennis's card is shown to Charles. Charles's card is shown to Xuan. Xuan's card is shown to Xuan. It is publicly announced that someone picked a red card. It is publicly announced that Xuan picked a red card. It is publicly announced that Dennis does not know whether or not everyone picked a red card. It is publicly announced that Dennis knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Dennis can now know that Xuan can know that Dennis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Charles","Xuan"],"index":1665,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5129795671,"difficulty":0.4870204329}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debbie's card is shown to Rosemary. Rosemary's card is shown to Debbie. It is publicly announced that someone picked a red card. It is publicly announced that Rosemary does not know whether Rosemary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1&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":"Rosemary can now know that Debbie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rosemary","Debbie"],"index":10938,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988945127,"difficulty":0.0011054873}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Cheryl. Tom's card is shown to Cheryl. Dawn's card is shown to Dawn. 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:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tom can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cheryl","Dawn","Tom"],"index":5623,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990008473,"difficulty":0.0009991527}
{"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 Tracey. Susan's card is shown to Susan. Tracey's card is shown to Jose. Susan'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 Tracey does not know whether or not everyone picked a red card. It is publicly announced that Susan knows whether Susan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jose can now know whether Tracey can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracey","Susan","Jose"],"index":50680,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994322658,"difficulty":0.0005677342}
{"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 David. Claude's card is shown to Steven. David's card is shown to Claude. 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)) ] (Agentc knows that 3)","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":"Claude can now know that Claude picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Steven","Claude"],"index":40930,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952457547,"difficulty":0.0047542453}
{"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. Charlotte's card is shown to Kristin. Charlotte's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Charlotte knows whether Charlotte picked a red card. It is publicly announced that Charlotte knows whether Charlotte picked a red card. It is publicly announced that Charlotte 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 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Christopher can now know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charlotte","Kristin","Christopher"],"index":31080,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5079874992,"difficulty":0.4920125008}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Amy'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 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Amy can now know that Paul can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Amy","Paul"],"index":4967,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9767599702,"difficulty":0.0232400298}
{"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 Linda. Linda's card is shown to Linda. Patricia's card is shown to Linda. Arnold's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Arnold does not know whether Linda picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] 0","hypothesis":"Arnold can now know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Arnold","Linda","Patricia"],"index":3108,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9898563623,"difficulty":0.0101436377}
{"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 Jessica. Florence's card is shown to Jessica. Jessica's card is shown to Olga. Jessica's card is shown to Florence. 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) ] Agentc knows whether (Agentb knows whether 1)","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":"Florence can now know whether Olga can know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Olga","Florence"],"index":27296,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989138842,"difficulty":0.0010861158}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ivette's card is shown to Howard. Jeanne's card is shown to Howard. Howard's card is shown to Ivette. Ivette's card is shown to Ivette. Steven's card is shown to Jeanne. It is publicly announced that someone picked a red card. It is publicly announced that Ivette 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:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ivette can now know whether Ivette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Howard","Steven","Ivette","Jeanne"],"index":52908,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9356247187,"difficulty":1.9356247187}
{"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 Juanita. Timothy's card is shown to Timothy. 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 (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Timothy can now know whether Juanita can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Juanita","Timothy"],"index":41895,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9952511787,"difficulty":0.0047488213}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juana's card is shown to Linda. Linda's card is shown to Juana. Juana's card is shown to Juana. Juana's card is shown to Beatrice. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Beatrice picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Beatrice knows whether 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) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Beatrice can now know whether Juana can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Juana","Beatrice"],"index":35332,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9939838052,"difficulty":0.0060161948}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carrol's card is shown to Carly. Carly's card is shown to Carrol. Carrol's card is shown to Carrol. Glenn's card is shown to Carrol. Glenn's card is shown to Glenn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Glenn can now know whether Carly can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carly","Carrol","Glenn"],"index":60533,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991280437,"difficulty":0.0008719563}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Enrique's card is shown to Enrique. Alexandra's card is shown to Enrique. Enrique's card is shown to Alexandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb: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:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stewart can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stewart","Enrique","Alexandra","Chris"],"index":39892,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989953637,"difficulty":0.0010046363}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlene's card is shown to Bernie. Stacie's card is shown to Stacie. Bernie's card is shown to Craig. Marlene's card is shown to Marlene. 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) ] (Agentb knows that 2)","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":"Stacie can now know that Stacie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernie","Stacie","Craig","Marlene"],"index":13048,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9936742783,"difficulty":0.0063257217}
{"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. Gary's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Thomas 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)) ] Agenta knows whether (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 (1|2)) ] 0","hypothesis":"Gary can now know whether Thomas can know that Gary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gary","Thomas"],"index":23567,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9369220734,"difficulty":0.0630779266}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Rodney. Rodney's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rodney","Richard","Kevin"],"index":63070,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983855486,"difficulty":0.0016144514}
{"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 Kevin. Kenneth's card is shown to Meredith. Meredith's card is shown to Meredith. Dolores's card is shown to Meredith. Dolores's card is shown to Dolores. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know whether Meredith can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Kenneth","Meredith","Dolores"],"index":20369,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993815422,"difficulty":0.0006184578}
{"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 Frank. Frank's card is shown to Sonya. Timothy's card is shown to Sonya. Patricia's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Frank picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Frank can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Sonya","Patricia","Timothy"],"index":11816,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989940524,"difficulty":0.0010059476}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shante's card is shown to Oscar. Oscar's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Oscar can now know that Earlene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earlene","Oscar","Janice","Shante"],"index":55809,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980683923,"difficulty":0.0019316077}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Rose. Rose's card is shown to Roy. Francis's card is shown to Francis. It is publicly announced that someone picked a red card. It is publicly announced that Francis 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 (Agenta knows whether 3)","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":"Roy can now know that Rose can know whether Roy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Michael","Roy","Francis"],"index":22860,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7935570478,"difficulty":1.7935570478}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lacey's card is shown to Joseph. Lacey's card is shown to Roseanne. Keith's card is shown to Roseanne. Keith's card is shown to Lacey. Roseanne'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 Keith does not know whether Lacey picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Lacey can now know whether Roseanne can know that Lacey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Roseanne","Lacey","Keith"],"index":64845,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8055714965,"difficulty":1.8055714965}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Crystal's card is shown to Erica. Aleida's card is shown to Crystal. Linda'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 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Aleida can now know that Crystal can know whether Crystal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Erica","Crystal","Aleida","Linda"],"index":21745,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5479358435,"difficulty":0.4520641565}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tabitha's card is shown to Robert. Tabitha's card is shown to Tabitha. 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 (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Tabitha can now know whether Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Tabitha"],"index":43368,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994130135,"difficulty":0.0005869865}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lyda's card is shown to Craig. Lyda's card is shown to Lyda. Richard's card is shown to Lyda. Craig's card is shown to Bruce. Bruce's card is shown to Bruce. Craig'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 Agentb:2,4 Agentc:1,3 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:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bruce can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Craig","Lyda","Bruce","Richard"],"index":55539,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9019395709,"difficulty":0.0980604291}
{"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 Rebecca. Rebecca's card is shown to Thomas. Thomas's card is shown to Thomas. Casey's card is shown to Thomas. Thomas's card is shown to Casey. Thomas's card is shown to James. James'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:1,2,3 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Thomas can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Thomas","Casey","James"],"index":18237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8463199139,"difficulty":0.1536800861}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Lettie. George's card is shown to Louis. Lettie's card is shown to George. Louis's card is shown to George. George'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:4 Agentc:2,3,4 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:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louis can now know that Lettie can know whether George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Lettie","Louis","George"],"index":56976,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9211332798,"difficulty":0.0788667202}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lakeisha's card is shown to Lakeisha. Betty's card is shown to Lakeisha. Frances's card is shown to Lakeisha. Lakeisha's card is shown to Betty. Betty's card is shown to Frances. Frances's card is shown to Debi. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether Betty picked a red card. It is publicly announced that Betty does not know whether Betty picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Betty can now know whether Frances can know whether Debi picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lakeisha","Betty","Frances","Debi"],"index":9865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985972047,"difficulty":0.0014027953}
