premise
stringlengths
104
712
smcdel_problem
stringlengths
72
285
n_announcements
int64
0
4
pbcheck
stringlengths
52
245
hypothesis
stringlengths
37
94
setup
stringclasses
4 values
hypothesis_depth
int64
0
1
n_agents
int64
2
4
label
stringclasses
2 values
names
sequencelengths
2
4
index
int64
1
67.7k
s-l
stringclasses
8 values
deberta_pred
int64
0
1
deberta_confidence
float64
0.5
1
difficulty
float64
0
2
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marjorie is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0
Christine can now know that Chris can know whether or not nobody is thirsty.
internal
1
4
entailment
[ "Michael", "Chris", "Christine", "Marjorie" ]
51,967
internal-1
1
0.99949
0.00051
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte is thirsty. It is publicly announced that Scott is not thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(2) ] (Agentb knows whether (1|2))
2
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(2) ] 0
Scott can now know whether someone is thirsty.
internal
0
2
entailment
[ "Charlotte", "Scott" ]
27,816
internal-1
1
0.999507
0.000493
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roy knows whether or not nobody is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agentd knows that 2)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0
Susan can now know that Everett is thirsty.
internal
0
4
not_entailment
[ "Roy", "Everett", "Randall", "Susan" ]
65,270
internal-0
0
0.998088
0.001912
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brittani's forehead is not muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows whether 2)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0
Jorge can now know whether Cory's forehead is muddy.
forehead
0
4
entailment
[ "Jorge", "Cory", "Brittani", "Richard" ]
56,092
forehead-1
1
0.999365
0.000635
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether someone's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agentc knows whether 2)
1
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0
Harold can now know that Maria can know whether Harold's forehead is muddy.
forehead_mirror
1
3
entailment
[ "Margaret", "Harold", "Maria" ]
51,455
forehead_mirror-1
1
0.999366
0.000634
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodney knows whether Cruz's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0
Silas can now know that George can know that nobody's forehead is muddy.
forehead_mirror
1
4
not_entailment
[ "Cruz", "Silas", "George", "Rodney" ]
47,106
forehead_mirror-0
0
0.998935
0.001065
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louie does not know whether Sandra is thirsty. It is publicly announced that Mario does not know whether or not everyone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that 1)
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0
Brenda can now know whether Mario can know that Sandra is thirsty.
internal
1
4
entailment
[ "Sandra", "Brenda", "Louie", "Mario" ]
20,075
internal-1
1
0.992505
0.007495
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gary knows whether Heather's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))
3
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0
Mary can now know that Heather can know that nobody's forehead is muddy.
forehead_mirror
1
4
not_entailment
[ "Gary", "Mary", "Patricia", "Heather" ]
12,659
forehead_mirror-0
0
0.998979
0.001021
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jamison knows whether or not nobody is thirsty. It is publicly announced that Jamison knows whether Jamison is thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))
2
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] 0
Maria can now know that Jamison can know that everyone is thirsty.
internal
1
2
not_entailment
[ "Maria", "Jamison" ]
8,973
internal-0
0
0.998854
0.001146
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stella does not know whether or not everyone's forehead is muddy. It is publicly announced that Shannon knows whether Shannon's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 1)
2
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] 0
Stella can now know whether Shannon can know that Shannon's forehead is muddy.
forehead
1
3
entailment
[ "Shannon", "Dorothy", "Stella" ]
9,812
forehead-1
1
0.842638
0.157362
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.
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)
1
VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0
Erin can now know that Rita can know that Rita picked a red card.
explicit
1
3
not_entailment
[ "George", "Rita", "Erin" ]
24,188
explicit-0
0
0.990364
0.009636
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.
VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)
0
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0
Donald can now know whether Adam picked a red card.
explicit
0
3
entailment
[ "Donald", "Randy", "Adam" ]
4,658
explicit-1
0
0.831802
1.831802
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhonda's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows that (Agenta knows that 3)
1
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0
Rhonda can now know that Felicia can know that Rhonda's forehead is muddy.
forehead_mirror
1
3
entailment
[ "Felicia", "Gina", "Rhonda" ]
41,030
forehead_mirror-1
0
0.810786
1.810786
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jasmine knows whether Anne's forehead is muddy. It is publicly announced that Anne does not know whether or not everyone's forehead is muddy. It is publicly announced that Jasmine knows whether Jesus's forehead is muddy. It is publicly announced that Jasmine knows whether Jeffery's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (Agentc knows whether (1|2|3|4))
4
VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0
Jeffery can now know whether someone's forehead is muddy.
forehead
0
4
entailment
[ "Jasmine", "Jesus", "Jeffery", "Anne" ]
17,500
forehead-1
1
0.999461
0.000539
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcia does not know whether Christopher is thirsty. It is publicly announced that Christopher does not know whether or not everyone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether (1|2|3|4))
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0
Christopher can now know that Joan can know whether someone is thirsty.
internal
1
4
entailment
[ "Marcia", "Christopher", "Joan", "Jessie" ]
48,282
internal-1
1
0.999497
0.000503
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.
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)
0
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0
Martha can now know that Harvey picked a red card.
explicit
0
4
not_entailment
[ "Jean", "Harvey", "Martha", "Perry" ]
22,457
explicit-0
0
0.998103
0.001897
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.
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)))
1
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
Ronald can now know that Brenda can know whether or not nobody picked a red card.
explicit
1
4
entailment
[ "Susan", "Brenda", "Karen", "Ronald" ]
32,077
explicit-1
1
0.999413
0.000587
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria knows whether or not everyone's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 1)
1
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0
Rebecca can now know whether Victoria can know whether Rebecca's forehead is muddy.
forehead
1
2
entailment
[ "Rebecca", "Victoria" ]
41,219
forehead-1
1
0.985748
0.014252
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmy knows whether or not nobody is thirsty. It is publicly announced that Debra does not know whether Jimmy is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows whether 1)
2
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0
Debra can now know whether Carmen can know whether Debra is thirsty.
internal
1
3
entailment
[ "Debra", "Jimmy", "Carmen" ]
55,760
internal-1
1
0.998914
0.001086
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Christine's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy. It is publicly announced that Danny knows whether Kevin's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (~(1|2|3)))
3
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0
Danny can now know that nobody's forehead is muddy.
forehead_mirror
0
3
not_entailment
[ "Kevin", "Christine", "Danny" ]
43,848
forehead_mirror-0
0
0.99902
0.00098
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen knows whether Karen is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (~(1|2|3|4)))
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0
Willie can now know whether or not nobody is thirsty.
internal
0
4
entailment
[ "Michelle", "Karen", "Willie", "Richard" ]
27,481
internal-1
1
0.99944
0.00056
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 3)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0
Scott can now know whether Maria can know that Ernie's forehead is muddy.
forehead_mirror
1
4
entailment
[ "Johnny", "Scott", "Ernie", "Maria" ]
41,141
forehead_mirror-1
1
0.999426
0.000574
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott does not know whether or not everyone's forehead is muddy. It is publicly announced that Sheri knows whether someone's forehead is muddy. It is publicly announced that Scott does not know whether or not everyone's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 3)
3
VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0
Thomas can now know that Mark can know that Sheri's forehead is muddy.
forehead
1
4
entailment
[ "Mark", "Scott", "Sheri", "Thomas" ]
38,754
forehead-1
0
0.98285
1.98285
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.
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)
1
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
David can now know whether James can know whether James picked a red card.
explicit
1
4
entailment
[ "Joseph", "James", "David", "Robert" ]
53,290
explicit-1
1
0.981529
0.018471
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brittney knows whether John's forehead is muddy. It is publicly announced that John knows whether Brittney's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentd knows whether (1&2&3&4))
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 0
Nancy can now know that Barbara can know whether or not everyone's forehead is muddy.
forehead
1
4
not_entailment
[ "Nancy", "Brittney", "John", "Barbara" ]
13,680
forehead-0
0
0.945442
0.054558
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 2)
0
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0
Deborah can now know that David can know that Wilma is thirsty.
internal
1
3
not_entailment
[ "David", "Wilma", "Deborah" ]
58,502
internal-0
0
0.996727
0.003273
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.
