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 Aubrey does not know whether or not everyone is thirsty. It is publicly announced that Aubrey does not know whether Jeremy 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 2) ] Agentd knows whether (Agenta knows whether 3)
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 2) ] 0
Nichole can now know whether Aubrey can know whether William is thirsty.
internal
1
4
entailment
[ "Aubrey", "Jeremy", "William", "Nichole" ]
61,652
internal-1
1
0.998557
0.001443
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that James does not know whether Ernestine 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) ] Agenta knows that (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)) ] [ ! ~(Agentd knows whether 2) ] 0
Maria can now know that Ernestine can know whether or not everyone is thirsty.
internal
1
4
not_entailment
[ "Maria", "Ernestine", "Walter", "James" ]
18,233
internal-0
0
0.573377
0.426623
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gabriel knows whether or not everyone is thirsty. It is publicly announced that Gabriel knows whether or not everyone is thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] (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 (1&2)) ] 0
Gabriel can now know that someone is thirsty.
internal
0
2
entailment
[ "Donna", "Gabriel" ]
14,405
internal-1
1
0.999776
0.000224
There are three persons. Everyone is visible 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 or 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) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (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) ] [ ! (Agentb knows whether (1&2&3)) ] 0
Kevin can now know that Tracie can know that nobody's forehead is muddy.
forehead_mirror
1
3
not_entailment
[ "Leon", "Kevin", "Tracie" ]
48,205
forehead_mirror-0
0
0.998431
0.001569
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether someone's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentd 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) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0
Gregory can now know that Chasity can know that Chasity's forehead is muddy.
forehead
1
4
not_entailment
[ "John", "Gregory", "Margaret", "Chasity" ]
64,687
forehead-0
0
0.998354
0.001646
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.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)
0
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0
Nona can now know whether Nona picked a red card.
explicit
0
3
not_entailment
[ "Annie", "Mary", "Nona" ]
1,845
explicit-0
0
0.808641
0.191359
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dominic is not thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows that (~(1|2|3)))
1
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0
Rogelio can now know whether Mary can know that nobody is thirsty.
internal
1
3
entailment
[ "Dominic", "Rogelio", "Mary" ]
44,838
internal-1
1
0.999484
0.000516
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina knows whether Lisa's forehead is muddy. It is publicly announced that Lisa'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 3) ] [ ! 3 ] Agentb knows that (Agentd knows whether 3)
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) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0
Linda can now know that Tina can know whether Lisa's forehead is muddy.
forehead_mirror
1
4
entailment
[ "Cynthia", "Linda", "Lisa", "Tina" ]
22,913
forehead_mirror-1
1
0.999742
0.000258
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marguerite is not thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb 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) ] [ ! ~(1) ] 0
Christine can now know that everyone is thirsty.
internal
0
4
not_entailment
[ "Marguerite", "Christine", "Rodney", "Lorraine" ]
17,309
internal-0
0
0.998511
0.001489
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy. It is publicly announced that Trenton knows whether Gerald's forehead is muddy. It is publicly announced that Richard knows whether Trenton'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 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agentb knows whether (Agentc knows that 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) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0
Richard can now know whether Trenton can know that Gerald's forehead is muddy.
forehead_mirror
1
4
entailment
[ "Barbara", "Richard", "Trenton", "Gerald" ]
65,712
forehead_mirror-1
1
0.999687
0.000313
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Jeremy'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) ] [ ! (Agentd knows whether 2) ] Agentc knows whether (Agentd knows whether (~(1|2|3|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) ] [ ! (Agentd knows whether 2) ] 0
Bessie can now know whether Daniel can know whether or not nobody's forehead is muddy.
forehead
1
4
entailment
[ "Kerry", "Jeremy", "Bessie", "Daniel" ]
50,369
forehead-1
1
0.999707
0.000293
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tyree does not know whether Michelle is thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 2)
1
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0
Michelle can now know whether Tyree can know whether Tyree is thirsty.
