Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronnie's card is shown to Laurie. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Laurie does not know whether Laurie picked a red card. It is publicly announced that not everyone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agenta knows that 3)

VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0

Hypothesis: Laurie can now know that Mary picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maricela's card is shown to Maricela. Ray's card is shown to Maricela. Dave's card is shown to Maricela. Dave's card is shown to Ray. Dave's card is shown to Dave. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))

VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0

Hypothesis: Ray can now know that Maricela can know whether someone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonette's card is shown to Louise. Marva's card is shown to Louise. Paula's card is shown to Antonette. Paula's card is shown to Marva. Antonette's card is shown to Marva. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1&2&3&4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Antonette can now know whether Louise can know that everyone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalyn's card is shown to Rosalyn. Priscilla's card is shown to Rosalyn. Priscilla's card is shown to Priscilla. It is publicly announced that someone picked a red card.

VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] (Agenta knows that 1)

VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] 0

Hypothesis: Rosalyn can now know that Rosalyn picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Malcolm. Juliette's card is shown to Juliette. Manuel's card is shown to Juliette. Manuel's card is shown to Ralph. Malcolm's card is shown to Manuel. Juliette's card is shown to Manuel. Ralph's card is shown to Manuel. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 2)

VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Manuel can now know whether Malcolm can know that Juliette picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rae's card is shown to Rae. Naomi's card is shown to Rae. Naomi's card is shown to Dana. Anderson's card is shown to Anderson. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 3)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Rae can now know whether Dana can know that Dana picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Kathryn. Kathryn's card is shown to Mark. Mark's card is shown to Mark. James's card is shown to Mark. Kathryn's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card. It is publicly announced that Mark knows whether James picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentb knows that 3)

VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0

Hypothesis: Kathryn can now know whether Mark can know that James picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Agnes's card is shown to Darlene. Bryan's card is shown to Darlene. Darlene's card is shown to Carlos. Agnes's card is shown to Carlos. Agnes's card is shown to Agnes. Agnes's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Agnes does not know whether or not everyone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that 1)

VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0

Hypothesis: Carlos can now know that Darlene picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Doris. Johnny's card is shown to Johnny. Mark's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Christopher picked a red card. It is publicly announced that Johnny does not know whether Christopher picked a red card. It is publicly announced that Johnny does not know whether Mark picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that 4)

VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] 0

Hypothesis: Mark can now know that Christopher picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodore's card is shown to Theodore. Alice's card is shown to Theodore. Keith's card is shown to Theodore. Theodore's card is shown to Alice. Keith's card is shown to Keith. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)

VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0

Hypothesis: Keith can now know that Theodore can know that Keith picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Randy. Steven's card is shown to Peter. Peter's card is shown to Peter. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1&2&3&4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Steven can now know whether Randy can know that everyone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Agnes's card is shown to William. Jaqueline's card is shown to Jaqueline. Agnes's card is shown to Jaqueline. Agnes's card is shown to Agnes. William's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 1)

VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0

Hypothesis: William can now know that Agnes can know that William picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chester's card is shown to Chester. Gregory's card is shown to Gregory. Mercedes's card is shown to Mercedes. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 4)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Gregory can now know that Chester can know whether Mercedes picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danny's card is shown to Julius. Emily's card is shown to Danny. Marsha's card is shown to Marsha. Emily's card is shown to Marsha. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 1)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Danny can now know whether Marsha can know that Julius picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Paul. Sheila's card is shown to Paul. Nancy's card is shown to Nancy. Paul's card is shown to Sheila. Nancy's card is shown to Sheila. Sheila's card is shown to Sheila. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0

Hypothesis: Paul can now know that everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Emma. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] 0

Hypothesis: Emma can now know whether or not everyone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Russel's card is shown to Wm. Wm's card is shown to Josefina. Justin's card is shown to Josefina. Russel's card is shown to Justin. Justin's card is shown to Justin. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Wm can now know that Russel picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nichole's card is shown to Jerry. Jerry's card is shown to Jerry. Jennifer's card is shown to Jerry. Nichole's card is shown to Jennifer. Jerry's card is shown to Jennifer. Jennifer's card is shown to Jennifer. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)

Hypothesis: Jerry can now know whether Nichole can know that Jerry picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Tamra. Tamra's card is shown to Peter. Vera's card is shown to Peter. Michael's card is shown to Vera. Peter's card is shown to Vera. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Michael can now know that everyone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Walter. Donna's card is shown to Willis. Walter's card is shown to Willis. Samuel's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether or not everyone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 2)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0

Hypothesis: Walter can now know that Walter picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clement's card is shown to Clement. Clement's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Clement knows whether someone picked a red card. It is publicly announced that Eric knows whether Eric picked a red card.

VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether 2)

VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] 0

Hypothesis: Eric can now know whether Eric picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Debra. Marla's card is shown to Debra. Marla's card is shown to Ashley. Paul's card is shown to Paul. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 1)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Debra can now know whether Ashley can know whether Debra picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francine's card is shown to Daniel. Daniel's card is shown to Francine. Francine's card is shown to Francine. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Daniel picked a red card. It is publicly announced that Francine picked a red card.

VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] Agenta knows that (Agentb knows that (~(1|2)))

Hypothesis: Daniel can now know that Francine can know that nobody picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Kim. Dorothy's card is shown to Dorothy. Lucille's card is shown to Lucille. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Dorothy does not know whether Kim picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that 1)

Hypothesis: Kim can now know whether Lucille can know that Kim picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aaron's card is shown to Pearlie. Edith's card is shown to Pearlie. Pearlie's card is shown to Aaron. Edith's card is shown to Aaron. Benjamin's card is shown to Benjamin. Aaron's card is shown to Edith. It is publicly announced that someone picked a red card. It is publicly announced that Pearlie knows whether or not nobody picked a red card. It is publicly announced that Pearlie picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 1 ] (Agenta knows whether (1|2|3|4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 1 ] 0

Hypothesis: Pearlie can now know whether someone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gertrude's card is shown to Gertrude. Elmer's card is shown to Gertrude. Billy's card is shown to Elmer. Billy's card is shown to Billy. Billy's card is shown to Sonia. It is publicly announced that someone picked a red card. It is publicly announced that Billy picked a red card. It is publicly announced that Gertrude picked a black card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(1) ] (Agenta knows that (1|2|3|4))

Hypothesis: Gertrude can now know that someone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to William. William's card is shown to Hector. Hector's card is shown to Hector. Michael's card is shown to Hector. Hector's card is shown to Michael. Hector's card is shown to Thomas. Michael's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that William picked a black card.

VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))

Hypothesis: Michael can now know that Hector can know that nobody picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Michelle. Rachel's card is shown to Michelle. Rachel's card is shown to Rachel. Michelle's card is shown to Heidi. Heidi's card is shown to Heidi. Rachel's card is shown to Marie. Marie's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Rachel picked a red card. It is publicly announced that Rachel knows whether or not nobody picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentc knows whether (Agenta knows whether 2)

Hypothesis: Heidi can now know whether Michelle can know whether Rachel picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Mary. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Matthew does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that someone picked a red card.

VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1|2))

VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] 0

Hypothesis: Matthew can now know whether Mary can know whether someone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Amanda. Thomas's card is shown to Thomas. Amanda's card is shown to Margaret. Thomas's card is shown to Margaret. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Amanda does not know whether or not everyone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows whether 4)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0

Hypothesis: Thomas can now know whether Amanda can know whether Margaret picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cassandra's card is shown to Walter. Cassandra's card is shown to Cassandra. Jenny's card is shown to Cassandra. Wayne's card is shown to Jenny. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether or not everyone picked a red card. It is publicly announced that Jenny does not know whether Walter picked a red card. It is publicly announced that Walter does not know whether Wayne picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows whether 4)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 4) ] 0

Hypothesis: Walter can now know whether Wayne picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marjorie's card is shown to Marjorie. Larry's card is shown to Marjorie. Mildred's card is shown to Larry. Joseph's card is shown to Mildred. Mildred's card is shown to Joseph. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 3)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Mildred can now know whether Joseph can know whether Mildred picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Rose. Rose's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether John picked a red card.

VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)

VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0

Hypothesis: Rose can now know that Rose picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sidney's card is shown to Jennifer. Whitney's card is shown to Jennifer. Jennifer's card is shown to Sidney. Jennifer's card is shown to Whitney. Sidney's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Sidney does not know whether Sidney picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1&2&3&4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0

Hypothesis: Jennifer can now know that everyone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Kenneth's card is shown to Abel. Abel's card is shown to Yvonne. Yvonne's card is shown to Yvonne. Yvonne's card is shown to Katheryn. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (1&2&3&4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Yvonne can now know whether Kenneth can know whether or not everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eldon's card is shown to Patricia. Ethel's card is shown to Ethel. Eldon's card is shown to Ethel. Ethel's card is shown to Eldon. Eldon's card is shown to Eldon. It is publicly announced that someone picked a red card. It is publicly announced that Eldon picked a red card. It is publicly announced that Eldon does not know whether Patricia picked a red card. It is publicly announced that Eldon knows whether someone picked a red card. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agenta knows that 2)

VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0

Hypothesis: Patricia can now know that Ethel picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eun's card is shown to Rachel. Sherry's card is shown to James. Rachel's card is shown to Eun. Rachel's card is shown to Sherry. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 3)

VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: James can now know that Rachel can know whether Eun picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reginald's card is shown to Debra. Gretchen's card is shown to Debra. Debra's card is shown to Gretchen. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)

VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0

Hypothesis: Debra can now know whether Debra picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Ruby. Ruby's card is shown to Marie. Marie's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether Marie picked a red card.

VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1|2))

VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0

Hypothesis: Ruby can now know that someone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Earl. Earl's card is shown to Kerry. Earl's card is shown to Shirley. Shirley's card is shown to Shirley. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 2)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Kerry can now know whether Earl can know that Earl picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lakiesha's card is shown to Larry. Michael's card is shown to Larry. Lakiesha's card is shown to Lakiesha. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Larry picked a red card. It is publicly announced that Lakiesha knows whether Lakiesha picked a red card. It is publicly announced that Lakiesha does not know whether or not everyone picked a red card. It is publicly announced that Michael knows whether Lakiesha picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 2) ] (Agentc knows whether (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 2) ] 0

Hypothesis: Michael can now know whether or not everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelly's card is shown to Shelly. David's card is shown to Shelly. Shelly's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Shelly does not know whether or not everyone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0

Hypothesis: Shelly can now know whether Jewel can know whether or not everyone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joe's card is shown to Joe. Joe's card is shown to Hazel. It is publicly announced that someone picked a red card. It is publicly announced that Hazel does not know whether or not everyone picked a red card. It is publicly announced that Hazel does not know whether or not everyone picked a red card. It is publicly announced that Joe knows whether or not nobody picked a red card. It is publicly announced that Joe does not know whether or not everyone picked a red card.

VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (1|2))

VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0

Hypothesis: Hazel can now know whether someone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clara's card is shown to Nancy. Andrew's card is shown to Nancy. Clara's card is shown to Clara. Nancy's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Nancy knows whether Clara picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 2)

VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0

Hypothesis: Clara can now know that Clara picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnulfo's card is shown to Ethel. Ethel's card is shown to David. David's card is shown to David. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1|2|3|4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: David can now know whether Arnulfo can know whether someone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Martin. Martin's card is shown to Donna. Paul's card is shown to Donna. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Paul does not know whether Martin picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentc knows that 3)

VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0

Hypothesis: Donna can now know whether Paul can know that Paul picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sean's card is shown to James. Jason's card is shown to Sean. Jason's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Sean does not know whether James picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 1)

VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0

Hypothesis: James can now know whether James picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geraldine's card is shown to Carolina. Emily's card is shown to Carolina. Israel's card is shown to Geraldine. Emily's card is shown to Geraldine. Carolina's card is shown to Israel. Israel's card is shown to Israel. Emily's card is shown to Emily. It is publicly announced that someone picked a red card. It is publicly announced that Emily does not know whether Geraldine picked a red card. It is publicly announced that Israel does not know whether Geraldine picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that (1&2&3&4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0

Hypothesis: Geraldine can now know that everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Deborah. Jack's card is shown to Deborah. Deborah's card is shown to Jack. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)

VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0

Hypothesis: Deborah can now know whether Jack picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Elizabeth's card is shown to Helen. Elizabeth's card is shown to Sharon. Helen's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agenta knows that (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0

Hypothesis: Sharon can now know that Helen can know that everyone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Carl's card is shown to Linda. Mary's card is shown to Linda. Carl's card is shown to Elmer. Carl's card is shown to Carl. Carl's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Elmer picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentd knows that 1)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0

Hypothesis: Elmer can now know that Mary can know that Linda picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Joyce. John's card is shown to Joyce. Joyce's card is shown to Emmanuel. John's card is shown to Emmanuel. Emmanuel's card is shown to John. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Joyce can now know whether Emmanuel can know whether or not everyone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Elizabeth. Christine's card is shown to Nadia. Nadia's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether or not everyone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 2)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0