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))
1
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
Cindy can now know that everyone picked a red card.
explicit
0
4
not_entailment
[ "Candi", "Mary", "Cindy", "Luciano" ]
60,585
explicit-0
0
0.99851
0.00149
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elaine knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether or not nobody's forehead is muddy. It is publicly announced that Brenda's forehead is not muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] (Agentb knows whether 2)
4
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] 0
Patricia can now know whether Patricia's forehead is muddy.
forehead
0
3
not_entailment
[ "Brenda", "Patricia", "Elaine" ]
50,055
forehead-0
0
0.984919
0.015081
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Farah knows whether or not nobody is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows whether 2)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0
Joseph can now know whether Alan can know whether James is thirsty.
internal
1
4
entailment
[ "Joseph", "James", "Alan", "Farah" ]
38,162
internal-1
1
0.999133
0.000867
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy is not thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether (1&2))
1
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0
Dong can now know whether Dorothy can know whether or not everyone is thirsty.
internal
1
2
entailment
[ "Dong", "Dorothy" ]
62,968
internal-1
1
0.987755
0.012245
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hector knows whether someone's forehead is muddy. It is publicly announced that Naomi's forehead is not muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agentc knows whether 3)
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0
Naomi can now know whether Naomi's forehead is muddy.
forehead
0
4
entailment
[ "Rosa", "Gloria", "Naomi", "Hector" ]
23,532
forehead-1
1
0.565503
0.434497
There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether someone's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1&2))
1
VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0
Cynthia can now know that everyone's forehead is muddy.
forehead_mirror
0
2
not_entailment
[ "Cynthia", "Carol" ]
8,428
forehead_mirror-0
0
0.998989
0.001011
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher knows whether someone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether 4)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0
Virginia can now know whether Virginia is thirsty.
internal
0
4
entailment
[ "William", "Christopher", "Travis", "Virginia" ]
18,739
internal-1
1
0.916828
0.083172
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christian knows whether Jaime is thirsty. It is publicly announced that Christian knows whether Jaime is thirsty. It is publicly announced that Jaime knows whether Christian is thirsty. It is publicly announced that Christian knows whether someone is thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows whether 1)
4
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0
Jaime can now know that Christian can know whether Christian is thirsty.
internal
1
2
entailment
[ "Christian", "Jaime" ]
4,401
internal-1
1
0.989631
0.010369
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows whether (~(1|2|3|4)))
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0
Edward can now know whether or not nobody's forehead is muddy.
forehead_mirror
0
4
entailment
[ "Loraine", "Robert", "Dollie", "Edward" ]
19,380
forehead_mirror-1
1
0.999266
0.000734
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon knows whether or not everyone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that 4)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0
Mary can now know that Pasquale can know that Gloria is thirsty.
internal
1
4
not_entailment
[ "Pasquale", "Sharon", "Mary", "Gloria" ]
14,889
internal-0
0
0.990574
0.009426
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia is not thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows whether 3)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0
Steven can now know whether Alex is thirsty.
internal
0
4
not_entailment
[ "Amy", "Patricia", "Alex", "Steven" ]
60,260
internal-0
0
0.997495
0.002505
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jenifer knows whether Jenifer's forehead is muddy. It is publicly announced that Amy knows whether Vicky's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentc knows that 4)
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0
Maryann can now know that Amy's forehead is muddy.
forehead_mirror
0
4
not_entailment
[ "Vicky", "Jenifer", "Maryann", "Amy" ]
52,602
forehead_mirror-0
0
0.997998
0.002002
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.
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)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0
Charles can now know whether Adrianne picked a red card.
explicit
0
4
not_entailment
[ "Charles", "Adrianne", "Robin", "Chad" ]
38,254
explicit-0
1
0.706396
1.706396
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 2)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0
Eric can now know whether Esther can know that Eric's forehead is muddy.
forehead
1
4
not_entailment
[ "Gary", "Eric", "Esther", "Sherwood" ]
43,408
forehead-0
0
0.992719
0.007281
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.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)
0
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0
Shellie can now know that Christopher picked a red card.
explicit
0
4
not_entailment
[ "Virginia", "Shellie", "Christopher", "Jennifer" ]
36,897
explicit-0
0
0.997135
0.002865
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jana knows whether or not everyone is thirsty. It is publicly announced that Martha knows whether or not nobody is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows whether (1&2&3&4))
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0
Aaron can now know whether or not everyone is thirsty.