{"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 Mary. Mary's card is shown to Roger. Roger's card is shown to Roger. Melanie's card is shown to Roger. Mary's card is shown to Melanie. Roger's card is shown to Melanie. 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:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Roger can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Roger","Melanie"],"index":25593,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993178844,"difficulty":0.0006821156}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Michael's card is shown to Eugene. Louis's card is shown to Eugene. Michael's card is shown to Michael. Louis's card is shown to Louis. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Louis 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 2)","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":"Louis can now know whether Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eugene","Michael","Louis"],"index":20557,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8739506006,"difficulty":1.8739506006}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Jerry. Darlene's card is shown to Darlene. It is publicly announced that someone picked a red card. It is publicly announced that Jerry does not know whether or not everyone picked a red card.","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 that (Agenta knows that (~(1|2|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":"Darlene can now know that Jerry can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Darlene","Frank"],"index":12340,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989357591,"difficulty":0.0010642409}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diana's card is shown to Deborah. Scott's card is shown to Scott. Deborah's card is shown to Diana. Scott's card is shown to Diana. 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:4 Agentb:3 Agentc:1,3 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:4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Bryan can now know that Bryan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deborah","Bryan","Scott","Diana"],"index":25242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8466079235,"difficulty":0.1533920765}
{"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 Danielle. Danielle's card is shown to Suzanne. Suzanne's card is shown to Suzanne. Suzanne's card is shown to Karin. 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) ] (Agenta knows that (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":"Danielle can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Danielle","Suzanne","Karin"],"index":40933,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994204044,"difficulty":0.0005795956}
{"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 Will. Bertha's card is shown to Will. Will's card is shown to Bertha. Adam's card is shown to Bertha. Will's card is shown to Adam. 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 Stephen knows whether Stephen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Will can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephen","Will","Bertha","Adam"],"index":56349,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994210005,"difficulty":0.0005789995}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Kimberly. Mallory's card is shown to Kimberly. Mallory's card is shown to Mallory. It is publicly announced that someone picked a red card. It is publicly announced that Mallory knows whether or not nobody picked a red card. It is publicly announced that Mallory does not know whether Kimberly picked a red card. It is publicly announced that Kimberly picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Kimberly can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kimberly","Mallory"],"index":36648,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9086900949,"difficulty":0.0913099051}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashlee's card is shown to Edward. Julie's card is shown to Edward. Ashlee's card is shown to Reuben. Reuben's card is shown to Reuben. Reuben'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 Ashlee 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 that (1|2|3|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":"Ashlee can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","Ashlee","Reuben","Julie"],"index":14916,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994120598,"difficulty":0.0005879402}
{"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. Harry's card is shown to Patricia. Edna's card is shown to Harry. Edna's card is shown to Edna. Jack's card is shown to Jack. 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 whether (1&2&3&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":"Jack can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Harry","Edna","Jack"],"index":1087,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.994664669,"difficulty":0.005335331}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Stacy. Susan's card is shown to Susan. Susan's card is shown to Marion. It is publicly announced that someone picked a red card. It is publicly announced that Stacy picked a red card. It is publicly announced that Stacy 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":"Marion can now know whether Susan can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stacy","Susan","Marion"],"index":31672,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9804852009,"difficulty":0.0195147991}
{"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 Leon. Mary's card is shown to Mary. Leon's card is shown to Justin. Mary's card is shown to Justin. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether Justin picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Leon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leon","Mary","Justin"],"index":60575,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999435246,"difficulty":0.000564754}
{"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. Margie's card is shown to Helen. Helen's card is shown to Jeffery. Bryan's card is shown to Margie. Helen's card is shown to Bryan. Jeffery's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Jeffery does not know whether Jeffery picked a red card. It is publicly announced that Jeffery does not know whether Margie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jeffery can now know whether Bryan can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Jeffery","Margie","Bryan"],"index":30051,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989688396,"difficulty":0.0010311604}
{"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 Genevieve. Victor's card is shown to Victor. Mike's card is shown to Victor. Victor's card is shown to Mike. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc: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:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Genevieve can now know whether Mike can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Genevieve","Victor","Mike"],"index":47510,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9929959178,"difficulty":0.0070040822}
{"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. Ida's card is shown to John. Ida's card is shown to Ida. Richard's card is shown to Ida. Mark's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 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:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ida can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","John","Ida","Richard"],"index":2006,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994081259,"difficulty":0.0005918741}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Carl. Velva's card is shown to Carl. Deborah's card is shown to Carl. Carl's card is shown to Donald. Donald's card is shown to Deborah. Deborah's card is shown to Deborah. 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 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know whether Velva can know whether Carl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Donald","Velva","Deborah"],"index":21845,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9968339801,"difficulty":0.0031660199}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenifer's card is shown to Michael. Jonathan's card is shown to Jenifer. Michael's card is shown to Jonathan. Jenifer's card is shown to Jonathan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jonathan can now know that Michael can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Jenifer","Jonathan"],"index":19046,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993702769,"difficulty":0.0006297231}
{"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 Alice. Alice's card is shown to Joan. 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:1 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 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Alice can now know whether Joan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alice","Jay","Joan"],"index":61144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6297245026,"difficulty":0.3702754974}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Eugene's card is shown to David. Eugene's card is shown to Faye. David's card is shown to Faye. Faye's card is shown to Faye. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eugene can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eugene","David","Faye"],"index":34534,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5232340097,"difficulty":0.4767659903}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to Rhonda. Brenda's card is shown to Gregory. Rhonda's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Rhonda's card is shown to Brenda. Brenda's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Gregory does not know whether Elizabeth picked a red card. It is publicly announced that Brenda picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] 0","hypothesis":"Elizabeth can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rhonda","Gregory","Elizabeth","Brenda"],"index":60703,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990419745,"difficulty":0.0009580255}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Helen's card is shown to Dennis. Dennis's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Helen knows whether someone 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)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Dennis can now know that Helen can know that Dennis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Helen","Dennis"],"index":39333,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925463796,"difficulty":0.0074536204}
{"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 Mike. Christopher's card is shown to Anthony. 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 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mike","Anthony","Christopher"],"index":35082,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7131146789,"difficulty":1.7131146789}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Sandra. Christina's card is shown to Christina. Carole's card is shown to Christina. Carole's card is shown to Clyde. Clyde's card is shown to Carole. 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:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christina can now know that Christina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Christina","Clyde","Carole"],"index":57825,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942713976,"difficulty":0.0057286024}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dee's card is shown to Phillip. Gordon's card is shown to Gordon. Phillip's card is shown to Dee. It is publicly announced that someone picked a red card. It is publicly announced that Dee does not know whether Gordon 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 whether 2) ] (Agenta knows whether (~(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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Phillip can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Phillip","Gordon","Dee"],"index":2319,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993517995,"difficulty":0.0006482005}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Jennifer. Jennifer's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ashley can now know whether Jennifer can know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Ashley"],"index":5683,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973716736,"difficulty":0.0026283264}
{"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 Richard. Craig's card is shown to Richard. Robert's card is shown to Craig. 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) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether Robert can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Robert","Craig"],"index":11434,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9778644443,"difficulty":0.0221355557}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffany's card is shown to Tiffany. Jean's card is shown to Tiffany. David's card is shown to David. Harriett's card is shown to David. David's card is shown to Jean. Jean's card is shown to Harriett. 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) ] (Agenta knows whether (~(1|2|3|4)))","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":"Tiffany can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tiffany","David","Jean","Harriett"],"index":38571,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993050098,"difficulty":0.0006949902}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Noemi's card is shown to Josephine. Ivan's card is shown to Noemi. Jacqueline's card is shown to Ivan. Ivan's card is shown to Jacqueline. It is publicly announced that someone picked a red card. It is publicly announced that Ivan does not know whether or not everyone picked a red card. It is publicly announced that Josephine does not know whether Josephine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jacqueline can now know that Ivan can know whether Noemi picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Josephine","Noemi","Ivan","Jacqueline"],"index":32206,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7213336229,"difficulty":0.2786663771}
