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

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

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

Hypothesis: Carol can now know that Wynona can know whether Wynona picked a red card.


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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Richard can now know whether Kathleen can know that nobody picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

Hypothesis: Danielle can now know that April can know that Shayne picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Stacey can now know that Adrianne can know whether or not nobody picked a red card.


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

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

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

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


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

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

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

Hypothesis: Leanna can now know whether Anne can know that Leanna picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Alice can now know that Scott can know that Jack picked a red card.


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

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

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

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


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

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

Hypothesis: Rita can now know whether Jose picked a red card.


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

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

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

Hypothesis: John can now know that Margarette picked a red card.


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

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

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

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


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

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

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

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


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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Clarence can now know whether Joanne can know whether Clarence picked a red card.


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

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

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

Hypothesis: Inez can now know that Ana picked a red card.


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

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

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

Hypothesis: Marshall can now know whether Glenn can know that Glenn picked a red card.


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

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

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

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


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

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

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


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

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

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

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


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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Corliss can now know that Judith picked a red card.


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

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

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

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


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

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

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

Hypothesis: Carolyn can now know whether Susan picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Dorothy can now know whether Duane can know that nobody picked a red card.


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

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

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

Hypothesis: Mable can now know whether Joseph can know that Susan picked a red card.


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

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

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

Hypothesis: Miguel can now know that Frederick can know that Miguel picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Jamie can now know whether Wayne can know that nobody picked a red card.


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

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

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

Hypothesis: Ruben can now know whether Dennis can know that Ruben picked a red card.


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

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

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

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


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

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

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

Hypothesis: Darlene can now know whether Bonnie can know that nobody picked a red card.


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

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

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

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


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

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

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

Hypothesis: Ruth can now know that Joseph picked a red card.


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

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

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

Hypothesis: Josephine can now know that Christina can know that Patrick picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Pam can now know whether Betsy can know that everyone picked a red card.


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

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

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

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


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

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

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

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


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

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

Hypothesis: Alyce 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). Jim's card is shown to Jim. Richard's card is shown to Jim. David's card is shown to Jim. Richard's card is shown to Richard. Jim's card is shown to David. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Jacob can now know whether Patricia can know that Beatrice picked a red card.


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

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

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

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


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

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

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

Hypothesis: Mary can now know whether Calvin can know that everyone picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Maureen can now know that Elizabeth picked a red card.


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

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

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

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


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

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

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

Hypothesis: Deloris can now know whether Josephine picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Juan can now know that Nicole picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Judith can now know whether Gladys can know that Judith picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Charles can now know that Mariano can know whether or not everyone picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Alma can now know that Delphia picked a red card.


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

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

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

Hypothesis: Rita can now know whether Carl can know that Sharon picked a red card.


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

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

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

Hypothesis: Timothy can now know that Delilah can know whether someone picked a red card.


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

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

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

Hypothesis: Bradley can now know that Tamara can know whether or not nobody picked a red card.


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

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

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

Hypothesis: Virginia can now know that Clarence picked a red card.


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

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

Hypothesis: Bessie can now know that Margaret can know whether Caren picked a red card.


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

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

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

Hypothesis: Juliette can now know whether Jeffrey can know that someone picked a red card.


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

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

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

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


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

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

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

Hypothesis: Catalina can now know whether Sheila picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Marcella can now know that Juan can know whether Thomas picked a red card.


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

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

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

Hypothesis: Brenda can now know whether David can know that nobody picked a red card.


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

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

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

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


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

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

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

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


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

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

Hypothesis: William can now 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). Marina's card is shown to Gaylene. Marina's card is shown to David. Marina's card is shown to Marina. Herbert's card is shown to Herbert. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

Hypothesis: Katherine 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). Eduardo's card is shown to Eduardo. Russell's card is shown to Lois. Lois's card is shown to Russell. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Joanne can now know whether Scott can know that Scott picked a red card.


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

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

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

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


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

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

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

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


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

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

Hypothesis: Robert can now 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). Silvia's card is shown to Leo. Leo's card is shown to Charles. Silvia's card is shown to Charles. Leo's card is shown to Silvia. It is publicly announced that someone picked a red card. It is publicly announced that Leo does not know whether Leo picked a red card.

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

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

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


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

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

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

Hypothesis: Bert can now know that Pedro can know whether Kenneth picked a red card.


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

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

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

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


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

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

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

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


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

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

Hypothesis: Kevin 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). Sherry's card is shown to Andrew. Andrew's card is shown to Sherry. Helen's card is shown to Sherry. Sherry's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Sherry knows whether or not nobody picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Claudine can now know whether Rita can know that someone picked a red card.


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

VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb 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: Katherine can now know that someone picked a red card.