internal
1
2
entailment
[ "Michelle", "Tyree" ]
18,013
internal-1
1
0.99865
0.00135
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agentc knows that (~(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) ] [ ! (1&2&3) ] 0
Michael can now know that Allan can know that nobody's forehead is muddy.
forehead_mirror
1
3
not_entailment
[ "Kenneth", "Michael", "Allan" ]
47,371
forehead_mirror-0
0
0.99429
0.00571
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charissa does not know whether Robert 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) ] Agenta knows that (Agentd 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) ] 0
Robert can now know that Karen can know that someone is thirsty.
internal
1
4
entailment
[ "Robert", "Charissa", "Domingo", "Karen" ]
41,198
internal-1
1
0.999776
0.000224
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.
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)
0
VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0
Stephanie can now know whether Estella can know whether Stephanie picked a red card.
explicit
1
3
entailment
[ "Stephanie", "Samuel", "Estella" ]
3,393
explicit-1
1
0.99701
0.00299
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernice knows whether Bernice is thirsty. It is publicly announced that Paul does not know whether Christopher is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 3) ] (Agentb 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) ] [ ! ~(Agentb knows whether 3) ] 0
Paul can now know whether or not nobody is thirsty.
internal
0
3
entailment
[ "Bernice", "Paul", "Christopher" ]
34,657
internal-1
1
0.999719
0.000281
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.
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)
2
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
Mavis can now know whether Velma picked a red card.
explicit
0
4
entailment
[ "Mavis", "Kevin", "Velma", "Marc" ]
41,014
explicit-1
0
0.575444
1.575444
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erica does not know whether Sherman is thirsty. It is publicly announced that Erica knows whether or not everyone is thirsty. It is publicly announced that Erica does not know whether Larry is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 1)
3
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0
Larry can now know that Erica is thirsty.
internal
0
3
not_entailment
[ "Erica", "Sherman", "Larry" ]
52,505
internal-0
0
0.897205
0.102795
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karl does not know whether or not everyone'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 2)
1
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0
Karl can now know that Hyacinth's forehead is muddy.
forehead
0
2
entailment
[ "Karl", "Hyacinth" ]
52,755
forehead-1
1
0.744651
0.255349
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew does not know whether Jeanne is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Joann is thirsty. It is publicly announced that Joann 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) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] (Agentb knows whether 2)
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) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] 0
Jeanne can now know whether Jeanne is thirsty.
internal
0
4
entailment
[ "Joann", "Jeanne", "Frances", "Matthew" ]
42,434
internal-1
1
0.999126
0.000874
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.
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)
1
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
George can now know whether Gary picked a red card.
explicit
0
3
entailment
[ "George", "Gary", "Doris" ]
52,587
explicit-1
1
0.878173
0.121827
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Gloria's forehead is muddy. It is publicly announced that Peter knows whether Gloria'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) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentc knows that 3)
2
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0
Gloria can now know that Peter can know that Peter's forehead is muddy.
forehead_mirror
1
3
not_entailment
[ "Richard", "Gloria", "Peter" ]
46,319
forehead_mirror-0
0
0.99786
0.00214
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Paul does not know whether Terry is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows that 3)
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0
Deena can now know that Paul can know that Terry is thirsty.
internal
1
4
not_entailment
[ "Deena", "Paul", "Terry", "Edith" ]
24,913
internal-0
0
0.994931
0.005069
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Van 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0
Jill can now know whether Daniel can know whether Daniel's forehead is muddy.
forehead
1
3
entailment
[ "Van", "Jill", "Daniel" ]
52,920
forehead-1
1
0.818864
0.181136
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy's forehead is muddy. It is publicly announced that Randy knows whether Randy'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 whether 3) ] Agentc knows whether (Agenta knows that 3)
2
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0
Randy can now know whether Adalberto can know that Randy's forehead is muddy.
forehead_mirror
1
3
entailment
[ "Adalberto", "King", "Randy" ]
30,504
forehead_mirror-1
1
0.99959
0.00041
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Terry is thirsty. It is publicly announced that Mary 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) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows that 2)
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) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0
George can now know that Michael is thirsty.