{"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 Robert. Jeremy's card is shown to Jeremy. Marcus's card is shown to Jeremy. Marcus's card is shown to Kathleen. Robert's card is shown to Marcus. Jeremy's card is shown to Marcus. Kathleen'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 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Jeremy can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Jeremy","Kathleen","Marcus"],"index":12409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.600885272,"difficulty":0.399114728}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sadie's card is shown to Sadie. Sadie's card is shown to Jacob. Jacob's card is shown to Jacob. It is publicly announced that someone picked a red card. It is publicly announced that Sadie knows whether someone 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)) ] Agentb knows whether (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 (1|2)) ] 0","hypothesis":"Jacob can now know whether Sadie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sadie","Jacob"],"index":61715,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993324876,"difficulty":0.0006675124}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittney's card is shown to Brittney. Nicolas's card is shown to Kimberly. Kimberly's card is shown to Naomi. Brittney's card is shown to Nicolas. Kimberly's card is shown to Nicolas. It is publicly announced that someone picked a red card. It is publicly announced that Naomi 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)) ] (Agenta knows whether (1|2|3|4))","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":"Brittney can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brittney","Kimberly","Naomi","Nicolas"],"index":30309,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994584918,"difficulty":0.0005415082}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wade's card is shown to Wade. Carl's card is shown to Wade. Carl's card is shown to Carl. It is publicly announced that someone picked a red card. It is publicly announced that Carl does not know whether or not everyone picked a red card. It is publicly announced that Carl does not know whether Wade 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:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Wade can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wade","Carl"],"index":64901,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977872372,"difficulty":0.0022127628}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Desiree's card is shown to Desiree. Desiree's card is shown to Angie. Julio's card is shown to Angie. Julio's card is shown to Julio. 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 that (Agentb knows whether 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":"Julio can now know that Angie can know whether Angie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Desiree","Angie","Julio"],"index":52043,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9421415329,"difficulty":0.0578584671}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Heidi. Heidi's card is shown to Valerie. It is publicly announced that someone picked a red card. It is publicly announced that Heidi does not know whether Heidi picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (~(1|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":"Heidi can now know whether Valerie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Heidi","Valerie"],"index":31594,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990724325,"difficulty":0.0009275675}
{"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 Tony. Tony's card is shown to Brian. Jeremy's card is shown to Brian. Tony's card is shown to Jeremy. Brian's card is shown to Jeremy. Jeremy's card is shown to Boyd. It is publicly announced that someone picked a red card. It is publicly announced that Boyd 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 that (Agentc knows whether 4)","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":"Brian can now know that Jeremy can know whether Boyd picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tony","Brian","Jeremy","Boyd"],"index":41319,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9864826202,"difficulty":0.0135173798}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joann's card is shown to Helen. Linda's card is shown to Anita. Helen's card is shown to Joann. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Anita can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Linda","Anita","Joann"],"index":41497,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9912921786,"difficulty":0.0087078214}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josh's card is shown to Dominick. Dominick's card is shown to Josh. It is publicly announced that someone picked a red card. It is publicly announced that Josh does not know whether Josh picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Josh can now know that Josh picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dominick","Josh"],"index":2912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9593834281,"difficulty":0.0406165719}
{"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 Shella. Mark's card is shown to Mark. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Lori 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) ] Agenta knows whether (Agentb knows that 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":"Lori can now know whether Shella can know that Maria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lori","Shella","Mark","Maria"],"index":4014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9528834224,"difficulty":0.0471165776}
{"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. Hazel's card is shown to Eileen. Tyree's card is shown to Hazel. Eileen's card is shown to Tyree. 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 that (~(1|2|3|4)))","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":"Hazel can now know that Tyree can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Eileen","Hazel","Tyree"],"index":19923,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990015626,"difficulty":0.0009984374}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Kelly. Joseph's card is shown to Kelly. Isidro's card is shown to Kelly. Isidro's card is shown to Joseph. Kelly's card is shown to Isidro. Isidro's card is shown to Isidro. 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:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kelly can now know whether Isidro can know whether Isidro picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelly","Joseph","Isidro"],"index":29313,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980303645,"difficulty":0.0019696355}
{"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 Jack. Chris's card is shown to Donald. Jack's card is shown to Sonja. Jack's card is shown to Chris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 2)","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":"Chris can now know that Donald can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jack","Donald","Sonja","Chris"],"index":65374,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953269958,"difficulty":0.0046730042}
{"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. Rosie's card is shown to Louise. Louise's card is shown to Rosie. Rosie's card is shown to Rosie. Imogene's card is shown to Rosie. Rosie's card is shown to Imogene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Louise can now know whether Imogene can know whether Louise picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louise","Rosie","Imogene"],"index":20939,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997831881,"difficulty":0.002168119}
{"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 Lana. Carolyn's card is shown to Lana. Gerry's card is shown to Lana. Lana's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Carolyn's card is shown to Gerry. 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) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lana","Roger","Carolyn","Gerry"],"index":19797,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989808202,"difficulty":0.0010191798}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nellie's card is shown to Nellie. Armand's card is shown to Nellie. Antonio's card is shown to Nellie. Antonio's card is shown to Armand. Nellie'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:1,2,3 Agentb:3 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:1,2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Antonio can now know that Armand can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nellie","Armand","Antonio"],"index":14382,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990310669,"difficulty":0.0009689331}
{"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 Joan. Betty's card is shown to Robert. Joseph's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card. It is publicly announced that Joseph knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Joan can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joan","Joseph","Robert","Betty"],"index":52386,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987447262,"difficulty":0.0012552738}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristi's card is shown to Kristi. Donna's card is shown to Kristi. Kristi's card is shown to Donna. Donna's card is shown to Donna. Zachary's card is shown to Donna. Kristi's card is shown to Zachary. Zachary's card is shown to Zachary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc: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:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donna can now know whether Kristi can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kristi","Donna","Zachary"],"index":57481,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992622733,"difficulty":0.0007377267}
{"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 Stacey. Margaret's card is shown to Margaret. 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 whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Margaret can now know whether Stacey can know that Stacey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stacey","Margaret"],"index":25429,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9065496922,"difficulty":1.9065496922}
{"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 Angela. Maria's card is shown to Angela. Angela's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether or not everyone picked a red card. It is publicly announced that Angela 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))) ] (Agenta knows that 3)","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":"Angela can now know that Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Angela","Linda","Maria"],"index":63474,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9362954497,"difficulty":1.9362954497}
{"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. Lourdes's card is shown to Barbara. Victoria's card is shown to Jenny. Jenny's card is shown to Jenny. 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:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Victoria can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Barbara","Jenny","Lourdes"],"index":13093,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995496273,"difficulty":0.004503727}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teddy's card is shown to Ronald. John's card is shown to Evelyn. Ronald's card is shown to John. Evelyn'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:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Teddy can now know that Evelyn can know that Teddy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Teddy","Ronald","Evelyn","John"],"index":58491,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982984662,"difficulty":0.0017015338}
{"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 Teresa. Donna's card is shown to Donna. 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 Betty picked a red card. It is publicly announced that Donna 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 that (~(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":"Donna can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Teresa","Donna","Betty"],"index":12297,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990451932,"difficulty":0.0009548068}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Paula's card is shown to Barbara. Barbara's card is shown to Tameka. Paula's card is shown to Tameka. Barbara's card is shown to Paula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Tameka","Paula"],"index":24918,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989877343,"difficulty":0.0010122657}
{"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 Alice. Kim's card is shown to Alice. Ashley's card is shown to Alice. Alice's card is shown to Kim. 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:1,2,3 Agentb:1 Agentc: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:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alice can now know that Ashley can know whether Kim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alice","Kim","Ashley"],"index":33682,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9920648932,"difficulty":0.0079351068}
{"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 Calvin. Mary's card is shown to Charles. Carol's card is shown to Mary. Mary'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:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether Carol can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Calvin","Charles","Mary","Carol"],"index":31374,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993652701,"difficulty":0.0006347299}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ian's card is shown to Ian. Gloria's card is shown to Ian. Gloria'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 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)) ] Agentb knows that (Agenta knows that (~(1|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":"Gloria can now know that Ian can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ian","Gloria"],"index":35003,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989087582,"difficulty":0.0010912418}