internal
0
4
entailment
[ "John", "Aaron", "Martha", "Jana" ]
50,387
internal-1
0
0.663701
1.663701
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Zelda is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentd knows that (Agenta knows that (1&2&3&4))
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0
Richard can now know that Linda can know that everyone is thirsty.
internal
1
4
not_entailment
[ "Linda", "Zelda", "Jacob", "Richard" ]
65,859
internal-0
0
0.998954
0.001046
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Andres is thirsty. It is publicly announced that Wilbur does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Andres does not know whether John is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agentc knows whether (1|2|3))
4
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0
Andres can now know that John can know whether someone is thirsty.
internal
1
3
entailment
[ "Wilbur", "Andres", "John" ]
19,811
internal-1
1
0.999454
0.000546
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lou knows whether Barbara is thirsty. It is publicly announced that Barbara is thirsty. It is publicly announced that Barbara knows whether or not nobody is thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether (~(1|2)))
3
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0
Lou can now know that Barbara can know whether or not nobody is thirsty.
internal
1
2
entailment
[ "Lou", "Barbara" ]
18,179
internal-1
1
0.999486
0.000514
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 1)
1
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0
Leonie can now know that Gregory's forehead is muddy.
forehead_mirror
0
3
not_entailment
[ "Gregory", "Barbara", "Leonie" ]
66,548
forehead_mirror-0
0
0.990683
0.009317
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juanita does not know whether Juanita's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows that 3)
1
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0
John can now know that Juanita can know that John's forehead is muddy.
forehead
1
3
not_entailment
[ "Juanita", "Kevin", "John" ]
30,110
forehead-0
0
0.996873
0.003127
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sylvia does not know whether Steven is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows whether (~(1|2|3)))
1
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0
Steven can now know that Jennifer can know whether or not nobody is thirsty.
internal
1
3
entailment
[ "Jennifer", "Steven", "Sylvia" ]
57,467
internal-1
1
0.999307
0.000693
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Irma's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1|2|3|4))
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0
Lawrence can now know whether someone's forehead is muddy.
forehead_mirror
0
4
entailment
[ "Irma", "Lawrence", "Reba", "Dan" ]
52,671
forehead_mirror-1
1
0.99939
0.00061
There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Modesto knows whether Shirley's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] (Agentb knows that 2)
2
VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0
Shirley can now know that Shirley's forehead is muddy.
forehead_mirror
0
2
not_entailment
[ "Modesto", "Shirley" ]
49,855
forehead_mirror-0
0
0.989136
0.010864
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether someone's forehead is muddy. It is publicly announced that Shannon's forehead is not muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] Agentc knows whether (Agentb knows that 3)
2
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] 0
Sharon can now know whether Daniel can know that Sharon's forehead is muddy.
forehead
1
3
not_entailment
[ "Shannon", "Daniel", "Sharon" ]
58,704
forehead-0
0
0.960067
0.039933
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.
VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that 1)
0
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0
Mike can now know that Noel can know that Noel picked a red card.
explicit
1
2
not_entailment
[ "Noel", "Mike" ]
11,314
explicit-0
0
0.992641
0.007359
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katie's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agenta knows whether 1)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0
Luis can now know that Joyce can know whether Joyce's forehead is muddy.
forehead_mirror
1
4
entailment
[ "Joyce", "Katie", "Emma", "Luis" ]
39,286
forehead_mirror-1
1
0.999475
0.000525
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether (1|2))
2
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0
Sonia can now know whether Mary can know whether someone is thirsty.
internal
1
2
entailment
[ "Sonia", "Mary" ]
60,761
internal-1
1
0.999457
0.000543
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.
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)
4
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
Hung can now know whether Roxie picked a red card.
explicit
0
3
entailment
[ "Roxie", "Hung", "Tamela" ]
20,419
explicit-1
1
0.97726
0.02274
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (1&2&3))
1
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0
David can now know that everyone's forehead is muddy.
forehead_mirror
0
3
not_entailment
[ "Arthur", "Sandy", "David" ]
987
forehead_mirror-0
0
0.998982
0.001018
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.