internal
0
4
not_entailment
[ "Mary", "Michael", "George", "Terry" ]
24,236
internal-0
0
0.998147
0.001853
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether John is thirsty. It is publicly announced that Jennifer does not know whether Eloise is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that 2)
2
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0
Eloise can now know that John is thirsty.
internal
0
3
not_entailment
[ "Eloise", "John", "Jennifer" ]
45,495
internal-0
0
0.997322
0.002678
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))
2
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0
Mary can now know that Patricia can know whether or not everyone's forehead is muddy.
forehead
1
2
not_entailment
[ "Patricia", "Mary" ]
40,968
forehead-0
1
0.962715
1.962715
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows whether (~(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
Marilyn can now know whether or not nobody's forehead is muddy.
forehead_mirror
0
4
entailment
[ "Freddie", "Ralph", "Marilyn", "Charles" ]
10,455
forehead_mirror-1
1
0.999763
0.000237
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susie knows whether Dorothy'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 3) ] (Agentb knows that 1)
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 3) ] 0
Susie can now know that Alan's forehead is muddy.
forehead
0
3
not_entailment
[ "Alan", "Susie", "Dorothy" ]
18,313
forehead-0
0
0.998223
0.001777
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luther 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)) ] Agentc knows whether (Agentb 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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0
Krista can now know whether Luther can know whether Peter is thirsty.
internal
1
4
entailment
[ "Peter", "Luther", "Krista", "Robert" ]
59,374
internal-1
1
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 Carol does not know whether Carol's forehead is muddy. It is publicly announced that Gregory knows whether Gregory's forehead is muddy. It is publicly announced that Gregory knows whether Gregory'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 3) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows that 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 3) ] [ ! (Agentc knows whether 3) ] 0
Sophie can now know whether Gregory can know that Gregory's forehead is muddy.
forehead
1
3
entailment
[ "Sophie", "Carol", "Gregory" ]
65,819
forehead-1
1
0.937987
0.062013
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.
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))
1
VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0
Lawrence can now know that someone picked a red card.
explicit
0
3
entailment
[ "Florida", "Lawrence", "Marivel" ]
37,267
explicit-1
1
0.99977
0.00023
There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Joseph is thirsty. It is publicly announced that Thomas is thirsty. It is publicly announced that Joseph is thirsty. It is publicly announced that Joseph is thirsty.
VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] Agentb knows that (Agenta knows whether (1|2))
4
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] 0
Joseph can now know that Thomas can know whether someone is thirsty.
internal
1
2
entailment
[ "Thomas", "Joseph" ]
33,521
internal-1
1
0.999781
0.000219
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neil does not know whether or not everyone's forehead is muddy. It is publicly announced that Neil does not know whether Neil'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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agenta knows whether 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0
Herbert can now know whether Neil's forehead is muddy.
forehead
0
4
entailment
[ "Herbert", "Maria", "Dana", "Neil" ]
38,099
forehead-1
1
0.999445
0.000555
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon knows whether someone is thirsty. It is publicly announced that Sharon knows whether Sharon is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that (1&2&3))
2
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] 0
Richard can now know that Sharon can know that everyone is thirsty.
internal
1
3
not_entailment
[ "Kendrick", "Richard", "Sharon" ]
26,163
internal-0
0
0.998378
0.001622
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether or not everyone's forehead is muddy. It is publicly announced that Heather knows whether or not nobody's forehead is muddy. It is publicly announced that Paul does not know whether Paul's forehead is muddy. It is publicly announced that Heather knows whether or not nobody's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))
4
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0
Paul can now know that nobody's forehead is muddy.
forehead
0
2
not_entailment
[ "Paul", "Heather" ]
32,894
forehead-0
0
0.997429
0.002571
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason's forehead is 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 that 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
Roy can now know that Roy's forehead is muddy.
forehead_mirror
0
4
not_entailment
[ "David", "Jason", "Damon", "Roy" ]
39,532
forehead_mirror-0
0
0.995963
0.004037
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows whether (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) ] [ ! (1|2|3) ] 0
Pauline can now know whether someone's forehead is muddy.
forehead
0
3
entailment
[ "Silvia", "Carol", "Pauline" ]
5,129
forehead-1
1
0.999747
0.000253
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.