{"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 Robert. Robert's card is shown to Elijah. Paul's card is shown to Marian. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a red card. It is publicly announced that Robert does not know whether Elijah picked a red card. It is publicly announced that Elijah does not know whether Marian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Elijah can now know that Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Robert","Elijah","Marian"],"index":15353,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994556308,"difficulty":0.0005443692}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Carmen. Andrea's card is shown to Andrea. Melanie's card is shown to Andrea. John's card is shown to Andrea. Andrea's card is shown to Melanie. It is publicly announced that someone picked a red card. It is publicly announced that Carmen does not know whether Melanie picked a red card. It is publicly announced that Andrea picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Carmen can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carmen","Andrea","Melanie","John"],"index":3274,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8698601127,"difficulty":0.1301398873}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ron's card is shown to Ron. Edgar's card is shown to Ron. Edgar's card is shown to Edgar. Ron's card is shown to Brenda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc: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:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Edgar can now know that Ron can know that Edgar picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ron","Edgar","Brenda"],"index":28642,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970858693,"difficulty":0.0029141307}
{"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 Marie. Danita's card is shown to Marie. Randy's card is shown to Randy. Randy's card is shown to Danita. 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:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Randy can now know whether Marie can know that Danita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marie","Randy","Danita"],"index":64164,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9456144571,"difficulty":1.9456144571}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Lou. Lou'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 nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (~(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":"Lou can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lou","William"],"index":17508,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990487695,"difficulty":0.0009512305}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Sarah. Sarah's card is shown to Karen. Roy's card is shown to Karen. Karen's card is shown to Roy. Roy's card is shown to Roy. It is publicly announced that someone 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 Roy 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 that (Agenta 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:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Karen can now know that Sarah can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","Robert","Karen","Roy"],"index":45344,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7315065265,"difficulty":1.7315065265}
{"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 Lou. Thomas's card is shown to Thomas. Jennifer's card is shown to William. Lou's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Thomas can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lou","Thomas","William","Jennifer"],"index":13736,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993608594,"difficulty":0.0006391406}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luke's card is shown to Luke. Carolyn's card is shown to Luke. Gary's card is shown to Luke. Karen's card is shown to Karen. Carolyn's card is shown to Carolyn. Karen's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Gary picked a red card. It is publicly announced that Luke knows whether Carolyn picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Carolyn can now know whether Karen can know whether Carolyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Luke","Karen","Carolyn","Gary"],"index":28567,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985498786,"difficulty":0.0014501214}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Elizabeth. Samuel's card is shown to John. Elizabeth's card is shown to Robert. John's card is shown to Robert. Samuel's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Elizabeth can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","John","Samuel","Robert"],"index":2414,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930155277,"difficulty":0.0069844723}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristin's card is shown to Suzanne. Ralph's card is shown to Isaac. Suzanne's card is shown to Isaac. Isaac's card is shown to Isaac. Kristin's card is shown to Isaac. Suzanne's card is shown to Kristin. Kristin's card is shown to Kristin. 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:2,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Suzanne can now know whether Isaac can know that Kristin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ralph","Suzanne","Isaac","Kristin"],"index":42507,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9169855118,"difficulty":0.0830144882}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sybil's card is shown to Sybil. Audrey's card is shown to Crystal. Crystal's card is shown to Audrey. It is publicly announced that someone picked a red card. It is publicly announced that Sybil 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)) ] (Agentc knows whether 1)","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":"Franklin can now know whether Sybil picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sybil","Crystal","Franklin","Audrey"],"index":60661,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9474049807,"difficulty":0.0525950193}
{"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 Dallas. Robert's card is shown to Dallas. Dallas's card is shown to Anna. Dallas's card is shown to Robert. Anna's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Anna does not know whether Anna 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) ] (Agentb knows whether (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":"Anna can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dallas","Anna","Robert","Christopher"],"index":30250,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9915581942,"difficulty":0.0084418058}
{"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 George. Glen's card is shown to Glen. George's card is shown to Hilton. Glen's card is shown to Hilton. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Hilton can now know that Hilton picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Glen","Hilton"],"index":41197,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9938394427,"difficulty":0.0061605573}
{"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 Jason. Nancy's card is shown to Jason. Laura's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Laura can now know whether Jason can know whether Laura picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Laura","Nancy"],"index":45888,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988299012,"difficulty":0.0011700988}
{"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 Christopher. Christopher's card is shown to Cheryl. Cheryl'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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Cheryl","James"],"index":35390,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998403132,"difficulty":0.001596868}
{"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 Grace. Thomas's card is shown to Grace. Grace's card is shown to Lisa. 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:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know that Thomas can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Grace","Lisa","Thomas"],"index":48012,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7574623227,"difficulty":0.2425376773}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynn's card is shown to Lynn. Ruby's card is shown to Ruby. Lynn's card is shown to Robert. Ruby'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:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Lynn can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lynn","Ruby","Robert"],"index":24319,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7443280816,"difficulty":1.7443280816}
{"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. Joanne's card is shown to Tim. Latanya's card is shown to Tim. Tim's card is shown to Joanne. Tim's card is shown to Latanya. Joanne's card is shown to Latanya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:2 Agentd:2,3 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:3,4 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Latanya can now know that Joanne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sara","Tim","Joanne","Latanya"],"index":45760,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953138828,"difficulty":0.0046861172}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Betty can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betty","Milagros","Jorge"],"index":17165,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988928437,"difficulty":0.0011071563}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joann's card is shown to Rick. Howard's card is shown to Rick. Howard's card is shown to Joann. Rick's card is shown to Howard. Howard's card is shown to Howard. 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:1,3 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:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Howard can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rick","Joann","Howard"],"index":53522,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947058558,"difficulty":0.0052941442}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Magda's card is shown to Magda. James's card is shown to Magda. Patrick's card is shown to Magda. Patrick's card is shown to Sharon. Magda's card is shown to Patrick. James's card is shown to Patrick. 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:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Magda can now know whether James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Magda","James","Sharon","Patrick"],"index":61570,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9853596091,"difficulty":0.0146403909}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Melissa's card is shown to Alberto. It is publicly announced that someone picked a red card. It is publicly announced that Alberto 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 (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":"Alberto can now know whether Melissa can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melissa","Alberto"],"index":27206,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9748138785,"difficulty":0.0251861215}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chrissy's card is shown to Chrissy. Sophie's card is shown to Chrissy. Sophie's card is shown to Sophie. 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) ] Agentb knows that (Agenta 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":"Sophie can now know that Chrissy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Chrissy","Sophie"],"index":31187,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994004965,"difficulty":0.0005995035}
{"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. Harlan's card is shown to William. Joyce's card is shown to Harlan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joyce","William","Dorothy","Harlan"],"index":58298,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993209839,"difficulty":0.0006790161}
{"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 Wayne. Richard's card is shown to Richard. Tom's card is shown to Richard. David's card is shown to Richard. Richard'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 Wayne does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Tom can now know that Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wayne","Richard","Tom","David"],"index":37608,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9196255207,"difficulty":0.0803744793}
