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

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

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

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


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

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

Hypothesis: Hunter can now know that Zaida picked a red card.


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

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

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

Hypothesis: Mattie can now know whether Michele can know whether Mattie picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Maria can now know whether Kristi can know that everyone picked a red card.


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

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

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

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


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

Hypothesis: Dennis can now 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). Rebecca's card is shown to Rebecca. Reggie's card is shown to Reggie. Jose's card is shown to Reggie. Reggie's card is shown to Brittany. Brittany's card is shown to Jose. Jose's card is shown to Jose. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Julie can now know that Rosa can know that Philip picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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: Levi can now know whether Penny 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). Tara's card is shown to Tara. Tara's card is shown to Juan. Juan's card is shown to Juan. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.

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

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

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


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

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

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


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

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

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

Hypothesis: Melvin can now know that Dexter can know whether or not nobody picked a red card.


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

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

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

Hypothesis: Tiffani can now know whether Milton can know that everyone picked a red card.


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

Hypothesis: Jessica 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). Floyd's card is shown to Floyd. Jeffrey's card is shown to Floyd. Floyd's card is shown to Jeffrey. Ha's card is shown to Arnold. Jeffrey's card is shown to Arnold. Arnold's card is shown to Arnold. It is publicly announced that someone picked a red card.

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

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

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


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

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

Hypothesis: Steven can now know whether Sharon can 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). Eula's card is shown to Craig. Craig's card is shown to Eula. Matthew's card is shown to Eula. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether or not everyone picked a red card.

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

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

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


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

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

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

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


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

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

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


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

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

Hypothesis: Claudia can now know that Carolyn can know that Roger picked a red card.


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

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

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

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


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

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

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

Hypothesis: Catherine can now know whether Zachary picked a red card.


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

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

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

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


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

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

Hypothesis: Joshua 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). Albert's card is shown to Albert. Albert's card is shown to Sharon. Thea's card is shown to Sharon. Duane's card is shown to Duane. Thea's card is shown to Duane. It is publicly announced that someone picked a red card.

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

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

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


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

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

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

Hypothesis: Deanna can now know that Lisa can know that Katherine picked a red card.


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Pedro can now know that Amy can know that Pedro picked a red card.


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

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

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

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


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

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

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

Hypothesis: Ernestine can now know whether Angeline can know that Angeline picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

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


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

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

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

Hypothesis: Floyd can now know that Peter can know that Richard picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

Hypothesis: Susanna can now know whether Mary can know that nobody picked a red card.


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

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

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

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


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

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

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

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


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

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

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


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

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

Hypothesis: Carol can now know that Anthony 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 Barbara. Leo's card is shown to Leo. Amy's card is shown to Leo. Barbara's card is shown to Amy. Leo's card is shown to Amy. Amy's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Leo does not know whether or not everyone picked a red card. It is publicly announced that Amy knows whether someone picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Andrea can now know whether Francisco can know whether Winnie picked a red card.


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

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

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

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


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

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

Hypothesis: Jesse can now know whether Coleen 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). Joseph's card is shown to Joseph. Abram's card is shown to Joseph. Joseph's card is shown to Abram. It is publicly announced that someone picked a red card.

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

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

Hypothesis: Abram can now know that Joseph can know whether or not nobody picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Keith can now know whether Christopher picked a red card.


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

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

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

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


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

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

Hypothesis: Annie can now 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). James's card is shown to Steven. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Steven knows whether someone picked a red card.

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

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

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


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

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

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

Hypothesis: Ian can now know whether Pablo can know whether Ian picked a red card.


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

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

Hypothesis: Matthew 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). Jacqueline's card is shown to Jacqueline. Diane's card is shown to Jacqueline. Diane's card is shown to Diane. It is publicly announced that someone picked a red card. It is publicly announced that Diane does not know whether or not everyone picked a red card.

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

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

Hypothesis: Diane can now know whether Jacqueline can know that Jacqueline picked a red card.


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

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

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

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


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

VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (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: Scott 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). Jose's card is shown to Matthew. Matthew's card is shown to Roger. Roger's card is shown to Roger. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Alan picked a red card.

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

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

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


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

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

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

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


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

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

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

Hypothesis: Cassondra can now know that Ann picked a red card.


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

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

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

Hypothesis: Dorothy can now know that Leonard can know whether someone picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Dora can now know whether Sarah can know whether Sarah picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Sebastian can now know whether Benjamin picked a red card.


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

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

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

Hypothesis: Hugh can now know that Laura can know whether or not everyone picked a red card.


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

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

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

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


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

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

Hypothesis: Stacie can now know that Norma can know that Ella 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. Jeanette's card is shown to Jeanette. James's card is shown to Jeanette. Bradley's card is shown to Bradley. It is publicly announced that someone picked a red card. It is publicly announced that Jeanette does not know whether Valerie picked a red card.

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Kyung can now know whether Aaron can know that someone picked a red card.


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

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

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

Hypothesis: Amos can now know that Janeen can know whether Joyce picked a red card.


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

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


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

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

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

Hypothesis: Marco can now know whether George can know that everyone picked a red card.


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

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

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

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


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

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

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

Hypothesis: Ian can now know whether Clifford can know whether Ian picked a red card.


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

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

Hypothesis: Eloy can now know whether Elizabeth can know that Jessie picked a red card.


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

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

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

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


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

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

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

Hypothesis: Joshua can now know whether Isabelle picked a red card.


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

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

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

Hypothesis: Amy can now know that Maurice can know that Maurice picked a red card.


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

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

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

Hypothesis: Sonia can now know that Martin can know whether or not nobody picked a red card.


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

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

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

Hypothesis: Donald can now know that Aaron can know that Sean picked a red card.


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

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

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

Hypothesis: Alaina can now know whether Dusti can know that nobody picked a red card.


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

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

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

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