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))
2
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
Megan can now know whether Jackie can know that someone picked a red card.
explicit
1
3
entailment
[ "Jackie", "Megan", "Kris" ]
38,467
explicit-1
1
0.999773
0.000227
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.
VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)
0
VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0
Janet can now know that Maurice picked a red card.
explicit
0
3
not_entailment
[ "Miyoko", "Janet", "Maurice" ]
15,606
explicit-0
0
0.998268
0.001732
There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 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
Maria can now know that Maria's forehead is muddy.
forehead_mirror
0
4
not_entailment
[ "Glenda", "Alex", "Maria", "Mary" ]
5,509
forehead_mirror-0
0
0.995777
0.004223
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura'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 ] (Agenta knows whether (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) ] [ ! 1 ] 0
Laura can now know whether someone's forehead is muddy.
forehead_mirror
0
3
entailment
[ "Laura", "Glynda", "Theresa" ]
58,231
forehead_mirror-1
1
0.999784
0.000216
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy. It is publicly announced that Randy knows whether Carl'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) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0
Carl can now know that Carl's forehead is muddy.
forehead_mirror
0
4
not_entailment
[ "Carl", "Barbara", "Randy", "Mattie" ]
18,197
forehead_mirror-0
0
0.997467
0.002533
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta 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) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0
Robert can now know whether Daniel can know that Robert's forehead is muddy.
forehead
1
3
not_entailment
[ "Daniel", "Abraham", "Robert" ]
61,742
forehead-0
0
0.923102
0.076898
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Dorian's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 2)
1
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0
Dorian can now know whether Dorian's forehead is muddy.
forehead
0
2
not_entailment
[ "Donald", "Dorian" ]
46,650
forehead-0
0
0.986511
0.013489
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Molly 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) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb 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) ] [ ! (Agentb knows whether (1|2|3)) ] 0
Molly can now know that someone's forehead is muddy.
forehead_mirror
0
3
entailment
[ "Betty", "Molly", "Cecile" ]
65,691
forehead_mirror-1
1
0.999745
0.000255
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.
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)
1
VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0
Dena can now know that Ruth can know that Ruth picked a red card.
explicit
1
3
not_entailment
[ "Ruth", "Dena", "Terrence" ]
12,902
explicit-0
1
0.934584
1.934584
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether 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 (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) ] [ ! (Agenta knows whether (1|2|3)) ] 0
Carl can now know that Rebecca can know that Joe's forehead is muddy.
forehead_mirror
1
3
not_entailment
[ "Rebecca", "Carl", "Joe" ]
44,022
forehead_mirror-0
0
0.998569
0.001431
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether 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 (1|2|3|4)) ] Agenta knows that (Agentd knows that 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|2|3|4)) ] 0
Kathleen can now know that Natasha can know that Natasha's forehead is muddy.
forehead_mirror
1
4
not_entailment
[ "Kathleen", "Charles", "Linda", "Natasha" ]
40,339
forehead_mirror-0
0
0.998313
0.001687
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.
VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)
0
VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0
Anna can now know that Rachel picked a red card.
explicit
0
4
not_entailment
[ "Anna", "Rachel", "Daryl", "Matthew" ]
22,874
explicit-0
0
0.998466
0.001534
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen'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 (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) ] [ ! ~(3) ] 0
Francis can now know whether Helen can know that Carole's forehead is muddy.
forehead
1
4
entailment
[ "Francis", "Carole", "Helen", "Steven" ]
56,710
forehead-1
1
0.997777
0.002223
There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Christopher knows whether 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)) ] (Agenta knows that (~(1|2)))
2
VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] 0
Christopher can now know that nobody's forehead is muddy.
forehead_mirror
0
2
not_entailment
[ "Christopher", "Brendan" ]
20,126
forehead_mirror-0
0
0.9942
0.0058
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.