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)
0
VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0
Clyde can now know that Jason can know that Jonathan picked a red card.
explicit
1
4
not_entailment
[ "Clyde", "Joseph", "Jonathan", "Jason" ]
27,780
explicit-0
0
0.998226
0.001774
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Jerry is not thirsty. It is publicly announced that Jerry knows whether someone is thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 1)
3
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] 0
Jerry can now know whether Robert can know whether Robert is thirsty.
internal
1
2
entailment
[ "Robert", "Jerry" ]
33,554
internal-1
1
0.99853
0.00147
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1|2|3|4))
0
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0
Anthony can now know whether Ruth can know whether someone's forehead is muddy.
forehead_mirror
1
4
entailment
[ "Ruth", "Anthony", "David", "Bettie" ]
3,003
forehead_mirror-1
1
0.999336
0.000664
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gloria does not know whether or not everyone is thirsty. It is publicly announced that Gloria does not know whether or not everyone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether (1|2|3|4))
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0
Colin can now know that Gloria can know whether someone is thirsty.
internal
1
4
entailment
[ "Gloria", "Michelle", "Colin", "Lyle" ]
64,054
internal-1
1
0.999482
0.000518
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dominick knows whether Dominick's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows that 2)
1
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0
Sara can now know that Ian can know that Ian's forehead is muddy.
forehead_mirror
1
3
not_entailment
[ "Sara", "Ian", "Dominick" ]
3,279
forehead_mirror-0
0
0.997975
0.002025
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bessie does not know whether or not everyone's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 1)
2
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0
Bessie can now know that James's forehead is muddy.
forehead
0
2
entailment
[ "James", "Bessie" ]
37,699
forehead-1
1
0.915285
0.084715
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.
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)
0
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
Margaret can now know that Margaret picked a red card.
explicit
0
4
not_entailment
[ "Joseph", "Agnes", "Margaret", "Sharri" ]
60,724
explicit-0
0
0.992953
0.007047
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon's forehead is muddy. It is publicly announced that Sharon knows whether Irene's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (~(1|2)))
2
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0
Sharon can now know whether or not nobody's forehead is muddy.
forehead
0
2
entailment
[ "Sharon", "Irene" ]
51,623
forehead-1
1
0.999454
0.000546
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy does not know whether Sergio is thirsty. It is publicly announced that Sergio does not know whether Glen is thirsty. It is publicly announced that Timothy does not know whether Sergio is thirsty. It is publicly announced that Timothy does not know whether Rachel is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentd knows that (Agentc knows that (1&2&3&4))
4
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0
Timothy can now know that Glen can know that everyone is thirsty.
internal
1
4
not_entailment
[ "Rachel", "Sergio", "Glen", "Timothy" ]
6,289
internal-0
0
0.998989
0.001011
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.
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))
0
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0
Shannon can now know whether Brandon can know that everyone picked a red card.
explicit
1
3
entailment
[ "Erica", "Brandon", "Shannon" ]
45,099
explicit-1
1
0.98064
0.01936
There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy. It is publicly announced that Kenneth's forehead is muddy. It is publicly announced that everyone's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] (Agentb knows that (~(1|2)))
3
VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] 0
Kenneth can now know that nobody's forehead is muddy.
forehead_mirror
0
2
not_entailment
[ "Pamela", "Kenneth" ]
25,715
forehead_mirror-0
0
0.989836
0.010164
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))
0
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0
Ben can now know that nobody's forehead is muddy.
forehead_mirror
0
4
not_entailment
[ "Ben", "Timothy", "Amanda", "Lloyd" ]
2,598
forehead_mirror-0
0
0.99829
0.00171
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raquel does not know whether Nicholas is thirsty. It is publicly announced that Kenneth does not know whether Nicholas is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] Agentd knows that (Agentc knows that 1)
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0
Nicholas can now know that Kenneth can know that Raquel is thirsty.
internal
1
4
not_entailment
[ "Raquel", "Susan", "Kenneth", "Nicholas" ]
65,111
internal-0
0
0.997727
0.002273
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.
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)
3
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
Sandra can now know that Jeffrey can know that Mathew picked a red card.
explicit
1
4
not_entailment
[ "Sandra", "Dale", "Jeffrey", "Mathew" ]
49,959
explicit-0
0
0.978863
0.021137
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah does not know whether Marcus is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty. It is publicly announced that David does not know whether Marcus is thirsty. It is publicly announced that Marcus does not know whether or not everyone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 4)
4
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0
Kelly can now know that Sarah can know whether David is thirsty.
internal
1
4
entailment
[ "Kelly", "Marcus", "Sarah", "David" ]
34,583
internal-1
0
0.922829
1.922829
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy. It is publicly announced that Julia's forehead is muddy.