{"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 Karen. Karen's card is shown to Kimberly. Kimberly's card is shown to Kimberly. Karen's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Karen 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:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Karen can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Kimberly","Richard"],"index":14753,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9843103886,"difficulty":0.0156896114}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelvin's card is shown to Melissa. Melissa's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Kelvin 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|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Kelvin can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kelvin","Melissa"],"index":62091,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993828535,"difficulty":0.0006171465}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brent's card is shown to Janie. Janie's card is shown to Barbara. Barbara's card is shown to Barbara. Barbara's card is shown to Brent. 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) ] (Agenta knows that 2)","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":"Janie can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janie","Barbara","Brent"],"index":522,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968115687,"difficulty":0.0031884313}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darryl's card is shown to Darryl. Darryl'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 (Agenta knows that 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 Darryl can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Darryl","Mary"],"index":25032,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5494231582,"difficulty":1.5494231582}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hilda's card is shown to Hilda. Ernestine's card is shown to Hilda. Margaret's card is shown to Ernestine. Marilyn's card is shown to Ernestine. 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) ] (Agenta 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":"Hilda can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Hilda","Ernestine","Margaret","Marilyn"],"index":33903,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994288087,"difficulty":0.0005711913}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jayne's card is shown to Jayne. Ruby's card is shown to Jayne. Jayne's card is shown to Christopher. Christopher's card is shown to Christopher. Ruby's card is shown to Christopher. Christopher's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether someone picked a red card. It is publicly announced that Christopher picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] Agentb knows whether (Agentc knows that (~(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":"Christopher can now know whether Ruby can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jayne","Christopher","Ruby"],"index":54819,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993195534,"difficulty":0.0006804466}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caroline's card is shown to Caroline. Charles's card is shown to Caroline. Jay's card is shown to Caroline. Caroline's card is shown to Charles. Charles's card is shown to Charles. Caroline's card is shown to Jay. Charles's card is shown to Jay. 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:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jay can now know whether Caroline can know whether Caroline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Caroline","Charles","Jay"],"index":56697,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9974166155,"difficulty":0.0025833845}
{"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 Hildegard. John's card is shown to John. Virginia's card is shown to John. Virginia's card is shown to Richard. Richard's card is shown to Virginia. 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) ] 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:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Hildegard can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hildegard","John","Richard","Virginia"],"index":21772,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993869066,"difficulty":0.0006130934}
{"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 George. George's card is shown to Rita. Erin's card is shown to Erin. It is publicly announced that someone picked a red card. It is publicly announced that George picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Erin can now know that Rita can know that Rita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Rita","Erin"],"index":24188,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9903637767,"difficulty":0.0096362233}
{"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. Randy's card is shown to Donald. Adam's card is shown to Donald. Donald's card is shown to Adam. 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 whether 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":"Donald can now know whether Adam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Randy","Adam"],"index":4658,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8318017721,"difficulty":1.8318017721}
{"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 Jean. Harvey's card is shown to Harvey. Martha's card is shown to Harvey. Jean's card is shown to Perry. Perry's card is shown to Perry. 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:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Martha can now know that Harvey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jean","Harvey","Martha","Perry"],"index":22457,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981027246,"difficulty":0.0018972754}
{"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. Karen's card is shown to Susan. Ronald's card is shown to Brenda. Ronald's card is shown to Karen. Ronald's card is shown to Ronald. 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 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ronald can now know that Brenda can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Brenda","Karen","Ronald"],"index":32077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994125366,"difficulty":0.0005874634}
{"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 Joseph. James's card is shown to James. David's card is shown to James. Robert's card is shown to David. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"David can now know whether James can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","James","David","Robert"],"index":53290,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.981529355,"difficulty":0.018470645}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Candi. Luciano's card is shown to Candi. Candi's card is shown to Cindy. Cindy's card is shown to Cindy. Mary's card is shown to Luciano. It is publicly announced that someone picked a red card. It is publicly announced that Cindy 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:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Cindy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Candi","Mary","Cindy","Luciano"],"index":60585,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985104203,"difficulty":0.0014895797}
{"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. Chad's card is shown to Charles. Robin's card is shown to Adrianne. It is publicly announced that someone picked a red card. It is publicly announced that Adrianne does not know whether Adrianne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Charles can now know whether Adrianne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Adrianne","Robin","Chad"],"index":38254,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7063955069,"difficulty":1.7063955069}
{"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. Jennifer's card is shown to Shellie. Christopher's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shellie can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Shellie","Christopher","Jennifer"],"index":36897,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971354008,"difficulty":0.0028645992}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mike's card is shown to Noel. Noel's card is shown to Mike. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Mike can now know that Noel can know that Noel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Noel","Mike"],"index":11314,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9926405549,"difficulty":0.0073594451}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roxie's card is shown to Roxie. Tamela's card is shown to Roxie. Roxie's card is shown to Hung. Tamela's card is shown to Hung. Roxie's card is shown to Tamela. Hung's card is shown to Tamela. 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 Roxie picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Hung knows whether Tamela picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Hung can now know whether Roxie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roxie","Hung","Tamela"],"index":20419,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9772597551,"difficulty":0.0227402449}
{"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 Clyde. Jonathan's card is shown to Joseph. Clyde's card is shown to Jonathan. Jason's card is shown to Jonathan. Clyde'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:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clyde can now know that Jason can know that Jonathan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clyde","Joseph","Jonathan","Jason"],"index":27780,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982256293,"difficulty":0.0017743707}
{"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 Joseph. Margaret's card is shown to Joseph. Agnes's card is shown to Agnes. Joseph's card is shown to Margaret. Margaret's card is shown to Margaret. Margaret's card is shown to Sharri. 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) ] (Agentc knows that 3)","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":"Margaret can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Agnes","Margaret","Sharri"],"index":60724,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9929530025,"difficulty":0.0070469975}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandon's card is shown to Erica. Shannon's card is shown to Erica. Erica's card is shown to Brandon. Brandon's card is shown to Shannon. 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 (Agentb knows that (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":"Shannon can now know whether Brandon can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erica","Brandon","Shannon"],"index":45099,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9806404114,"difficulty":0.0193595886}
{"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. Sandra's card is shown to Dale. Mathew's card is shown to Dale. Sandra's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Sandra does not know whether Mathew picked a red card. It is publicly announced that Jeffrey knows whether or not everyone picked a red card. It is publicly announced that Sandra does not know whether Dale 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) ] Agenta knows that (Agentc knows that 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":"Sandra can now know that Jeffrey can know that Mathew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Dale","Jeffrey","Mathew"],"index":49959,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9788634181,"difficulty":0.0211365819}
{"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 Christopher. Christopher's card is shown to Ernest. Ernest's card is shown to Ernest. 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: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 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Christopher can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christopher","Ernest"],"index":57114,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993664622,"difficulty":0.0006335378}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryn's card is shown to Kathryn. Charles's card is shown to Kathryn. Kathryn's card is shown to Walter. Walter's card is shown to Walter. Charles's card is shown to Walter. Kathryn's card is shown to Charles. Walter's card is shown to Charles. 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:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathryn can now know whether Charles can know that Walter picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathryn","Walter","Charles"],"index":17293,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9321140647,"difficulty":1.9321140647}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Sherry. Theodore's card is shown to Brenda. Brenda's card is shown to Theodore. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Barbara can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sherry","Barbara","Brenda","Theodore"],"index":3179,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990509152,"difficulty":0.0009490848}
{"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 David. David's card is shown to Carmen. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janice can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Janice","Carmen"],"index":10302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990019202,"difficulty":0.0009980798}
{"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 Dorothy. Amy's card is shown to Troy. 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 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Troy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Troy","Amy"],"index":13660,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958003163,"difficulty":0.0041996837}
{"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 Jason. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Ruth picked a red card. It is publicly announced that Jason picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Jason can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leslie","Jason","Ruth"],"index":11464,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994588494,"difficulty":0.0005411506}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Cecil. Richard's card is shown to Richard. Nelson's card is shown to George. Cecil's card is shown to George. Richard's card is shown to George. George's card is shown to George. 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 everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Cecil can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nelson","Cecil","Richard","George"],"index":59445,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9926819205,"difficulty":0.0073180795}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffany's card is shown to Tiffany. Tiffany's card is shown to Jonathan. Richard's card is shown to Jonathan. Richard's card is shown to Richard. Jason'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:1 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Jonathan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tiffany","Jonathan","Richard","Jason"],"index":58237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99939394,"difficulty":0.00060606}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ramon's card is shown to William. Juan's card is shown to William. Juan's card is shown to Ramon. William's card is shown to Carmella. Juan's card is shown to Juan. 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) ] (Agentb knows that 1)","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":"Ramon can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Ramon","Carmella","Juan"],"index":43750,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981335998,"difficulty":0.0018664002}
{"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 Mattie. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Monica 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 that (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":"Mattie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Monica","Mattie","Catherine"],"index":22238,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994605184,"difficulty":0.0005394816}