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)
0
VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0
Willie can now know whether Anja can know whether Anja picked a red card.
explicit
1
4
entailment
[ "Anja", "Grace", "Willie", "Robert" ]
35,251
explicit-1
1
0.991716
0.008284
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that Linda's forehead is muddy.
VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] (Agentc knows whether 3)
4
VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0
Pete can now know whether Pete's forehead is muddy.
forehead
0
3
entailment
[ "Linda", "David", "Pete" ]
4,609
forehead-1
0
0.916953
1.916953
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol does not know whether Marion 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 (Agentb 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) ] [ ! ~(Agentc knows whether 4) ] 0
Carol can now know whether Larry can know that Ruth is thirsty.
internal
1
4
entailment
[ "Ruth", "Larry", "Carol", "Marion" ]
12,808
internal-1
1
0.995165
0.004835
There are four persons. Everyone is visible 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 Christopher knows whether Claude'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 3) ] (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) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0
Claude can now know whether William's forehead is muddy.
forehead_mirror
0
4
entailment
[ "William", "Christopher", "Claude", "Julia" ]
25,273
forehead_mirror-1
1
0.999718
0.000282
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.
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)
0
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
Pei can now know that Danielle can know whether Pei picked a red card.
explicit
1
4
not_entailment
[ "Gary", "Ignacio", "Pei", "Danielle" ]
5,414
explicit-0
0
0.673981
0.326019
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oliver's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Kimberly knows whether Oliver'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) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agenta knows whether (~(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) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0
Shannon can now know whether Kimberly can know whether or not nobody's forehead is muddy.
forehead_mirror
1
3
entailment
[ "Kimberly", "Shannon", "Oliver" ]
56,657
forehead_mirror-1
1
0.99975
0.00025
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia knows whether Virginia is thirsty. It is publicly announced that Cara knows whether or not nobody is thirsty.
VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether 1)
2
VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0
Billy can now know whether Cara is thirsty.
internal
0
3
not_entailment
[ "Cara", "Billy", "Virginia" ]
18,509
internal-0
0
0.902964
0.097036
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether Paul's forehead is muddy. It is publicly announced that Ozell'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 2) ] [ ! 4 ] Agentc knows that (Agentb 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 2) ] [ ! 4 ] 0
Louis can now know that Paul can know whether or not nobody's forehead is muddy.
forehead
1
4
entailment
[ "Kyle", "Paul", "Louis", "Ozell" ]
58,277
forehead-1
1
0.999714
0.000286
There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Seymour does not know whether or not everyone is thirsty. It is publicly announced that Seymour does not know whether Todd is thirsty. It is publicly announced that Todd does not know whether Genevieve is thirsty. It is publicly announced that 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 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] (Agentc knows that 1)
4
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 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] 0
Todd can now know that Genevieve is thirsty.
internal
0
3
entailment
[ "Genevieve", "Seymour", "Todd" ]
38,245
internal-1
1
0.98703
0.01297
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.
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)
2
VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0
Wilfred can now know that Robert can know that Robert picked a red card.
explicit
1
2
not_entailment
[ "Robert", "Wilfred" ]
35,452
explicit-0
0
0.980965
0.019035
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Philip knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that (1&2))
2
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0
Elizabeth can now know whether Philip can know that everyone's forehead is muddy.
forehead
1
2
entailment
[ "Philip", "Elizabeth" ]
28,895
forehead-1
1
0.997254
0.002746
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.