Hypothesis: Nadia can now know whether Brian picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Monica. Joyce's card is shown to Lori. Lori's card is shown to Lori. Kari's card is shown to Lori. Monica's card is shown to Kari. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Joyce picked a black card. It is publicly announced that Joyce picked a black card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] [ ! ~(2) ] Agentb knows whether (Agentc knows whether 4)

Hypothesis: Joyce can now know whether Lori can know whether Kari picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Constance's card is shown to Constance. Constance's card is shown to Michelle. Steven's card is shown to Matthew. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Michelle can now know that Steven can know that nobody picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Margaret. Margaret's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John picked a red card. It is publicly announced that John knows whether someone picked a red card.

VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1|2))

VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] 0

Hypothesis: Margaret can now know that someone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rex's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Kenneth picked a red card.

VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1&2))

VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0

Hypothesis: Kenneth can now know whether or not everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Michael. Richard's card is shown to Darrell. Michael's card is shown to Richard. Darrell's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card. It is publicly announced that Michael knows whether someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agenta knows whether (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0

Hypothesis: Richard can now know whether Michael can know whether or not everyone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alec's card is shown to Alec. Alec's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Robert picked a red card. It is publicly announced that Alec does not know whether or not everyone picked a red card.

VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))

VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0

Hypothesis: Alec can now know that Robert can know that nobody picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darnell's card is shown to Darnell. Johnnie's card is shown to Darnell. Nicole's card is shown to Holly. Darnell's card is shown to Johnnie. Nicole's card is shown to Johnnie. Holly's card is shown to Nicole. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Darnell picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Johnnie picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))

VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0

Hypothesis: Darnell can now know that Johnnie can know whether or not nobody picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carol. Colleen's card is shown to Carol. Erica's card is shown to Carol. Carol's card is shown to Delmar. Erica's card is shown to Delmar. Carol's card is shown to Erica. It is publicly announced that someone picked a red card. It is publicly announced that Delmar knows whether or not everyone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows whether (1|2|3|4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0

Hypothesis: Colleen can now know whether someone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alissa's card is shown to Alissa. Lisa's card is shown to Alissa. Alissa's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Alissa picked a black card.

VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (1&2))

Hypothesis: Lisa can now know that Alissa can know that everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Mavis's card is shown to John. George's card is shown to Mavis. Mavis's card is shown to Mavis. It is publicly announced that someone picked a red card. It is publicly announced that George knows whether John picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)

VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0

Hypothesis: John can now know whether John picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Tracey. Thomas's card is shown to Thomas. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)

VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0

Hypothesis: Thomas can now know that Michael picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mamie's card is shown to Mamie. Malka's card is shown to Leonora. Leonora's card is shown to Malka. It is publicly announced that someone picked a red card. It is publicly announced that Madeline does not know whether or not everyone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))

Hypothesis: Leonora can now know that someone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Chris. Chris's card is shown to William. William's card is shown to Eva. Eva's card is shown to Eva. Eva's card is shown to Sherry. It is publicly announced that someone picked a red card. It is publicly announced that Sherry does not know whether Chris picked a red card. It is publicly announced that Chris does not know whether William picked a red card. It is publicly announced that Eva knows whether Eva picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] (Agentd knows whether (1|2|3|4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0

Hypothesis: Sherry can now know whether someone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Billy's card is shown to Christopher. Christopher's card is shown to Evelyn. Billy's card is shown to Evelyn. Kenneth's card is shown to Evelyn. Billy's card is shown to Billy. Billy's card is shown to Kenneth. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,3,4 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows that 1)

Hypothesis: Evelyn can now know that Christopher picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leonard's card is shown to Michael. Leonard's card is shown to Brian. Brian's card is shown to Brian. Brian's card is shown to Ronald. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1&2&3&4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Brian can now know that Michael can know whether or not everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Selena's card is shown to Robert. Robert's card is shown to Richard. Robert's card is shown to Selena. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)

VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0

Hypothesis: Robert can now know that Richard can know whether Richard picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adrian's card is shown to Adrian. James's card is shown to James. Armando's card is shown to Edgar. Edgar's card is shown to Edgar. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Adrian can now know that nobody picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Carlos. Carlos's card is shown to Carlos. Lisa's card is shown to Mark. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)

VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0

Hypothesis: Lisa can now know whether Carlos can know that Carlos picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindi's card is shown to Cindi. Liana's card is shown to Cindi. Cindi's card is shown to Liana. Liana's card is shown to Liana. It is publicly announced that someone picked a red card. It is publicly announced that Cindi knows whether Liana picked a red card. It is publicly announced that Cindi picked a red card.

VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 1 ] (Agentb knows whether 1)

VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 1 ] 0

Hypothesis: Liana can now know whether Cindi picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to Janice. David's card is shown to Janice. Arthur's card is shown to Janice. David's card is shown to David. Arthur's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Arthur picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentc knows whether (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0

Hypothesis: David can now know whether Arthur can know whether or not everyone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Joshua. Joshua's card is shown to Anne. It is publicly announced that someone picked a red card. It is publicly announced that Joshua does not know whether or not everyone picked a red card. It is publicly announced that Anne knows whether Anne picked a red card.

VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))

VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0

Hypothesis: Joshua can now know that Anne can know that everyone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Carl. Emily's card is shown to Joyce. Jennie's card is shown to Joyce. Carl's card is shown to Emily. Jennie's card is shown to Emily. It is publicly announced that someone picked a red card. It is publicly announced that Carl does not know whether Jennie picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentc knows that 4)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0

Hypothesis: Carl can now know whether Emily can know that Jennie picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Michael. Lisa's card is shown to Michael. Michael's card is shown to Angel. Donald's card is shown to Angel. Lisa's card is shown to Angel. Michael's card is shown to Donald. Angel's card is shown to Lisa. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 3)

VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Donald can now know whether Michael can know whether Donald picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Beverly. Emilio's card is shown to Beverly. Tammy's card is shown to Beverly. Tammy's card is shown to Emilio. Emilio's card is shown to Tammy. Tammy's card is shown to Tammy. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Emilio can now know whether David picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daphine's card is shown to Daphine. William's card is shown to Daphine. Ellen's card is shown to Ellen. William's card is shown to Ellen. Daphine's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0

Hypothesis: William can now know whether Daphine can know that everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandra's card is shown to Sandra. Travis's card is shown to Sandra. Travis's card is shown to Travis. Sandra's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Travis does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] (Agenta knows whether (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0

Hypothesis: Sandra can now know whether or not everyone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kylie's card is shown to Kylie. Deanna's card is shown to Norman. Norman's card is shown to James. Kylie's card is shown to Deanna. Norman's card is shown to Deanna. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether or not everyone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 2)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0

Hypothesis: Norman can now know whether Norman picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vincenzo's card is shown to Cody. David's card is shown to David. David's card is shown to Jared. It is publicly announced that someone picked a red card. It is publicly announced that David picked a black card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows whether (~(1|2|3|4)))

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0

Hypothesis: Vincenzo can now know whether or not nobody picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonio's card is shown to Antonio. James's card is shown to Antonio. Antonio's card is shown to Michael. James's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Antonio knows whether or not nobody picked a red card. It is publicly announced that James knows whether Michael picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 1)

Hypothesis: Antonio can now know that Antonio picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Susannah. Tessa's card is shown to Tessa. Susannah's card is shown to Dorothy. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Tessa does not know whether or not everyone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether 3)

VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0

Hypothesis: Susannah can now know whether Dorothy picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Charlotte. Charlotte's card is shown to Patsy. Patsy's card is shown to Patsy. Jared's card is shown to Patsy. Charlotte's card is shown to Jared. It is publicly announced that someone picked a red card. It is publicly announced that Jared does not know whether or not everyone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 1)

VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0

Hypothesis: Jared can now know that Charlotte can know that Charlotte picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Lewis's card is shown to John. Annie's card is shown to John. John's card is shown to Lewis. Lewis's card is shown to Paula. Annie's card is shown to Paula. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1|2|3|4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Paula can now know whether Lewis can know whether someone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sidney's card is shown to Matthew. Matthew's card is shown to Sidney. Dawn's card is shown to Sidney. Sidney's card is shown to Dawn. It is publicly announced that someone picked a red card. It is publicly announced that Sidney knows whether or not nobody picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that (1|2|3))

VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0

Hypothesis: Matthew can now know that Sidney can know that someone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nydia's card is shown to Bill. Nydia's card is shown to Nydia. It is publicly announced that someone picked a red card. It is publicly announced that Bill knows whether someone picked a red card.

VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (1|2))

VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0

Hypothesis: Nydia can now know that someone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcia's card is shown to Ramona. Ramona's card is shown to Marcia. Jeanne's card is shown to Jeanne. It is publicly announced that someone picked a red card. It is publicly announced that Jeanne knows whether Jeanne picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 1)

VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0

Hypothesis: Marcia can now know that Ramona picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Aurora. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Aurora picked a red card.

VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 1)

VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0

Hypothesis: Richard can now know whether Aurora picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erica's card is shown to Erica. Estela's card is shown to Marc. Estela's card is shown to Jason. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Marc can now know whether Erica picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Eddie. Eddie's card is shown to Jennifer. Eddie's card is shown to Jessica. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)

VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0

Hypothesis: Jessica can now know that Jennifer can know whether Jessica picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Rosemary. Paula's card is shown to Doug. Doug's card is shown to Doug. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))

VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0

Hypothesis: Paula can now know whether someone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Ruby. James's card is shown to Keith. Isaiah's card is shown to James. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Ruby can now know whether Isaiah picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Stephen's card is shown to Charles. Charles's card is shown to Charles. Erin's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether Fred picked a red card. It is publicly announced that Erin picked a red card. It is publicly announced that Charles does not know whether or not everyone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0

Hypothesis: Fred can now know whether or not everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Charles's card is shown to Dorothy. Charles's card is shown to Charles. Bryan's card is shown to Charles. Dorothy's card is shown to Bryan. Charles's card is shown to Bryan. Bryan's card is shown to Bryan. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))

VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0

Hypothesis: Dorothy can now know whether or not everyone picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mathew's card is shown to Robert. Glenda's card is shown to Mathew. Robert's card is shown to Glenda. Mathew's card is shown to Glenda. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))

VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0

Hypothesis: Robert can now know that someone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ray's card is shown to Brandon. Brandon's card is shown to Ray. Ray's card is shown to Ray. It is publicly announced that someone picked a red card. It is publicly announced that Ray picked a black card.

VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2)))

VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0

Hypothesis: Ray can now know that Brandon can know that nobody picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edmund's card is shown to Edmund. Gwendolyn's card is shown to Timothy. Edmund's card is shown to Timothy. Timothy's card is shown to Robert. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Gwendolyn can now know that Edmund can know that Robert picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Dale. Lori's card is shown to Dale. Lori's card is shown to Lori. Michael's card is shown to Lori. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that (1|2|3))

Hypothesis: Dale can now know that someone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gaylord's card is shown to Lois. Lois's card is shown to Gaylord. It is publicly announced that someone picked a red card. It is publicly announced that Gaylord knows whether or not nobody picked a red card.

VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether (1|2))

VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0

Hypothesis: Gaylord can now know whether someone picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luis's card is shown to Sue. Sue's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Sue does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.

VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows that (1&2))

VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0

Hypothesis: Luis can now know that everyone picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Yu's card is shown to Chris. Michael's card is shown to Yu. Chris's card is shown to Michael. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 3)

VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Yu can now know that Michael can know whether Yu picked a red card.


Premise: There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Heather. Christine's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Christine does not know whether or not everyone picked a red card. It is publicly announced that Heather does not know whether or not everyone picked a red card.

VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that 1)

VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0

Hypothesis: Heather can now know that Heather picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremiah's card is shown to Jeremiah. William's card is shown to William. Jeremiah's card is shown to Manuel. It is publicly announced that someone picked a red card. It is publicly announced that Manuel does not know whether Manuel picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (~(1|2|3)))

VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0

Hypothesis: William can now know that nobody picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Micaela. Micaela's card is shown to Brigette. James's card is shown to Brigette. Brigette's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Brigette knows whether or not everyone picked a red card. It is publicly announced that Brigette knows whether James picked a red card. It is publicly announced that Brigette knows whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows that 2)

VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0

Hypothesis: Brigette can now know whether James can know that Brigette picked a red card.


Premise: There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fae's card is shown to Cara. Cara's card is shown to Susan. Fae's card is shown to Susan. Cara's card is shown to Fae. Susan's card is shown to Fae. Fae's card is shown to Fae. It is publicly announced that someone picked a red card.

VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 2)

VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0

Hypothesis: Cara can now know that Fae can know whether Susan picked a red card.


Premise: There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Olga. Norbert's card is shown to Lorraine. Margaret's card is shown to Norbert. Norbert's card is shown to Norbert. It is publicly announced that someone picked a red card.

VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)

VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0

Hypothesis: Lorraine can now know that Norbert picked a red card.