{"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 Myrtle. Victor's card is shown to Nathaniel. Myrtle's card is shown to Betty. 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 whether (Agentc knows that 2)","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":"Victor can now know whether Nathaniel can know that Myrtle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victor","Myrtle","Nathaniel","Betty"],"index":61898,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9704491496,"difficulty":1.9704491496}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eusebio's card is shown to Robert. Jason's card is shown to Robert. Robert's card is shown to Eusebio. Eusebio's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Eusebio 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","Eusebio","Jason"],"index":62356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987213016,"difficulty":0.0012786984}
{"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 Debbie. Bobby's card is shown to Marie. Marie's card is shown to Bobby. Bobby's card is shown to Bobby. It is publicly announced that someone picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Bobby can now know whether Bobby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debbie","Marie","Bobby"],"index":25907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8892871141,"difficulty":0.1107128859}
{"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 Mark. Leonard's card is shown to Leonard. It is publicly announced that someone 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 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gladys can now know whether Leonard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","Gladys","Crystal","Leonard"],"index":35180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9087187052,"difficulty":0.0912812948}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorenzo's card is shown to Danielle. Danielle'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 Lorenzo does not know whether Carolyn 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 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Lorenzo can now know that Carolyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danielle","Lorenzo","Carolyn","Sharon"],"index":8017,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979025126,"difficulty":0.0020974874}
{"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 Mark. Miguel's card is shown to Mark. Jennifer's card is shown to Jennifer. Mark's card is shown to Victor. Miguel's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card. It is publicly announced that Miguel does not know whether Victor picked a red card. It is publicly announced that Miguel does not know whether Victor 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:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jennifer can now know that Miguel can know whether Victor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Jennifer","Miguel","Victor"],"index":55187,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5340263844,"difficulty":1.5340263844}
{"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 Wayne. Norma's card is shown to Wayne. Adam's card is shown to Adam. Norma's card is shown to Adam. Wayne's card is shown to Francis. Adam's card is shown to Norma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 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:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Norma can now know that Francis can know that Wayne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wayne","Adam","Francis","Norma"],"index":8194,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978613257,"difficulty":0.0021386743}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to June. Mary's card is shown to June. June'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 picked a black card. It is publicly announced that June 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) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"June can now know whether Mary can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["June","Mary"],"index":50465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9464741349,"difficulty":0.0535258651}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Thelma. Kristina's card is shown to Thelma. Kristina's card is shown to Kristina. Thelma's card is shown to Antonio. Antonio's card is shown to Antonio. Kristina's card is shown to Carlos. Carlos's card is shown to Carlos. 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 Kristina picked a red card. It is publicly announced that Kristina 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))) ] Agenta knows that (Agentd knows whether (1|2|3|4))","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":"Thelma can now know that Carlos can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thelma","Kristina","Antonio","Carlos"],"index":19790,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994459748,"difficulty":0.0005540252}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Mark. Mark's card is shown to Jose. Jose's card is shown to Jose. Mark's card is shown to Angela. Jose'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 does not know whether Angela picked a red card. It is publicly announced that Mark knows whether Angela 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) ] Agentd knows that (Agenta 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":"Ruth can now know that Mark can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Jose","Angela","Ruth"],"index":66206,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9314599037,"difficulty":0.0685400963}
{"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. Stanley's card is shown to Eugenio. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Eugenio picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Stanley can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stanley","Charles","Eugenio"],"index":45848,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9921988845,"difficulty":0.0078011155}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Michelle. Michelle's card is shown to Manuel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charlotte can now know whether Michelle can know whether Manuel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Charlotte","Manuel"],"index":7453,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988352656,"difficulty":0.0011647344}
{"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. Raymond's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan 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) ] (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 (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Raymond can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Raymond","Jonathan"],"index":35422,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989404082,"difficulty":0.0010595918}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yaeko's card is shown to Yaeko. Sandra's card is shown to Eunice. Eunice's card is shown to Sandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eldridge can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Yaeko","Eunice","Eldridge","Sandra"],"index":61913,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988406301,"difficulty":0.0011593699}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Michael. Timothy's card is shown to Michael. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Arlene does not know whether Arlene picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Arlene can now know that Michael can know whether Timothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Arlene","Timothy"],"index":42025,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5927060246,"difficulty":1.5927060246}
{"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 Joanne. Carlos's card is shown to Paulene. Kelly's card is shown to Kelly. Carlos's card is shown to Carlos. 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: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 Agentb:4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paulene can now know whether Carlos picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joanne","Paulene","Kelly","Carlos"],"index":13831,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9209313393,"difficulty":0.0790686607}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Randall. Randall's card is shown to Dana. Dana's card is shown to Dana. William's card is shown to William. Randall's card is shown to Dennis. William's card is shown to Dennis. 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:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dana can now know whether Dana picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Randall","Dana","William","Dennis"],"index":17531,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8593598604,"difficulty":1.8593598604}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gordon's card is shown to Gordon. Lisa's card is shown to Marianne. Marianne's card is shown to Lisa. Lisa'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:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gordon can now know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Gordon","Marianne","Lisa"],"index":20289,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943060279,"difficulty":0.0056939721}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Derrick. Michael's card is shown to Derrick. Ashley's card is shown to Ashley. Michael's card is shown to Ashley. Derrick's card is shown to Michael. Ashley'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 Michael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Derrick can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Derrick","Ashley","Michael"],"index":53106,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994347692,"difficulty":0.0005652308}
{"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. Mark's card is shown to Stacy. Stacy's card is shown to Mark. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Stacy knows whether Mark 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) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mark can now know that Stacy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stacy","Mark"],"index":13026,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994398952,"difficulty":0.0005601048}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wallace's card is shown to Micheal. John's card is shown to John. Wallace's card is shown to John. Wallace's card is shown to Wallace. 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) ] Agenta knows whether (Agentc knows whether 2)","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":"Micheal can now know whether Wallace can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Micheal","John","Wallace"],"index":65991,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998709321,"difficulty":0.001290679}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erline's card is shown to John. Carolyn's card is shown to Ilene. Erline's card is shown to Ilene. John's card is shown to Carolyn. 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. It is publicly announced that Carolyn picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"John can now know whether Ilene can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Ilene","Carolyn","Erline"],"index":5287,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9964821339,"difficulty":0.0035178661}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Faye's card is shown to Evelyn. Evelyn's card is shown to Faye. Faye's card is shown to Faye. 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) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Evelyn can now know that Faye can know that Evelyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Evelyn","Faye"],"index":63631,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959874749,"difficulty":0.0040125251}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Savannah's card is shown to Savannah. William's card is shown to Marvin. It is publicly announced that someone picked a red card. It is publicly announced that Savannah picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Savannah can now know whether Marvin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Savannah","Marvin"],"index":62359,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9837501645,"difficulty":0.0162498355}
{"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. Rebecca's card is shown to Beverly. Rebecca's card is shown to Esther. Mary's card is shown to Esther. Rebecca's card is shown to Rebecca. Esther'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 Rebecca does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverly","Esther","Rebecca","Mary"],"index":1984,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7659649849,"difficulty":0.2340350151}
{"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 Patricia. Carolyn's card is shown to Patricia. James's card is shown to George. George's card is shown to George. James's card is shown to Carolyn. 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 Agentc:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether George can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Patricia","George","Carolyn"],"index":43216,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993809462,"difficulty":0.0006190538}
{"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 Debra. Debra's card is shown to Scott. Scott's card is shown to Scott. Scott's card is shown to Louise. 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 that (Agenta knows that 2)","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":"Scott can now know that Debra can know that Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debra","Scott","Louise"],"index":35191,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974915981,"difficulty":0.0025084019}