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)
1
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
Melissa can now know that Roy can know whether Michael picked a red card.
explicit
1
4
not_entailment
[ "Melissa", "Michael", "Darlene", "Roy" ]
9,610
explicit-0
0
0.939258
0.060742
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margo knows whether someone's forehead is muddy. It is publicly announced that Margo does not know whether or not everyone's forehead is muddy. It is publicly announced that Margo does not know whether or not everyone's forehead is muddy. It is publicly announced that Jeannine knows whether Jeannine'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)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 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)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0
Jordan can now know that Jeannine's forehead is muddy.
forehead
0
3
entailment
[ "Jordan", "Jeannine", "Margo" ]
21,959
forehead-1
1
0.912898
0.087102
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.
VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)
0
VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0
Stacy can now know that Shannon can know that Stacy picked a red card.
explicit
1
3
not_entailment
[ "Shannon", "Stacy", "Shirley" ]
4,284
explicit-0
0
0.998059
0.001941
There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether Andrew's forehead is muddy. It is publicly announced that Eric does not know whether or not everyone's forehead is muddy. It is publicly announced that Andrew knows whether or not everyone's forehead is muddy. It is publicly announced that Andrew knows whether Eric's forehead is muddy.
VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)
4
VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0
Andrew can now know that Eric's forehead is muddy.
forehead
0
2
not_entailment
[ "Eric", "Andrew" ]
18,495
forehead-0
1
0.803723
1.803723
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (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) ] [ ! (1&2&3&4) ] 0
Bruce can now know that Linda is thirsty.
internal
0
4
entailment
[ "Rebecca", "Linda", "Ryan", "Bruce" ]
24,507
internal-1
1
0.997608
0.002392
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy knows whether Wendy's forehead is muddy. It is publicly announced that 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) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] (Agentb knows whether 3)
2
VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0
Wendy can now know whether Donald's forehead is muddy.
forehead_mirror
0
3
entailment
[ "Woodrow", "Wendy", "Donald" ]
28,354
forehead_mirror-1
1
0.99972
0.00028
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lourdes's forehead is not muddy. It is publicly announced that Lourdes's forehead is not muddy. It is publicly announced that Lourdes'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) ] [ ! ~(2) ] [ ! ~(2) ] Agentb knows that (Agentc knows that 1)
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) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0
Lourdes can now know that William can know that Gertrude's forehead is muddy.
forehead_mirror
1
4
not_entailment
[ "Gertrude", "Lourdes", "William", "Tiffany" ]
36,280
forehead_mirror-0
0
0.761097
0.238903
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Christopher's forehead is muddy. It is publicly announced that Mary'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) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentb knows that (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 3) ] [ ! ~(1) ] 0
Donald can now know that Christopher can know that Jesse's forehead is muddy.
forehead_mirror
1
4
not_entailment
[ "Mary", "Donald", "Christopher", "Jesse" ]
60,391
forehead_mirror-0
0
0.997327
0.002673
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.
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)
1
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
Rachael can now know that Stacey picked a red card.
explicit
0
3
not_entailment
[ "Robert", "Rachael", "Stacey" ]
3,298
explicit-0
0
0.988873
0.011127
There are four persons. Everyone is visible 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 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) ] [ ! (1|2|3|4) ] 0
Cheryl can now know that Joe's forehead is muddy.
forehead_mirror
0
4
not_entailment
[ "Joe", "Cheryl", "Ronald", "Sandra" ]
55,985
forehead_mirror-0
0
0.99848
0.00152
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Kevin knows whether Michael's forehead is muddy. It is publicly announced that Thomas'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) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] (Agentd 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) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] 0
Athena can now know that Michael's forehead is muddy.
forehead
0
4
entailment
[ "Kevin", "Thomas", "Michael", "Athena" ]
28,934
forehead-1
1
0.996745
0.003255
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.
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)
1
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
Kimberly can now know that Donna can know that Donna picked a red card.
explicit
1
3
not_entailment
[ "Kimberly", "Donna", "Patricia" ]
67,521
explicit-0
0
0.994642
0.005358
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason does not know whether Jason'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 2) ] (Agentc knows that (1&2&3&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) ] [ ! ~(Agentb knows whether 2) ] 0
Vickie can now know that everyone's forehead is muddy.
forehead
0
4
not_entailment
[ "Bailey", "Jason", "Vickie", "Paul" ]
62,264
forehead-0
0
0.998609
0.001391
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Joseph'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) ] (Agentb knows whether (1&2&3&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
Arthur can now know whether or not everyone's forehead is muddy.
forehead
0
4
entailment
[ "James", "Arthur", "Joseph", "Dawn" ]
13,345
forehead-1
0
0.99118
1.99118
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.
VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)
0
VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0
Janet can now know whether Carrie picked a red card.
explicit
0
3
entailment
[ "Janet", "Suzanne", "Carrie" ]
2,692
explicit-1
0
0.60389
1.60389
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows whether (~(1|2|3|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) ] [ ! (~(1&2&3&4)) ] 0
Nell can now know that Madeleine can know whether or not nobody's forehead is muddy.
forehead
1
4
entailment
[ "Lilly", "Madeleine", "Valerie", "Nell" ]
59,678
forehead-1
1
0.999729
0.000271
There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darlene'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) ] [ ! ~(1) ] Agenta knows that (Agentc 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) ] [ ! ~(1) ] 0
Darlene can now know that Patrick can know that Patrick's forehead is muddy.
forehead
1
3
not_entailment
[ "Darlene", "Francis", "Patrick" ]
59,476
forehead-0
0
0.993333
0.006667
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen's forehead is not muddy.
VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that 3)
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) ] [ ! ~(4) ] 0
Stephen can now know that Shasta's forehead is muddy.
forehead
0
4
not_entailment
[ "Keith", "Liliana", "Shasta", "Stephen" ]
37,734
forehead-0
0
0.993013
0.006987
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose'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) ] [ ! 4 ] (Agentb 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) ] [ ! 4 ] 0
Mildred can now know whether Rose's forehead is muddy.
forehead_mirror
0
4
entailment
[ "Jerry", "Mildred", "Paul", "Rose" ]
9,978
forehead_mirror-1
1
0.99974
0.00026
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tracey knows whether or not nobody is thirsty. It is publicly announced that Loretta does not know whether Tracey is thirsty. It is publicly announced that Tracey 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) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))
3
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))) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0
Estela can now know that everyone is thirsty.
internal
0
4
not_entailment
[ "Tracey", "Estela", "Sheri", "Loretta" ]
46,745
internal-0
0
0.997902
0.002098
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jarvis knows whether Donald's forehead is muddy. It is publicly announced that Victoria'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) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that (~(1|2|3|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 3) ] [ ! ~(1) ] 0
Victoria can now know whether Donald can know that nobody's forehead is muddy.
forehead_mirror
1
4
entailment
[ "Victoria", "Jarvis", "Donald", "Steve" ]
15,350
forehead_mirror-1
1
0.999689
0.000311
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.
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))
0
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
Samuel can now know whether Scott can know whether someone picked a red card.
explicit
1
4
entailment
[ "Kathryn", "Samuel", "Scott", "Emily" ]
50,455
explicit-1
1
0.999776
0.000224
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.
VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that 1)
1
VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0
Willie can now know that Shellie picked a red card.
explicit
0
2
not_entailment
[ "Shellie", "Willie" ]
28,392
explicit-0
0
0.606901
0.393099
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte 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 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) ] [ ! ~(2) ] 0
Gracie can now know that Charlotte is thirsty.
internal
0
4
not_entailment
[ "Elizabeth", "Charlotte", "Michael", "Gracie" ]
30,715
internal-0
0
0.950562
0.049438
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.
VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that 3)
0
VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0
Mildred can now know that Mildred picked a red card.
explicit
0
3
not_entailment
[ "Bart", "James", "Mildred" ]
47,396
explicit-0
0
0.994372
0.005628
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 Dwayne's forehead is not muddy.
VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)
1
VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0
Dwayne can now know that Christopher can know that Dwayne's forehead is muddy.
forehead_mirror
1
2
not_entailment
[ "Dwayne", "Christopher" ]
29,674
forehead_mirror-0
0
0.955491
0.044509
There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley knows whether Larry's forehead is muddy. It is publicly announced that John's forehead is not muddy. It is publicly announced that Stanley knows whether Stanley'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 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] Agentd knows whether (Agenta knows that (1&2&3&4))
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 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0
John can now know whether Stanley can know that everyone's forehead is muddy.
forehead
1
4
entailment
[ "Stanley", "Cody", "Larry", "John" ]
63,540
forehead-1
1
0.996517
0.003483
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Silvia is thirsty. It is publicly announced that Silvia knows whether or not nobody is thirsty. It is publicly announced that Silvia 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) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 2)
3
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0
Silvia can now know whether James is thirsty.
internal
0
4
not_entailment
[ "Silvia", "James", "Rose", "Lawrence" ]
60
internal-0
1
0.770721
1.770721
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 Milton knows whether or not 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)) ] (Agentb knows that (1|2))
1
VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0
Milton can now know that someone's forehead is muddy.
forehead_mirror
0
2
entailment
[ "Jane", "Milton" ]
50,703
forehead_mirror-1
1
0.999774
0.000226
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric is not thirsty. It is publicly announced that Jerry does not know whether John is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 3)
2
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] 0
Daisy can now know whether John is thirsty.
internal
0
4
not_entailment
[ "Daisy", "Jerry", "John", "Eric" ]
41,398
internal-0
0
0.974159
0.025841
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.
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))
2
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
Monica can now know that everyone picked a red card.
explicit
0
4
not_entailment
[ "Monica", "Lisa", "Carol", "Kyle" ]
59,118
explicit-0
0
0.998298
0.001702
There are four persons. Everyone is visible to others. It is publicly announced that 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 (Agenta knows that 1)
0
VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0
Lisa can now know whether Carolyn can know that Carolyn is thirsty.
internal
1
4
not_entailment
[ "Carolyn", "Lisa", "Joseph", "Edith" ]
31,301
internal-0
0
0.91007
0.08993
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephanie knows whether or not nobody is thirsty. It is publicly announced that Stephanie does not know whether Tracey 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 3) ] Agentd knows whether (Agenta knows whether 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))) ] [ ! ~(Agentd knows whether 3) ] 0
Stephanie can now know whether Vickie can know whether Stephanie is thirsty.
internal
1
4
entailment
[ "Vickie", "Jessica", "Tracey", "Stephanie" ]
63,403
internal-1
1
0.998814
0.001186
There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodney knows whether Rodney's forehead is muddy. It is publicly announced that Lisa knows whether Rodney's forehead is muddy. It is publicly announced that Rodney knows whether Lorena'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) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentd knows that 2)
4
VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] 0
Lorena can now know that Patricia can know that Lorena's forehead is muddy.
forehead_mirror
1
4
not_entailment
[ "Lisa", "Lorena", "Rodney", "Patricia" ]
46,583
forehead_mirror-0
0
0.996669
0.003331
There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille'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 ] Agentc knows whether (Agentb knows whether 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 ] 0
Doris can now know whether Dewey can know whether Lucille's forehead is muddy.
forehead_mirror
1
3
entailment
[ "Lucille", "Dewey", "Doris" ]
16,566
forehead_mirror-1
1
0.999722
0.000278
There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.
VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentd 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) ] [ ! (1&2&3&4) ] 0
Joshua can now know whether Timothy can know that someone is thirsty.
internal
1
4
entailment
[ "Joshua", "Betty", "Pamela", "Timothy" ]
14,946
internal-1
1
0.999786
0.000214

Mindgame dataset

Code: https://github.com/sileod/llm-theory-of-mind

Article (Accepted at EMNLP 2023 Findings): https://arxiv.org/abs/2305.03353

@article{sileo2023mindgames,
  title={MindGames: Targeting Theory of Mind in Large Language Models with Dynamic Epistemic Modal Logic},
  author={Sileo, Damien and Lernould, Antoine},
  journal={arXiv preprint arXiv:2305.03353},
  year={2023}
}
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