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)
2
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0
Scott can now know that Julia can know that Julia's forehead is muddy.
forehead
1
2
entailment
[ "Scott", "Julia" ]
14,416
forehead-1
0
0.590212
1.590212
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.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether (~(1|2)))
1
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0
Christopher can now know whether or not nobody picked a red card.
explicit
0
2
entailment
[ "Christopher", "Ernest" ]
57,114
explicit-1
1
0.999366
0.000634
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda is not thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agenta knows whether 1)
1
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0
Carol can now know that John can know whether John is thirsty.
internal
1
3
entailment
[ "John", "Amanda", "Carol" ]
24,794
internal-1
1
0.96308
0.03692
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.
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)
0
VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0
Kathryn can now know whether Charles can know that Walter picked a red card.
explicit
1
3
not_entailment
[ "Kathryn", "Walter", "Charles" ]
17,293
explicit-0
1
0.932114
1.932114
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.
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)))
1
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
Barbara can now know that nobody picked a red card.
explicit
0
4
not_entailment
[ "Sherry", "Barbara", "Brenda", "Theodore" ]
3,179
explicit-0
0
0.999051
0.000949
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that June does not know whether June's forehead is muddy. It is publicly announced that Ethel knows whether June's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 3)
3
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0
June can now know whether Ethel's forehead is muddy.
forehead
0
3
entailment
[ "Robert", "June", "Ethel" ]
24,804
forehead-1
1
0.997341
0.002659
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellen knows whether someone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentd knows whether 1)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0
Ellen can now know whether Jesse is thirsty.
internal
0
4
not_entailment
[ "Jesse", "Lisa", "Bertram", "Ellen" ]
62,424
internal-0
0
0.997646
0.002354
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Javier's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows whether (Agenta knows that 1)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0
Janis can now know whether Harold can know that Harold's forehead is muddy.
forehead_mirror
1
4
entailment
[ "Harold", "Julio", "Javier", "Janis" ]
49,213
forehead_mirror-1
1
0.999333
0.000667
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.
VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))
0
VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0
Janice can now know that everyone picked a red card.
explicit
0
3
not_entailment
[ "David", "Janice", "Carmen" ]
10,302
explicit-0
0
0.999002
0.000998
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia's forehead is not muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that (~(1|2|3|4)))
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0
Janet can now know that nobody's forehead is muddy.
forehead_mirror
0
4
not_entailment
[ "Janet", "Marshall", "Michael", "Julia" ]
64,130
forehead_mirror-0
0
0.998882
0.001118
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie knows whether someone's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows whether 4)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0
Stephanie can now know that Sherry can know whether Sherry's forehead is muddy.
forehead_mirror
1
4
entailment
[ "Stephanie", "Allan", "Elsie", "Sherry" ]
16,547
forehead_mirror-1
1
0.999295
0.000705
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margorie does not know whether or not everyone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0
Joseph can now know that Susan can know that nobody is thirsty.
internal
1
4
not_entailment
[ "Maura", "Margorie", "Susan", "Joseph" ]
21,833
internal-0
0
0.999001
0.000999
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Clinton is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agenta knows that 1)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0
Hope can now know that Hope is thirsty.
internal
0
4
not_entailment
[ "Hope", "Alex", "Clinton", "Linda" ]
55,986
internal-0
0
0.988692
0.011308
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Felicia does not know whether James is thirsty. It is publicly announced that Felicia does not know whether Ruth is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that 1)
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0
Ruth can now know that James can know that Felicia is thirsty.
internal
1
4
not_entailment
[ "Felicia", "Ruth", "James", "Ashley" ]
36,429
internal-0
0
0.997864
0.002136
There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vaughn knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.