{"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 Lori. Lori's card is shown to Anna. Anna's card is shown to Anna. Christine's card is shown to Anna. Anna's card is shown to Christine. Anna's card is shown to Claire. Christine's card is shown to Claire. It is publicly announced that someone picked a red card. It is publicly announced that Lori picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 Agentd:2,3 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:3 Agentb:1,2,3 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Christine can now know whether Anna can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lori","Anna","Christine","Claire"],"index":44305,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993035793,"difficulty":0.0006964207}
{"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. Gary's card is shown to Debra. Debra's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Debra picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Debra can now know whether Gary can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gary","Debra"],"index":48192,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994538426,"difficulty":0.0005461574}
{"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 Samuel. Kathy's card is shown to Brian. Kathy's card is shown to Kathy. 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) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Samuel can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Samuel","Brian","Kathy"],"index":42439,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993231297,"difficulty":0.0006768703}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Ruth. Lorna's card is shown to Lorna. Ruth's card is shown to Bonnie. Lorna's card is shown to Bonnie. Bonnie's card is shown to Bonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 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 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ruth can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ruth","Lorna","Bonnie"],"index":9222,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993131161,"difficulty":0.0006868839}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Christopher. Christopher's card is shown to Curtis. Trevor's card is shown to Trevor. 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: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:3 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ivan can now know that Christopher can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ivan","Christopher","Curtis","Trevor"],"index":37157,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993211031,"difficulty":0.0006788969}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Tiffany. Elsie's card is shown to Tiffany. Elsie's card is shown to Barbara. Tiffany's card is shown to Elsie. 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 whether 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":"Elsie can now know whether Tiffany can know whether Elsie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tiffany","Barbara","Elsie"],"index":60384,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982773066,"difficulty":0.0017226934}
{"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. George's card is shown to Paul. James's card is shown to Jeremy. Paul's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that George does not know whether George picked a red card. It is publicly announced that Paul 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)) ] (Agenta knows whether (1|2|3|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":"Paul can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","George","Jeremy","James"],"index":58981,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999447763,"difficulty":0.000552237}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Natalie's card is shown to Natalie. Lonny's card is shown to Natalie. Natalie's card is shown to Lonny. Lonny's card is shown to Lonny. It is publicly announced that someone picked a red card. It is publicly announced that Lonny 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))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Natalie can now know that Lonny can know that Lonny picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Natalie","Lonny"],"index":26956,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9882795811,"difficulty":0.0117204189}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ramon's card is shown to David. Robert's card is shown to Linda. David's card is shown to Ramon. Ramon's card is shown to Ramon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,4 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 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Linda","Robert","Ramon"],"index":42398,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940132499,"difficulty":0.0059867501}
{"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 Amber. Amber's card is shown to Nancy. Nancy's card is shown to Nancy. Sarah's card is shown to Nancy. Amber's card is shown to Sarah. It is publicly announced that someone 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:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Amber can now know that Nancy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amber","Nancy","Sarah"],"index":57630,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994309545,"difficulty":0.0005690455}
{"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 Mary. Mary's card is shown to Michele. Michele'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 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cathy can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Michele","Cathy"],"index":6666,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8698000908,"difficulty":1.8698000908}
{"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 Bari. Mary's card is shown to Lisa. 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. It is publicly announced that Mary does not know whether Bari picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Bari can now know that Mary can know that Bari picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Bari","Lisa"],"index":60947,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8859009743,"difficulty":0.1140990257}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to Ramona. Ramona's card is shown to Lauren. Lauren's card is shown to Lauren. June's card is shown to Lauren. June's card is shown to June. 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: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:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lauren can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ramona","Lauren","June"],"index":46801,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994101524,"difficulty":0.0005898476}
{"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 Eva. Patricia's card is shown to Eva. Dora's card is shown to Dora. Eva's card is shown to Ronald. Dora's card is shown to Ronald. Eva's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Ronald does not know whether Ronald picked a red card. It is publicly announced that Ronald does not know whether Ronald 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) ] Agenta knows whether (Agentc 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":"Eva can now know whether Ronald can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eva","Dora","Ronald","Patricia"],"index":54985,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992139339,"difficulty":0.0007860661}
{"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 John. Dorothy's card is shown to Dorothy. Dorothy's card is shown to Randy. Randy's card is shown to Randy. Randy's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Randy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Dorothy","Randy","William"],"index":62874,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9104470611,"difficulty":1.9104470611}
{"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. Gerald's card is shown to Beatrice. Joseph's card is shown to Beatrice. John's card is shown to Gerald. John'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 Gerald 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)) ] (Agenta knows that (~(1|2|3|4)))","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":"John can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Beatrice","Gerald","Joseph"],"index":31785,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989734888,"difficulty":0.0010265112}
{"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 Leonard. Allyson's card is shown to Leonard. Manuel's card is shown to Louise. Leonard's card is shown to Manuel. Allyson's card is shown to Manuel. Leonard's card is shown to Allyson. Allyson's card is shown to Allyson. It is publicly announced that someone picked a red card. It is publicly announced that Louise does not know whether Allyson 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 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":"Manuel can now know that Allyson picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leonard","Louise","Manuel","Allyson"],"index":8981,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9929161072,"difficulty":0.0070838928}
{"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 Patty. Benjamin's card is shown to Patty. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Patty does not know whether Billy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Patty can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patty","Robert","Benjamin","Billy"],"index":43404,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993885756,"difficulty":0.0006114244}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Elizabeth. Leigh's card is shown to Elizabeth. Elizabeth's card is shown to Leigh. It is publicly announced that someone picked a red card. It is publicly announced that Leigh 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 (Agenta knows that 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":"Leigh can now know whether Elizabeth can know that Leigh picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elizabeth","Leigh"],"index":43922,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9507312775,"difficulty":0.0492687225}
{"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. Sarah's card is shown to Avril. Avril's card is shown to Edward. Joan's card is shown to Sarah. Edward'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:2 Agentd:1,3 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:4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Avril can now know whether Joan can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joan","Avril","Edward","Sarah"],"index":64709,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9811713696,"difficulty":0.0188286304}
{"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 John. Sarah's card is shown to John. Charles's card is shown to Sarah. John's card is shown to Janet. Sarah's card is shown to Janet. 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 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Charles can know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Charles","Sarah","Janet"],"index":2009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988691211,"difficulty":0.0011308789}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwain's card is shown to Dwain. Cindy's card is shown to Cindy. 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) ] (Agentb knows whether (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Cindy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dwain","Cindy"],"index":16304,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9928014278,"difficulty":0.0071985722}
{"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. Katharine's card is shown to William. William's card is shown to Katharine. Katharine's card is shown to Katharine. Katharine's card is shown to Deloris. Deloris's card is shown to Deloris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deloris can now know that Katharine can know whether Deloris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Katharine","Deloris"],"index":60926,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5753446817,"difficulty":1.5753446817}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dean's card is shown to Vivian. Rosa's card is shown to Phil. Dean's card is shown to Dean. 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) ] Agentb knows whether (Agentc knows that 2)","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":"Phil can now know whether Dean can know that Phil picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vivian","Phil","Dean","Rosa"],"index":49126,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6406978369,"difficulty":1.6406978369}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luke's card is shown to Luke. Amber's card is shown to Luke. Luke's card is shown to Bernice. Bernice's card is shown to Bernice. Bernice's card is shown to Amber. Amber's card is shown to Amber. It is publicly announced that someone picked a red card. It is publicly announced that Amber does not know whether Luke picked a red card. It is publicly announced that Bernice 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 (Agentc knows whether (1&2&3))","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":"Bernice can now know whether Amber can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Luke","Bernice","Amber"],"index":59200,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6041947007,"difficulty":0.3958052993}
{"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. Gail's card is shown to Kenneth. Willie's card is shown to Gail. Kenneth'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 or 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) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know whether Gail can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Gail","Willie"],"index":60708,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.845762372,"difficulty":0.154237628}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Ernest. Janet's card is shown to Ian. Ian'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 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Janet can now know that Ernest can know that Ian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ernest","Ian","Janet"],"index":12487,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997000277,"difficulty":0.002999723}
{"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 Gail. Gail's card is shown to Helen. Marcus's card is shown to Marcus. Marcus's card is shown to Reginald. It is publicly announced that someone picked a red card. It is publicly announced that Reginald does not know whether Helen 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 (Agentd knows that 3)","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":"Helen can now know that Reginald can know that Marcus picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gail","Helen","Marcus","Reginald"],"index":13393,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996388793,"difficulty":0.003611207}
{"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 Augusta. Jonathan's card is shown to Joan. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Augusta 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) ] (Agentc knows whether (~(1|2|3)))","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":"Jonathan can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Augusta","Joan","Jonathan"],"index":33620,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993703961,"difficulty":0.0006296039}
{"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. Darrell's card is shown to Lesli. Stephen's card is shown to Lesli. Darrell's card is shown to Darrell. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc: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:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Darrell picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Lesli","Darrell","Stephen"],"index":28578,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970350266,"difficulty":0.0029649734}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Edwin. Holly's card is shown to Edwin. Jerry'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:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know that Edwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edwin","Jerry","Holly","Nancy"],"index":33494,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975591898,"difficulty":0.0024408102}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Louise. Daisy's card is shown to Louise. Louise's card is shown to Daisy. Daisy's card is shown to Daisy. Louise's card is shown to Roger. Daisy's card is shown to Roger. 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:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daisy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Louise","Daisy","Roger","John"],"index":46085,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990215302,"difficulty":0.0009784698}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerardo's card is shown to Marilyn. Gerardo's card is shown to Ronny. John's card is shown to Gerardo. Gerardo's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marilyn","Ronny","Gerardo","John"],"index":3694,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989674091,"difficulty":0.0010325909}
{"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 Laurence. Laurence's card is shown to Sarah. Karen's card is shown to Sarah. Jewel's card is shown to Sarah. Sarah's card is shown to Jewel. It is publicly announced that someone picked a red card. It is publicly announced that Laurence 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)) ] (Agenta knows whether 1)","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":"Laurence can now know whether Laurence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laurence","Sarah","Karen","Jewel"],"index":45943,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5029165149,"difficulty":1.5029165149}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrel's card is shown to Eddie. Chester's card is shown to Chester. Darrel's card is shown to Chester. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Chester does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Chester can now know that Michael can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eddie","Chester","Michael","Darrel"],"index":16533,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994280934,"difficulty":0.0005719066}
{"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. John's card is shown to Christopher. Rebecca'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:1,2 Agentb:3 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:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether John can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","John","Rebecca"],"index":46637,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.746972084,"difficulty":0.253027916}
{"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. Rosie's card is shown to Darrell. Jewel's card is shown to Patricia. Darrell's card is shown to Rosie. Patricia's card is shown to Rosie. Jewel's card is shown to Jewel. 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:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jewel can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darrell","Patricia","Rosie","Jewel"],"index":35049,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989230037,"difficulty":0.0010769963}
{"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 Dennis. Donald's card is shown to Dennis. Jennifer's card is shown to Dennis. Dennis's card is shown to Jennifer. Donald's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dennis can now know that Donald can know whether Dennis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Dennis","Donald","Jennifer"],"index":40991,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5705665946,"difficulty":1.5705665946}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to June. June's card is shown to Dean. Dean's card is shown to Dean. Silvia's card is shown to Dean. June's card is shown to Silvia. Dean's card is shown to Silvia. It is publicly announced that someone picked a red card. It is publicly announced that June knows whether June picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Silvia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["June","Dean","Silvia"],"index":28579,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994475245,"difficulty":0.0005524755}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Willie. Willie's card is shown to Roberta. Roberta's card is shown to Roberta. Valerie's card is shown to Roberta. Roberta's card is shown to Valerie. 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) ] Agenta knows that (Agentc knows that 2)","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":"Willie can now know that Valerie can know that Roberta picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Willie","Roberta","Valerie"],"index":4034,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974727035,"difficulty":0.0025272965}
{"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 Robert. Barbara's card is shown to Robert. Robert's card is shown to David. Jessica's card is shown to Barbara. David's card is shown to Jessica. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessica can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","David","Barbara","Jessica"],"index":1515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989567995,"difficulty":0.0010432005}
{"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 Eva. Alisa's card is shown to Eva. Alisa's card is shown to Alisa. Jeremy's card is shown to Alisa. Jeremy's card is shown to Jeremy. 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:3 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeremy can now know whether Eva picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eva","Alisa","Jeremy"],"index":30652,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5613088608,"difficulty":1.5613088608}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Pauline. Yolanda's card is shown to Pauline. Esther's card is shown to Yolanda. Pauline's card is shown to Benjamin. Benjamin's card is shown to Benjamin. Esther's card is shown to Benjamin. 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:1,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pauline can now know that Yolanda can know that Benjamin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pauline","Yolanda","Benjamin","Esther"],"index":15147,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983958602,"difficulty":0.0016041398}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathan's card is shown to Leslie. Leslie's card is shown to Thomas. Thomas's card is shown to Thomas. Jean's card is shown to Thomas. Thomas's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Thomas does not know whether Leslie 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 (Agentb knows that 2)","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":"Leslie can now know that Nathan can know that Nathan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leslie","Nathan","Thomas","Jean"],"index":58930,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969556332,"difficulty":0.0030443668}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fred's card is shown to Jeremy. Michael's card is shown to Jeremy. Fred's card is shown to Fred. Fred's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeremy can now know that Fred can know that Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeremy","Fred","Michael"],"index":12125,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963921905,"difficulty":0.0036078095}
{"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. Nicole's card is shown to Doris. Annette's card is shown to Doris. Annette's card is shown to Nicole. Doris's card is shown to Annette. Doris's card is shown to Barbara. Nicole's card is shown to Barbara. Annette's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Doris knows whether Nicole picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Barbara can now know that Annette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doris","Nicole","Annette","Barbara"],"index":29937,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925040007,"difficulty":0.0074959993}
{"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 Linda. Linda's card is shown to Linda. James's card is shown to Randy. Linda's card is shown to Randy. James's card is shown to Matthew. Linda's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Randy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Linda","Randy","Matthew"],"index":17939,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9877609015,"difficulty":0.0122390985}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Robert. Joe's card is shown to Robert. Robert's card is shown to John. Joe's card is shown to Melissa. 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 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Robert can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","John","Melissa","Joe"],"index":3830,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980549812,"difficulty":0.0019450188}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leland's card is shown to Leland. Peggy's card is shown to Peggy. Shawn's card is shown to Peggy. 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 that (~(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":"Peggy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leland","Peggy","Shawn"],"index":48731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989145994,"difficulty":0.0010854006}
{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Therese. Helen's card is shown to Helen. George's card is shown to Helen. Therese's card is shown to George. Helen's card is shown to George. George's card is shown to George. Helen's card is shown to Harold. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 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:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Therese can now know that George can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Therese","Helen","George","Harold"],"index":35002,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9881249666,"difficulty":0.0118750334}
{"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. Juanita's card is shown to Juanita. 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) ] (Agentb 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":"Juanita can now know that Juanita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sarah","Juanita"],"index":16796,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9416999817,"difficulty":0.0583000183}
{"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. John's card is shown to Richard. Richard's card is shown to Richard. Richard'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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc: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:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Richard","Randall","William"],"index":50099,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994075298,"difficulty":0.0005924702}
{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Elaine. Kimberly's card is shown to Kimberly. Oscar'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 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elaine can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elaine","Kimberly","Oscar"],"index":37824,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994126558,"difficulty":0.0005873442}
{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucretia's card is shown to Lucretia. Ethel's card is shown to Lucretia. Lucretia's card is shown to Ethel. It is publicly announced that someone picked a red card. It is publicly announced that Ethel 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)) ] (Agenta 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":"Lucretia can now know whether Ethel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lucretia","Ethel"],"index":43150,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9403698444,"difficulty":0.0596301556}
{"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. 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) ] [ ! (Agentb knows whether (1|2)) ] (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 (1|2)) ] 0","hypothesis":"Mary can now know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dorothy","Mary"],"index":45627,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.988363564,"difficulty":0.011636436}