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 that 1)
2
VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0
Vaughn can now know whether Ingrid can know that Vaughn's forehead is muddy.
forehead_mirror
1
2
entailment
[ "Vaughn", "Ingrid" ]
56,542
forehead_mirror-1
1
0.999213
0.000787
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Veronica does not know whether Veronica's forehead is muddy. It is publicly announced that Donald does not know whether or not everyone's forehead is muddy. It is publicly announced that Jenny knows whether Donald's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] (Agenta knows that 1)
3
VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] 0
Veronica can now know that Veronica's forehead is muddy.
forehead
0
4
entailment
[ "Veronica", "Donald", "Bobby", "Jenny" ]
54,885
forehead-1
0
0.75409
1.75409
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carrie does not know whether Ross is thirsty. It is publicly announced that Carrie does not know whether Marian is thirsty. It is publicly announced that Ross does not know whether Marian is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows whether 3)
3
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0
Carrie can now know whether Carrie is thirsty.
internal
0
4
entailment
[ "Marian", "James", "Carrie", "Ross" ]
36,377
internal-1
1
0.995728
0.004272
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald knows whether or not everyone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows whether 2)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0
Ronald can now know whether Colleen is thirsty.
internal
0
4
not_entailment
[ "Kelly", "Colleen", "Lois", "Ronald" ]
64,025
internal-0
0
0.996714
0.003286
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos does not know whether Carlos's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that 4)
1
VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0
Terrance can now know that Carlos can know that Jason's forehead is muddy.
forehead
1
4
not_entailment
[ "Terrance", "Millie", "Carlos", "Jason" ]
15,086
forehead-0
0
0.997436
0.002564
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether Brian's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows whether 3)
1
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0
James can now know whether Brian can know whether James's forehead is muddy.
forehead
1
3
entailment
[ "Michael", "Brian", "James" ]
42,786
forehead-1
1
0.997833
0.002167
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arturo does not know whether or not everyone is thirsty. It is publicly announced that Arturo does not know whether Ruth is thirsty. It is publicly announced that Ruth knows whether or not everyone is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))
3
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2&3)) ] 0
Ruth can now know whether or not everyone is thirsty.
internal
0
3
entailment
[ "Ruth", "Arturo", "Patricia" ]
59,629
internal-1
1
0.51585
0.48415
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Twanna does not know whether or not everyone's forehead is muddy. It is publicly announced that Cory knows whether Cory's forehead is muddy.
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 (1|2))
2
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0
Twanna can now know whether someone's forehead is muddy.
forehead
0
2
entailment
[ "Cory", "Twanna" ]
51,990
forehead-1
1
0.999463
0.000537
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory does not know whether or not everyone is thirsty. It is publicly announced that Gregory does not know whether or not everyone is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether (1&2&3))
2
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0
Anna can now know that Gregory can know whether or not everyone is thirsty.
internal
1
3
not_entailment
[ "Gregory", "Michael", "Anna" ]
47,028
internal-0
0
0.68107
0.31893
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.
VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (1&2&3))
1
VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0
Troy can now know that everyone picked a red card.
explicit
0
3
not_entailment
[ "Dorothy", "Troy", "Amy" ]
13,660
explicit-0
0
0.9958
0.0042
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jewel knows whether Noel's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Linda's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentb knows that (Agentc knows that 2)
3
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0
Louis can now know that Jewel can know that Louis's forehead is muddy.
forehead_mirror
1
4
not_entailment
[ "Linda", "Louis", "Jewel", "Noel" ]
45,639
forehead_mirror-0
0
0.989461
0.010539
There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Rudy knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (~(1|2)))
3
VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0
Rudy can now know whether James can know whether or not nobody's forehead is muddy.
forehead_mirror
1
2
entailment
[ "Rudy", "James" ]
4,137
forehead_mirror-1
1
0.999223
0.000777
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (1&2&3))
1
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0
Randi can now know that Tim can know that everyone's forehead is muddy.
forehead
1
3
not_entailment
[ "Randi", "William", "Tim" ]
27,496
forehead-0
0
0.981291
0.018709
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Kevin's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether 1)
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0
Linda can now know whether Paul can know whether Kevin's forehead is muddy.
forehead_mirror
1
4
entailment
[ "Kevin", "Linda", "Paul", "Theodore" ]
14,386
forehead_mirror-1
1
0.999438
0.000562
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.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] (Agentb knows that (1|2|3))
2
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] 0
Jason can now know that someone picked a red card.
explicit
0
3
entailment
[ "Leslie", "Jason", "Ruth" ]
11,464
explicit-1
1
0.999459
0.000541